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37 pages, 2139 KiB  
Article
A Review of the Multiple-Readout Concept and Its Application in an Integrally Active Calorimeter
by Corrado Gatto, Vito Di Benedetto and Anna Mazzacane
Instruments 2024, 8(4), 49; https://doi.org/10.3390/instruments8040049 - 14 Nov 2024
Viewed by 635
Abstract
A comprehensive multi-jet physics program is anticipated for experiments at future colliders. Key physics processes necessitate detectors that can distinguish signals from W and Z bosons and the Higgs boson. Typical examples include channels with W+W or  [...] Read more.
A comprehensive multi-jet physics program is anticipated for experiments at future colliders. Key physics processes necessitate detectors that can distinguish signals from W and Z bosons and the Higgs boson. Typical examples include channels with W+W or ZoZo pairs and processes involving new physics in those cases where neutral particles must be disentangled from charged ones due to the presence of W or Z bosons in their final states. Such a physics program demands calorimetric energy resolution at or beyond the limits of traditional calorimetric techniques. Multiple-readout calorimetry, which aims to reduce fluctuations in energy measurements of hadronic showers, is a promising approach. The first part of this article reviews dual- and triple-readout calorimetry within a mathematical framework describing the underlying compensating mechanism. The second part proposes a potential implementation using an integrally active and total absorption detector. This model serves as the basis for several Monte Carlo studies, illustrating how the response of a multiple-readout calorimeter depends on construction parameters. Among the layouts considered, one configuration operating in triple-readout mode shows the potential to achieve an energy resolution approaching 20%/E. Full article
Show Figures

Figure 1

Figure 1
<p>Photoelectrons from scintillating (<b>left</b>) and quartz (<b>right</b>) fibers vs. impinging point for 40 GeV electrons in a brass-based sampling dual-readout calorimeter with 1 mm fiber spacing. The detector is tilted at <math display="inline"><semantics> <mrow> <mn>2.7</mn> </mrow> </semantics></math>° with respect to the vertical plane (ILCroot simulation [<a href="#B17-instruments-08-00049" class="html-bibr">17</a>]).</p>
Full article ">Figure 2
<p>Scatter plot of Cherenkov and scintillating signals for 40 GeV <math display="inline"><semantics> <msup> <mi>π</mi> <mo>−</mo> </msup> </semantics></math> in a brass-based sampling dual-readout calorimeter with 1 mm fiber spacing (ILCroot simulations). The slope of thick red line equals tan(<math display="inline"><semantics> <msub> <mi>θ</mi> <mrow> <mi>C</mi> <mo>/</mo> <mi>S</mi> </mrow> </msub> </semantics></math>). The blue line corresponds to a calorimeter with no compensation. Refer to text for explanation of the symbols.</p>
Full article ">Figure 3
<p>Scatter plot of the Cherenkov signal (A.U.) and the fraction of energy deposited by neutrons in a shower generated by a 45 GeV <math display="inline"><semantics> <msup> <mi>π</mi> <mo>−</mo> </msup> </semantics></math> (ILCroot simulation).</p>
Full article ">Figure 4
<p>Time distribution of scintillating light of protons ((<b>left</b>) plot) and neutrons ((<b>right</b>) plot) for a 100 GeV <math display="inline"><semantics> <msup> <mi>π</mi> <mo>−</mo> </msup> </semantics></math> impinging onto a fiber calorimeter. The x-axis is in nsec [<a href="#B23-instruments-08-00049" class="html-bibr">23</a>].</p>
Full article ">Figure 5
<p>Neutron capture cross-section vs. energy for natural Gd (IRDFF 1.0) (<b>left</b>) and radiative photon spectrum (<b>right</b>) (from Ref. [<a href="#B24-instruments-08-00049" class="html-bibr">24</a>]).</p>
Full article ">Figure 6
<p>Refractive indices of several lead glass candidates for use as the active absorber for <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>D</mi> <mi>R</mi> <mi>I</mi> <mi>A</mi> <mi>N</mi> <mi>O</mi> </mrow> </semantics></math>.</p>
Full article ">Figure 7
<p>Attenuation length of several lead glass candidates for use as the active absorber for <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>D</mi> <mi>R</mi> <mi>I</mi> <mi>A</mi> <mi>N</mi> <mi>O</mi> </mrow> </semantics></math>.</p>
Full article ">Figure 8
<p>Individual module layout of the <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>D</mi> <mi>R</mi> <mi>I</mi> <mi>A</mi> <mi>N</mi> <mi>O</mi> </mrow> </semantics></math> module. Green fibers at the center of each side are WLS fibers, while the blue fibers are scintillating fibers.</p>
Full article ">Figure 9
<p>Absorption and emission spectra of BCF-92A WLS fibers.</p>
Full article ">Figure 10
<p>Quantum efficiency of the FBK SiPM simulated in ILCroot.</p>
Full article ">Figure 11
<p>Development of a typical shower induced by a 40 GeV pion impinging on the <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>D</mi> <mi>R</mi> <mi>I</mi> <mi>A</mi> <mi>N</mi> <mi>O</mi> </mrow> </semantics></math> calorimeter.</p>
Full article ">Figure 12
<p>Longitudinal (<b>left</b>) and lateral (<b>right</b>) development of the center of gravity of the scintillating light for a typical shower induced by a 40 GeV pion in the ADRIANO calorimeter.</p>
Full article ">Figure 13
<p>Hadronic (blue) and EM (red) scintillation signals (A.U.) for showers induced by 40 GeV pion (<b>left</b>) and electrons (<b>right</b>) in the <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>D</mi> <mi>R</mi> <mi>I</mi> <mi>A</mi> <mi>N</mi> <mi>O</mi> </mrow> </semantics></math> calorimeter. The black histogram corresponds to the sum of the two components.</p>
Full article ">Figure 14
<p>Hadronic (blue) and EM (red) Cherenkov signals (A.U.) for showers induced by 40 GeV pion (<b>left</b>) and electrons (<b>right</b>) in the <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>D</mi> <mi>R</mi> <mi>I</mi> <mi>A</mi> <mi>N</mi> <mi>O</mi> </mrow> </semantics></math> calorimeter. The black histogram corresponds to the sum of the two components.</p>
Full article ">Figure 15
<p>Hadronic (blue) and EM (red) scintillation signals (A.U.) for showers induced by 40 GeV pion (<b>left</b>) and electrons (<b>right</b>) in a DRS fiber calorimeter. The black histogram corresponds to the sum of the two components.</p>
Full article ">Figure 16
<p>Hadronic (blue) and EM (red) Cherenkov signals (A.U.) for showers induced by 40 GeV pion (<b>left</b>) and electrons (<b>right</b>) in a DRS fiber calorimeter. The black histogram corresponds to the sum of the two components.</p>
Full article ">Figure 17
<p>Scatter plot of simulated Cherenkov and scintillating signals for 40 GeV electrons in the <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>D</mi> <mi>R</mi> <mi>I</mi> <mi>A</mi> <mi>N</mi> <mi>O</mi> </mrow> </semantics></math> calorimeter.</p>
Full article ">Figure 18
<p>Scatter plots of <span class="html-italic">S</span> vs. <span class="html-italic">C</span> for the <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>D</mi> <mi>R</mi> <mi>I</mi> <mi>A</mi> <mi>N</mi> <mi>O</mi> </mrow> </semantics></math> (red) and the DRS (blue) detectors for 40 GeV pions.</p>
Full article ">Figure 19
<p>Scatter plots of <span class="html-italic">S</span> vs. <span class="html-italic">C</span> for the <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>D</mi> <mi>R</mi> <mi>I</mi> <mi>A</mi> <mi>N</mi> <mi>O</mi> </mrow> </semantics></math> detector for pions with different energies impinging in the center of the module.</p>
Full article ">Figure 20
<p><math display="inline"><semantics> <mrow> <mi>t</mi> <mi>a</mi> <mi>n</mi> <mo>(</mo> <msub> <mi>θ</mi> <mrow> <mi>C</mi> <mo>/</mo> <mi>S</mi> </mrow> </msub> <mo>)</mo> </mrow> </semantics></math> values from fit to the profile of <span class="html-italic">S</span> vs. <span class="html-italic">C</span> for the <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>D</mi> <mi>R</mi> <mi>I</mi> <mi>A</mi> <mi>N</mi> <mi>O</mi> </mrow> </semantics></math> detector for pions with different energies impinging in the center of the module.</p>
Full article ">Figure 21
<p>Corrected energy <math display="inline"><semantics> <msub> <mi>E</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>r</mi> <mi>r</mi> </mrow> </msub> </semantics></math> for showers induced by 40 GeV negative pions and version (<math display="inline"><semantics> <mrow> <mn>4</mn> <mo>×</mo> <mn>4</mn> </mrow> </semantics></math>) of detector layout.</p>
Full article ">Figure 22
<p>Plots of <math display="inline"><semantics> <mrow> <msub> <mi>E</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>a</mi> <mi>m</mi> </mrow> </msub> <mo>/</mo> <msub> <mi>E</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>r</mi> <mi>r</mi> </mrow> </msub> </mrow> </semantics></math> for negative pions with different energies. The detector has been calibrated with two samples of pions at 40 GeV and 70 GeV.</p>
Full article ">Figure 23
<p>Coordinate rotation of the reference by the angle system <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>C</mi> <mo>,</mo> <mi>S</mi> <mo>)</mo> </mrow> </semantics></math> by the angle <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mrow> <mi>C</mi> <mo>/</mo> <mi>S</mi> </mrow> </msub> <mrow> <mo>(</mo> <mo>∼</mo> <mn>37</mn> <mo>.</mo> <msup> <mn>8</mn> <mo>∘</mo> </msup> <mo>)</mo> </mrow> </mrow> </semantics></math>. <math display="inline"><semantics> <msub> <mi>σ</mi> <mrow> <mi>s</mi> <mi>c</mi> <mi>i</mi> <mi>n</mi> <mi>t</mi> </mrow> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>σ</mi> <mi>C</mi> </msub> </semantics></math> are the uncertainties in the original <span class="html-italic">S</span> and <span class="html-italic">C</span> while <math display="inline"><semantics> <msub> <mi>σ</mi> <msub> <mi>E</mi> <mrow> <mi>H</mi> <mi>C</mi> <mi>A</mi> <mi>L</mi> </mrow> </msub> </msub> </semantics></math> is the uncertainty in the rotated distribution.</p>
Full article ">Figure 24
<p>Energy resolution of five ADRIANO layouts for showers induced by negative pions of different energies. Several detector layouts are considered. Fits with Formula (<a href="#FD16-instruments-08-00049" class="html-disp-formula">16</a>) are superimposed to individual points.</p>
Full article ">Figure 25
<p>Plots of <math display="inline"><semantics> <mrow> <msub> <mi>E</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>a</mi> <mi>m</mi> </mrow> </msub> <mo>/</mo> <msub> <mi>E</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>r</mi> <mi>r</mi> </mrow> </msub> </mrow> </semantics></math> in <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>D</mi> <mi>R</mi> <mi>I</mi> <mi>A</mi> <mi>N</mi> <mi>O</mi> </mrow> </semantics></math> for negative pions with different energies. Several detector layouts are considered.</p>
Full article ">Figure 26
<p>Average time distribution of the scintillating signal for 40 GeV negative pions. The exponential fit superimposed on the distribution has two different characteristic times.</p>
Full article ">Figure 27
<p>Standard deviation of corrected energy <math display="inline"><semantics> <msubsup> <mi>E</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>r</mi> <mi>r</mi> </mrow> <mrow> <mi>T</mi> <mi>R</mi> </mrow> </msubsup> </semantics></math> for showers induced by negative pions with different energies. Several detector layouts are considered. Fits to curves described by Equation (<a href="#FD16-instruments-08-00049" class="html-disp-formula">16</a>) are superimposed to individual points.</p>
Full article ">Figure 28
<p>Estimated energy <math display="inline"><semantics> <msub> <mi>E</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>r</mi> <mi>r</mi> </mrow> </msub> </semantics></math> for showers induced by 40 GeV negative pions in a 180 cm long <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>D</mi> <mi>R</mi> <mi>I</mi> <mi>A</mi> <mi>N</mi> <mi>O</mi> </mrow> </semantics></math> module.</p>
Full article ">Figure 29
<p><math display="inline"><semantics> <mrow> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mrow> <mi>f</mi> <mi>o</mi> <mi>r</mi> <mi>w</mi> <mi>a</mi> <mi>r</mi> <mi>d</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>E</mi> <mrow> <mi>b</mi> <mi>a</mi> <mi>c</mi> <mi>k</mi> <mi>w</mi> <mi>a</mi> <mi>r</mi> <mi>d</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>/</mo> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mrow> <mi>f</mi> <mi>o</mi> <mi>r</mi> <mi>w</mi> <mi>a</mi> <mi>r</mi> <mi>d</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>E</mi> <mrow> <mi>b</mi> <mi>a</mi> <mi>c</mi> <mi>k</mi> <mi>w</mi> <mi>a</mi> <mi>r</mi> <mi>d</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </semantics></math> plotted versus the center of gravity of the light produced in showers induced by 40 GeV negative pions.</p>
Full article ">Figure 30
<p>Uncertainty in the CoG of a shower estimated with the light division method for different energies of the pion.</p>
Full article ">Figure 31
<p>(<math display="inline"><semantics> <mrow> <msub> <mi>E</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>r</mi> <mi>r</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>E</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>a</mi> <mi>m</mi> </mrow> </msub> <mrow> <mo>)</mo> <mo>/</mo> </mrow> <msub> <mi>E</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>a</mi> <mi>m</mi> </mrow> </msub> </mrow> </semantics></math> vs. <math display="inline"><semantics> <msub> <mi>η</mi> <mrow> <mi>F</mi> <mi>B</mi> </mrow> </msub> </semantics></math> for 40 GeV negative pions impinging on a 180 cm long ADRIANO module.</p>
Full article ">Figure 32
<p><math display="inline"><semantics> <mrow> <msub> <mi>E</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>r</mi> <mi>r</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>E</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>a</mi> <mi>m</mi> </mrow> </msub> </mrow> </semantics></math> vs. <math display="inline"><semantics> <msub> <mi>η</mi> <mrow> <mi>F</mi> <mi>B</mi> </mrow> </msub> </semantics></math> for 100 GeV negative pions for a 180 cm long detector module after correction for longitudinal leakage.</p>
Full article ">Figure 33
<p>Hadronic energy resolution for a 180 cm long ADRIANO triple-readout module after correction for longitudinal leakage. The individual points are fitted with the curve described in Formula (<a href="#FD20-instruments-08-00049" class="html-disp-formula">20</a>).</p>
Full article ">Figure 34
<p><math display="inline"><semantics> <msub> <mi>E</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>r</mi> <mi>r</mi> </mrow> </msub> </semantics></math> for 40 GeV electrons impinging with an angle of <math display="inline"><semantics> <msup> <mn>3</mn> <mo>∘</mo> </msup> </semantics></math> on a 180 cm long module.</p>
Full article ">Figure 35
<p><span class="html-italic">C</span> signal for 40 GeV electrons impinging with an angle of ≈<math display="inline"><semantics> <msup> <mn>3</mn> <mo>∘</mo> </msup> </semantics></math> on a 180 cm long module.</p>
Full article ">Figure 36
<p><math display="inline"><semantics> <msub> <mi>R</mi> <mrow> <mi>C</mi> <mi>S</mi> </mrow> </msub> </semantics></math> for 40 GeV electrons (red) and negative pions (blue) in a 180 cm long <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>D</mi> <mi>R</mi> <mi>I</mi> <mi>A</mi> <mi>N</mi> <mi>O</mi> </mrow> </semantics></math> module. C and S are the Cherenkov and scintillating signals, respectively.</p>
Full article ">Figure 37
<p><math display="inline"><semantics> <msub> <mi>R</mi> <mn>20</mn> </msub> </semantics></math> for 40 GeV electrons (red) and negative pions (blue) in a 180 cm long <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>D</mi> <mi>R</mi> <mi>I</mi> <mi>A</mi> <mi>N</mi> <mi>O</mi> </mrow> </semantics></math> module.</p>
Full article ">Figure 38
<p>Energy resolution for electrons after PID selection in a 180 cm long detector module after correction for longitudinal leakage. The individual points are fitted with the curve described in Formula (<a href="#FD16-instruments-08-00049" class="html-disp-formula">16</a>). See text for further details.</p>
Full article ">
16 pages, 515 KiB  
Article
Evaporation of Primordial Charged Black Holes: Timescale and Evolution of Thermodynamic Parameters
by José Antonio de Freitas Pacheco
Symmetry 2024, 16(7), 895; https://doi.org/10.3390/sym16070895 - 13 Jul 2024
Viewed by 821
Abstract
The evolution of primordial black holes formed during the reheating phase is revisited. For reheating temperatures in the range of 10121013 GeV, the initial masses are respectively of the order of 1010108MP, [...] Read more.
The evolution of primordial black holes formed during the reheating phase is revisited. For reheating temperatures in the range of 10121013 GeV, the initial masses are respectively of the order of 1010108MP, where MP is the Planck mass. These newborn black holes have a small charge-to-mass ratio of the order of 103, a consequence of statistical fluctuations present in the plasma constituting the collapsing matter. Charged black holes can be rapidly discharged by the Schwinger mechanism, but one expects that, for very light black holes satisfying the condition M/MP<<MP/mW (mW is the mass of the heaviest standard model charged W-boson), the pair production process is probably strongly quenched. Under these conditions, these black holes evaporate until attaining extremality with final masses of about 107105MP. Timescales to reach extremality as a function of the initial charge excess were computed, as well as the evolution of the horizon temperature and the charge-to-mass ratio. The behavior of the horizon temperature can be understood in terms of the well-known discontinuity present in the heat capacity for a critical charge-to-mass ratio Q/GM=3/2. Full article
(This article belongs to the Special Issue Symmetry in Gravity Theories and Cosmology)
Show Figures

Figure 1

Figure 1
<p>Number density of black holes formed per unit of mass as a function of the black hole mass in units of the Planck mass. The vertical axis has relative units due to the normalization procedure adopted to perform the plot.</p>
Full article ">Figure 2
<p>Ratio between the evaporation lifetime of a Reissner-Nordstrom and that of a Schwarzschild black hole as a function of the initial charge-to-mass ratio.</p>
Full article ">Figure 3
<p>Plot of the luminosity (blue curve), charge-to-mass parameter <math display="inline"><semantics> <mi>ε</mi> </semantics></math> (red curve), and horizon temperature (black curve) as a function of the dimensionless time <math display="inline"><semantics> <mrow> <mi>x</mi> <mo>=</mo> <mi>l</mi> <mi>g</mi> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mi>τ</mi> <mo>)</mo> </mrow> </semantics></math>. Ordinates are in arbitrary units in order to permit all curves to be plotted in the same figure. On the left panel, curves correspond to a model characterized by <math display="inline"><semantics> <mrow> <msub> <mi>y</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, while on the right panel, the model is defined by <math display="inline"><semantics> <mrow> <msub> <mi>y</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.60</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 4
<p>Evolution of the horizon temperature for two different values of the initial charge-to-mass ratio: <math display="inline"><semantics> <mrow> <msub> <mi>y</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.40</mn> </mrow> </semantics></math> (black curve) and <math display="inline"><semantics> <mrow> <msub> <mi>y</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.90</mn> </mrow> </semantics></math> (blue curve).</p>
Full article ">
8 pages, 241 KiB  
Article
Cosmological Mass of the Photon Related to Stueckelberg and Higgs Mechanisms
by Lorenzo Gallerani Resca
Particles 2024, 7(2), 289-296; https://doi.org/10.3390/particles7020017 - 29 Mar 2024
Viewed by 1590
Abstract
I consider the electro-weak (EW) masses and interactions generated by photons using vacuum expectation values of Stueckelberg and Higgs fields. I provide a prescription to relate their parametric values to a cosmological range derived from the fundamental Heisenberg uncertainty principle and the Einstein–de [...] Read more.
I consider the electro-weak (EW) masses and interactions generated by photons using vacuum expectation values of Stueckelberg and Higgs fields. I provide a prescription to relate their parametric values to a cosmological range derived from the fundamental Heisenberg uncertainty principle and the Einstein–de Sitter cosmological constant and horizon. This yields qualitative connections between microscopic ranges acquired by W± or Z0 gauge Bosons and the cosmological scale and minimal mass acquired by g-photons. I apply this procedure to an established Stueckelberg–Higgs mechanism, while I consider a similar procedure for a pair of Higgs fields that may spontaneously break all U(1) × SU(2) gauge invariances. My estimates of photon masses and their additional parity-breaking interactions with leptons and neutrinos may be detectable in suitable accelerator experiments. Their effects may also be observable astronomically through massive g-photon condensates that may contribute to dark matter and dark energy. Full article
(This article belongs to the Special Issue Feature Papers for Particles 2023)
16 pages, 1048 KiB  
Article
On the Breaking of the U(1) Peccei–Quinn Symmetry and Its Implications for Neutrino and Dark Matter Physics
by Osvaldo Civitarese
Symmetry 2024, 16(3), 364; https://doi.org/10.3390/sym16030364 - 18 Mar 2024
Viewed by 1161
Abstract
The Standard Model of electroweak interactions is based on the fundamental SU(2)weak × U(1)elect representation. It assumes massless neutrinos and purely left-handed massive W± and Z0 bosons to which one should add the massless photon. The existence, [...] Read more.
The Standard Model of electroweak interactions is based on the fundamental SU(2)weak × U(1)elect representation. It assumes massless neutrinos and purely left-handed massive W± and Z0 bosons to which one should add the massless photon. The existence, verified experimentally, of neutrino oscillations poses a challenge to this scheme, since the oscillations take place between at least three massive neutrinos belonging to a mass hierarchy still to be determined. One should also take into account the possible existence of sterile neutrino species. In a somehow different context, the fundamental nature of the strong interaction component of the forces in nature is described by the, until now, extremely successful representation based on the SU(3)strong group which, together with the confining rule, give a description of massive hadrons in terms of quarks and gluons. To this is added the minimal U(1) Higgs group to give mass to the otherwise massless generators. This representation may also be challenged by the existence of both dark matter and dark energy, of still unknown composition. In this note, we shall discuss a possible connection between these questions, namely the need to extend the SU(3)strong × SU(2)weak × U(1)elect to account for massive neutrinos and dark matter. The main point of it is related to the role of axions, as postulated by Roberto Peccei and Helen Quinn. The existence of neutral pseudo-scalar bosons, that is, the axions, has been proposed long ago by Peccei and Quinn to explain the suppression of the electric dipole moment of the neutron. The associated U(1)PQ symmetry breaks at very high energy, and it guarantees that the interaction of other particles with axions is very weak. We shall review the axion properties in connection with the apparently different contexts of neutrino and dark matter physics. Full article
(This article belongs to the Special Issue Role of Symmetries in Nuclear Physics)
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Figure 1

Figure 1
<p>Interaction between neutrinos and particles belonging to the environment.</p>
Full article ">Figure 2
<p>Real (upper plot) and imaginary (lower plot) matrix elements of the neutrino density matrix as a function of time for the three-flavor scheme. We used the following parameters: <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>u</mi> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math> for the Gaussian function and the coupling to the environment. The relative time scale (<span class="html-italic">t</span> divided by <span class="html-italic">ℏ</span> ) is expressed in units of 10<sup>7</sup>.</p>
Full article ">Figure 3
<p>Diagrams showing the double beta decay transitions, for the case of zero neutrino double beta decay channels, and an equivalent process mediated by W bosons. The neutrinoless double beta decay process is not allowed by the Standard Model, since it implies that the neutrino is a Majorana particle.</p>
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<p>View of the close connection existing between experimental, nuclear, and particle physics focusing on the determination of neutrino properties, as well as on the non-trivial extensions of the minimal Standard Model.</p>
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10 pages, 1113 KiB  
Article
Identifying D Mesons from Radiative W Decays at the Large Hadron Collider
by Evelin Bakos, Nicolo de Groot and Nenad Vranjes
Symmetry 2023, 15(10), 1948; https://doi.org/10.3390/sym15101948 - 20 Oct 2023
Viewed by 1000
Abstract
In this paper, we present two machine learning algorithms to identify D mesons produced in a colour singlet state from radiative W boson decays at the LHC. The combined network algorithm is able to identify D mesons via its hadronic decays with an [...] Read more.
In this paper, we present two machine learning algorithms to identify D mesons produced in a colour singlet state from radiative W boson decays at the LHC. The combined network algorithm is able to identify D mesons via its hadronic decays with an efficiency of 47% while suppressing a background of quark and gluon jets by a factor of 100. Using the developed algorithm, we perform a prospective study for the measurement of B(WDsγ). Full article
(This article belongs to the Section Physics)
Show Figures

Figure 1

Figure 1
<p>Distributions of the variables used for <math display="inline"><semantics> <msub> <mi>D</mi> <mi>s</mi> </msub> </semantics></math> identification, using DNN. The signal is presented with a solid blue line, while the <math display="inline"><semantics> <mrow> <mi>g</mi> <mi>g</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>q</mi> <mi>q</mi> </mrow> </semantics></math> backgrounds are drawn with dashed red and dotted green lines, respectively.</p>
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<p>Feature importance plot of DNN. The blue bars represent the weight of each feature (variable) within the network.</p>
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<p>Jet image construction from low level variables, where (<b>a</b>) shows 2 different signal and (<b>b</b>) 2 different background events. The hadronic deposit is noted with blue circle pattern, the electromagnetic deposit with green square grid and the track transverse momentum with red star pattern composing an RGB input picture to the CNN algorithm.</p>
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<p>ROC curves for the different network types.</p>
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<p>Output of the different networks for background (blue dotted pattern) and signal (red square grid pattern).</p>
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<p>Distribution of the invariant mass of <math display="inline"><semantics> <msub> <mi>D</mi> <mi>s</mi> </msub> </semantics></math> tagged jet-plus-photon system. The signal is scaled with a factor of 10<math display="inline"><semantics> <msup> <mrow/> <mn>4</mn> </msup> </semantics></math>.</p>
Full article ">Figure 7
<p>Expected upper limit on branching fraction of the <math display="inline"><semantics> <mrow> <mi>W</mi> <mo>→</mo> <msub> <mi>D</mi> <mi>s</mi> </msub> <mi>γ</mi> </mrow> </semantics></math> decay. The vertical line corresponds to <math display="inline"><semantics> <mrow> <mi>C</mi> <msub> <mi>L</mi> <mi>s</mi> </msub> <mspace width="3.33333pt"/> <mo>=</mo> <mspace width="3.33333pt"/> </mrow> </semantics></math>0.05. The branching fractions higher than <math display="inline"><semantics> <mrow> <mn>2.87</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </mrow> </semantics></math> are excluded at 95% CL.</p>
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37 pages, 2670 KiB  
Review
Single-Top Quark Physics at the LHC: From Precision Measurements to Rare Processes and Top Quark Properties
by Jérémy Andrea and Nicolas Chanon
Universe 2023, 9(10), 439; https://doi.org/10.3390/universe9100439 - 30 Sep 2023
Viewed by 1873
Abstract
Since the initial measurements of single-top quark production at the Tevatron in 2009, tremendous progress has been made at the LHC. While LHC Run 1 marked the beginning of a precision era for the single-top quark measurements in some of the main production [...] Read more.
Since the initial measurements of single-top quark production at the Tevatron in 2009, tremendous progress has been made at the LHC. While LHC Run 1 marked the beginning of a precision era for the single-top quark measurements in some of the main production mechanisms, LHC Run 2 witnessed the emergence and exploration of new processes associating top quark production with a neutral boson. In this paper, we review the measurements of the three main production mechanisms (t-channel, s-channel, and tW production), and of the associated production with a photon, a Z boson, or a Higgs boson. Differential cross-sections are measured for several of these processes and compared with theoretical predictions. The top quark properties that can be measured in single-top quark processes are scrutinized, such as Wtb couplings and top quark couplings with neutral bosons, and the polarizations of both the W boson and top quark. The effective field theory framework is emerging as a standard for interpreting property measurements. Perspectives for LHC Run 3 and the HL-LHC are discussed in the conclusions. Full article
(This article belongs to the Special Issue Top Quark at the New Physics Frontier)
Show Figures

Figure 1

Figure 1
<p>Examples of Feynman diagrams for single-top production at LO: <span class="html-italic">t</span>-channel (<b>top left</b>), <span class="html-italic">s</span>-channel (<b>top right</b>), and <math display="inline"><semantics> <mrow> <mi>t</mi> <mi>W</mi> </mrow> </semantics></math> production (<b>bottom</b>).</p>
Full article ">Figure 2
<p>Summary of cross-sections for top quark processes measured by ATLAS [<a href="#B17-universe-09-00439" class="html-bibr">17</a>] and compared with SM predictions.</p>
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<p>Summary of measured cross-sections for single-top quark production at CMS [<a href="#B18-universe-09-00439" class="html-bibr">18</a>]. Theoretical calculations for the <span class="html-italic">t</span>-channel, <span class="html-italic">s</span>-channel, and <span class="html-italic">W</span>-associated production have been provided by N. Kidonakis to the CMS collaboration.</p>
Full article ">Figure 4
<p>Feynman diagrams for single-top <span class="html-italic">t</span>-channel production at the LO in pQCD [<a href="#B32-universe-09-00439" class="html-bibr">32</a>], in the 5-flavor scheme (<b>left</b>), and 4-flavor scheme (<b>right</b>).</p>
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<p>Distribution of the transverse mass of the <span class="html-italic">W</span> boson in the muon channel of the <math display="inline"><semantics> <mrow> <mn>2</mn> <mi>j</mi> <mn>0</mn> <mi>t</mi> </mrow> </semantics></math> region (<b>left</b>), the BDT discriminant in the <math display="inline"><semantics> <mrow> <mn>2</mn> <mi>j</mi> <mn>1</mn> <mi>t</mi> </mrow> </semantics></math> category (<b>right</b>) [<a href="#B32-universe-09-00439" class="html-bibr">32</a>].</p>
Full article ">Figure 6
<p>Distributions in the cosine of the top quark polarization angle with a background-dominated selection (<b>left</b>) and a signal-enriched selection (<b>right</b>) for events in the <math display="inline"><semantics> <mrow> <mn>2</mn> <mi>j</mi> <mn>1</mn> <mi>t</mi> </mrow> </semantics></math> region [<a href="#B32-universe-09-00439" class="html-bibr">32</a>].</p>
Full article ">Figure 7
<p>Evolution of the relative total uncertainty in the inclusive <span class="html-italic">t</span>-channel cross-section measurements, plotted as a function of the integrated luminosity at <math display="inline"><semantics> <mrow> <msqrt> <mi>s</mi> </msqrt> <mo>=</mo> </mrow> </semantics></math>7, 8, and 13 TeV.</p>
Full article ">Figure 8
<p>Unfolded differential cross-section measurements: top quark <math display="inline"><semantics> <msub> <mi>p</mi> <mi>T</mi> </msub> </semantics></math> (<b>upper row</b>), charge ratio as a function of the rapidity <span class="html-italic">y</span> (middle row), and <math display="inline"><semantics> <mrow> <mo form="prefix">cos</mo> <msup> <mi>θ</mi> <mo>*</mo> </msup> </mrow> </semantics></math> (<b>bottom row</b>) at the parton level <b>(left</b>) and particle level (<b>right</b>) [<a href="#B32-universe-09-00439" class="html-bibr">32</a>].</p>
Full article ">Figure 9
<p>Example of the Feynman diagram for <math display="inline"><semantics> <mrow> <mi>t</mi> <mi>W</mi> </mrow> </semantics></math> production at the LO in pQCD within the 5FS [<a href="#B51-universe-09-00439" class="html-bibr">51</a>].</p>
Full article ">Figure 10
<p>Examples of Feynman diagrams for the production of <math display="inline"><semantics> <mrow> <mi>t</mi> <mi>W</mi> <mi>b</mi> </mrow> </semantics></math> with (<b>left</b>) and without (<b>right</b>) an on-shell top.</p>
Full article ">Figure 11
<p>Categories in the number of jets and b-jets in the <math display="inline"><semantics> <mrow> <mi>t</mi> <mi>W</mi> </mrow> </semantics></math> dilepton analysis by ATLAS [<a href="#B61-universe-09-00439" class="html-bibr">61</a>] (<b>left</b>) and CMS [<a href="#B62-universe-09-00439" class="html-bibr">62</a>] (<b>right</b>).</p>
Full article ">Figure 12
<p>Invariant mass of the dilepton and b-jet in the <math display="inline"><semantics> <mrow> <mi>t</mi> <mi>W</mi> </mrow> </semantics></math> dilepton analysis by ATLAS [<a href="#B61-universe-09-00439" class="html-bibr">61</a>] (<b>left</b>) and CMS [<a href="#B62-universe-09-00439" class="html-bibr">62</a>] (<b>right</b>), comparing data and several predictions for <math display="inline"><semantics> <mrow> <mi>t</mi> <mi>W</mi> </mrow> </semantics></math> modeling.</p>
Full article ">Figure 13
<p>Data comparison of MC predictions for the normalized differential cross-section of the <math display="inline"><semantics> <mrow> <mi>t</mi> <mi>W</mi> </mrow> </semantics></math> process in a region maximizing the interference, as a function of the <math display="inline"><semantics> <msubsup> <mi>m</mi> <mrow> <mi>b</mi> <mi mathvariant="script">l</mi> </mrow> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> <mi>i</mi> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msubsup> </semantics></math> variable [<a href="#B68-universe-09-00439" class="html-bibr">68</a>]. The region sensitive to the interference lies above <math display="inline"><semantics> <msqrt> <mrow> <msubsup> <mi>m</mi> <mi>t</mi> <mn>2</mn> </msubsup> <mo>−</mo> <msubsup> <mi>m</mi> <mi>W</mi> <mn>2</mn> </msubsup> </mrow> </msqrt> </semantics></math>.</p>
Full article ">Figure 14
<p>Feynman diagram for single-top <span class="html-italic">s</span>-channel production at the LO in pQCD in the 5FS [<a href="#B9-universe-09-00439" class="html-bibr">9</a>].</p>
Full article ">Figure 15
<p>Measured cross-sections for the <span class="html-italic">s</span>-channel at the Tevatron along with their combined results [<a href="#B8-universe-09-00439" class="html-bibr">8</a>].</p>
Full article ">Figure 16
<p>Results of the <span class="html-italic">s</span>-channel searches by ATLAS: (<b>left</b>) post-fit distribution comparing data and simulation for the MEM likelihood, and (<b>right</b>) signal distribution after the background subtraction [<a href="#B10-universe-09-00439" class="html-bibr">10</a>].</p>
Full article ">Figure 17
<p>Examples of Feynman diagrams for <math display="inline"><semantics> <mrow> <mi>t</mi> <mi>γ</mi> <mi>q</mi> </mrow> </semantics></math> processes at the LO in pQCD [<a href="#B79-universe-09-00439" class="html-bibr">79</a>].</p>
Full article ">Figure 18
<p>Discriminants used in the <math display="inline"><semantics> <mrow> <mi>t</mi> <mi>γ</mi> <mi>q</mi> </mrow> </semantics></math> signal extraction: BDT output at CMS [<a href="#B79-universe-09-00439" class="html-bibr">79</a>] (<b>left</b>) and DNN output by ATLAS [<a href="#B81-universe-09-00439" class="html-bibr">81</a>] (<b>right</b>) in the signal region with one forward jet.</p>
Full article ">Figure 19
<p>Representative Feynman diagrams for the <math display="inline"><semantics> <mrow> <mi>t</mi> <mi>Z</mi> <mi>q</mi> </mrow> </semantics></math> production at the LO in pQCD [<a href="#B87-universe-09-00439" class="html-bibr">87</a>].</p>
Full article ">Figure 20
<p>Distributions of the NN output in the signal regions <math display="inline"><semantics> <mrow> <mn>2</mn> <mi>j</mi> <mn>1</mn> <mi>b</mi> </mrow> </semantics></math> (<b>left</b>) and <math display="inline"><semantics> <mrow> <mn>3</mn> <mi>j</mi> <mn>1</mn> <mi>b</mi> </mrow> </semantics></math> (<b>right</b>) in the ATLAS analysis [<a href="#B89-universe-09-00439" class="html-bibr">89</a>].</p>
Full article ">Figure 21
<p>Normalized differential cross-sections measured at the parton level as a function of <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <mi>Z</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> (<b>top left</b>) and <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> (<b>top right</b>) at the parton level, and as a function of <math display="inline"><semantics> <mrow> <mo>|</mo> <mi>η</mi> <mo>(</mo> <msup> <mi>j</mi> <mo>′</mo> </msup> <mo>)</mo> <mo>|</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo form="prefix">cos</mo> <msubsup> <mi>θ</mi> <mrow> <mi>p</mi> <mi>o</mi> <mi>l</mi> <mo>.</mo> </mrow> <mo>*</mo> </msubsup> </mrow> </semantics></math> at the particle level [<a href="#B87-universe-09-00439" class="html-bibr">87</a>]. The inner and outer vertical bars represent the systematic and total uncertainties, respectively.</p>
Full article ">Figure 22
<p>Examples of Feynman diagrams for <math display="inline"><semantics> <mrow> <mi>t</mi> <mi>H</mi> <mi>q</mi> </mrow> </semantics></math> processes at the LO in pQCD [<a href="#B94-universe-09-00439" class="html-bibr">94</a>].</p>
Full article ">Figure 23
<p>(<b>Right</b>) Cross-section for the Higgs boson production as a function of <math display="inline"><semantics> <msqrt> <mi>s</mi> </msqrt> </semantics></math>. (<b>Left</b>) branching ratio for the Higgs boson decay [<a href="#B92-universe-09-00439" class="html-bibr">92</a>].</p>
Full article ">Figure 24
<p>Likelihood contour as a function of the signal strengths for <math display="inline"><semantics> <mrow> <mi>t</mi> <mover accent="true"> <mi>t</mi> <mo>¯</mo> </mover> <mi>H</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>t</mi> <mi>H</mi> </mrow> </semantics></math> processes in the multilepton analysis [<a href="#B99-universe-09-00439" class="html-bibr">99</a>].</p>
Full article ">Figure 25
<p>Log-likelihood as a function of the <math display="inline"><semantics> <msub> <mi>κ</mi> <mi>t</mi> </msub> </semantics></math> parameter, in the ATLAS <math display="inline"><semantics> <mrow> <mi>H</mi> <mo>→</mo> <mi>γ</mi> <mi>γ</mi> </mrow> </semantics></math> analysis [<a href="#B96-universe-09-00439" class="html-bibr">96</a>] (<b>left</b>), and in the CMS multilepton analysis [<a href="#B99-universe-09-00439" class="html-bibr">99</a>] (<b>right</b>).</p>
Full article ">Figure 26
<p>Summary of the ATLAS and CMS extractions of the CKM matrix element <math display="inline"><semantics> <msub> <mi>V</mi> <mrow> <mi>t</mi> <mi>b</mi> </mrow> </msub> </semantics></math> from single-top quark measurements [<a href="#B40-universe-09-00439" class="html-bibr">40</a>], compared with theoretical predictions at NLO+NNLL accuracy [<a href="#B71-universe-09-00439" class="html-bibr">71</a>,<a href="#B109-universe-09-00439" class="html-bibr">109</a>,<a href="#B110-universe-09-00439" class="html-bibr">110</a>].</p>
Full article ">Figure 27
<p>The differential decay rate as a function of <math display="inline"><semantics> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <msup> <mi>θ</mi> <mo>*</mo> </msup> </mrow> </semantics></math> in several scenarios for <span class="html-italic">W</span> boson polarization [<a href="#B113-universe-09-00439" class="html-bibr">113</a>].</p>
Full article ">Figure 28
<p>Top quark polarization in the single-top <span class="html-italic">t</span>-channel production along <math display="inline"><semantics> <msup> <mi>x</mi> <mo>′</mo> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mi>z</mi> <mo>′</mo> </msup> </semantics></math> directions for the top and antitop quarks [<a href="#B125-universe-09-00439" class="html-bibr">125</a>].</p>
Full article ">Figure 29
<p>Summary of single-top quark cross-section measurements by ATLAS and CMS in the <span class="html-italic">t</span>-channel, <math display="inline"><semantics> <mrow> <mi>t</mi> <mi>W</mi> </mrow> </semantics></math> production, and <span class="html-italic">s</span>-channel, as functions of the center of mass energy, compared with theoretical predictions at NNLO [<a href="#B11-universe-09-00439" class="html-bibr">11</a>], approximate NNLO+N<sup>3</sup>LL [<a href="#B12-universe-09-00439" class="html-bibr">12</a>], and NLO [<a href="#B14-universe-09-00439" class="html-bibr">14</a>,<a href="#B132-universe-09-00439" class="html-bibr">132</a>] accuracy, provided by the LHC<span class="html-italic">top</span>WG [<a href="#B133-universe-09-00439" class="html-bibr">133</a>].</p>
Full article ">Figure 30
<p>Summary of single-top quark cross-section measurements by ATLAS and CMS in the associated production with a <span class="html-italic">Z</span> boson or a photon compared with theoretical predictions at NLO [<a href="#B78-universe-09-00439" class="html-bibr">78</a>] accuracy; provided by the LHC<span class="html-italic">top</span>WG [<a href="#B133-universe-09-00439" class="html-bibr">133</a>].</p>
Full article ">
24 pages, 1262 KiB  
Article
Prospects for Charged Higgs Bosons in Natural SUSY Models at the High-Luminosity LHC
by Howard Baer, Vernon Barger, Xerxes Tata and Kairui Zhang
Symmetry 2023, 15(8), 1475; https://doi.org/10.3390/sym15081475 - 25 Jul 2023
Viewed by 1167
Abstract
We continue our examination of prospects for the discovery of heavy Higgs bosons of natural SUSY (natSUSY) models at the high luminosity LHC (HL-LHC), this time focusing on charged Higgs bosons. In natSUSY, higgsinos are expected at the few hundred GeV scale whilst [...] Read more.
We continue our examination of prospects for the discovery of heavy Higgs bosons of natural SUSY (natSUSY) models at the high luminosity LHC (HL-LHC), this time focusing on charged Higgs bosons. In natSUSY, higgsinos are expected at the few hundred GeV scale whilst electroweak gauginos inhabit the TeV scale and the heavy Higgs bosons, H, A and H± could range up tens of TeV without jeopardizing naturalness. For TeV-scale heavy SUSY Higgs bosons H, A and H±, as currently required by LHC searches, SUSY decays into gaugino plus higgsino can dominate H± decays provided these decays are kinematically accessible. The visible decay products of higgsinos are soft making them largely invisible, whilst the gauginos decay to W, Z or h plus missing transverse energy (ET). Charged Higgs bosons are dominantly produced at LHC14 via the parton subprocess, gbH±t. In this paper, we examine the viability of observing signatures from H±τν, H±tb and H±W,Z,h+ET events produced in association with a top quark at the HL-LHC over large Standard Model (SM) backgrounds from (mainly) tt¯, tt¯V and tt¯h production (where V=W,Z). We find that the greatest reach is found via the SM H±(τν)+t channel with a subdominant contribution from the H±(tb)+t channel. Unlike for neutral Higgs searches, the SUSY decay modes appear to be unimportant for H± searches at the HL-LHC. We delineate regions of the mA vs. tanβ plane, mostly around mA 1–2 TeV, where signals from charged Higgs bosons would serve to confirm signals of a heavy, neutral Higgs boson at the 5σ level or, alternatively, to exclude heavy Higgs bosons at the 95% confidence level at the high luminosity LHC. Full article
(This article belongs to the Special Issue Higgs Bosons and Supersymmetry in High Energy Physics)
Show Figures

Figure 1

Figure 1
<p>The total cross section for <math display="inline"><semantics><mrow><mi>p</mi><mi>p</mi><mo>→</mo><msup><mi>H</mi><mo>±</mo></msup><mo>+</mo><mi>X</mi></mrow></semantics></math> via various production mechanisms at LHC14 for <math display="inline"><semantics><mrow><mo>tan</mo><mi>β</mi><mo>=</mo><mn>10</mn></mrow></semantics></math> (solid) and <math display="inline"><semantics><mrow><mo>tan</mo><mi>β</mi><mo>=</mo><mn>40</mn></mrow></semantics></math> (dashed).</p>
Full article ">Figure 2
<p>The dominant <math display="inline"><semantics><mrow><mi>p</mi><mi>p</mi><mo>→</mo><mi>t</mi><msup><mi>H</mi><mo>±</mo></msup><mo>+</mo><mi>X</mi></mrow></semantics></math> cross section at <math display="inline"><semantics><mrow><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>14</mn></mrow></semantics></math> TeV in the <math display="inline"><semantics><msub><mi>m</mi><mi>A</mi></msub></semantics></math> vs. <math display="inline"><semantics><mrow><mo>tan</mo><mi>β</mi></mrow></semantics></math> plane. The region to the left of the dashed blue line is currently excluded at the 95% confidence level by limits from ATLAS searches for <math display="inline"><semantics><mrow><mi>p</mi><mi>p</mi><mo>→</mo><mi>H</mi><mo>,</mo><mspace width="4pt"/><mi>A</mi><mo>→</mo><msup><mi>τ</mi><mo>+</mo></msup><msup><mi>τ</mi><mo>−</mo></msup></mrow></semantics></math> [<a href="#B44-symmetry-15-01475" class="html-bibr">44</a>].</p>
Full article ">Figure 3
<p>Branching fractions in the <math display="inline"><semantics><msub><mi>m</mi><mi>A</mi></msub></semantics></math> vs. <math display="inline"><semantics><mrow><mo>tan</mo><mi>β</mi></mrow></semantics></math> plane for <math display="inline"><semantics><msup><mi>H</mi><mo>+</mo></msup></semantics></math> to (<b>a</b>) <math display="inline"><semantics><mrow><mi>t</mi><mover accent="true"><mi>b</mi><mo>¯</mo></mover></mrow></semantics></math>, (<b>b</b>) <math display="inline"><semantics><mrow><msup><mi>τ</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>τ</mi></msub></mrow></semantics></math>, (<b>c</b>) <math display="inline"><semantics><mrow><msubsup><mover accent="true"><mi>χ</mi><mo>˜</mo></mover><mn>2</mn><mo>+</mo></msubsup><msubsup><mover accent="true"><mi>χ</mi><mo>˜</mo></mover><mn>1</mn><mn>0</mn></msubsup></mrow></semantics></math>, (<b>d</b>) <math display="inline"><semantics><mrow><msubsup><mover accent="true"><mi>χ</mi><mo>˜</mo></mover><mn>2</mn><mo>+</mo></msubsup><msubsup><mover accent="true"><mi>χ</mi><mo>˜</mo></mover><mn>2</mn><mn>0</mn></msubsup></mrow></semantics></math>, (<b>e</b>) <math display="inline"><semantics><mrow><msubsup><mover accent="true"><mi>χ</mi><mo>˜</mo></mover><mn>1</mn><mo>+</mo></msubsup><msubsup><mover accent="true"><mi>χ</mi><mo>˜</mo></mover><mn>4</mn><mn>0</mn></msubsup></mrow></semantics></math> and (<b>f</b>) <math display="inline"><semantics><mrow><msubsup><mover accent="true"><mi>χ</mi><mo>˜</mo></mover><mn>1</mn><mo>+</mo></msubsup><msubsup><mover accent="true"><mi>χ</mi><mo>˜</mo></mover><mn>3</mn><mn>0</mn></msubsup></mrow></semantics></math> from Isajet 7.88 [<a href="#B35-symmetry-15-01475" class="html-bibr">35</a>] for the model line introduced in the text.</p>
Full article ">Figure 3 Cont.
<p>Branching fractions in the <math display="inline"><semantics><msub><mi>m</mi><mi>A</mi></msub></semantics></math> vs. <math display="inline"><semantics><mrow><mo>tan</mo><mi>β</mi></mrow></semantics></math> plane for <math display="inline"><semantics><msup><mi>H</mi><mo>+</mo></msup></semantics></math> to (<b>a</b>) <math display="inline"><semantics><mrow><mi>t</mi><mover accent="true"><mi>b</mi><mo>¯</mo></mover></mrow></semantics></math>, (<b>b</b>) <math display="inline"><semantics><mrow><msup><mi>τ</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>τ</mi></msub></mrow></semantics></math>, (<b>c</b>) <math display="inline"><semantics><mrow><msubsup><mover accent="true"><mi>χ</mi><mo>˜</mo></mover><mn>2</mn><mo>+</mo></msubsup><msubsup><mover accent="true"><mi>χ</mi><mo>˜</mo></mover><mn>1</mn><mn>0</mn></msubsup></mrow></semantics></math>, (<b>d</b>) <math display="inline"><semantics><mrow><msubsup><mover accent="true"><mi>χ</mi><mo>˜</mo></mover><mn>2</mn><mo>+</mo></msubsup><msubsup><mover accent="true"><mi>χ</mi><mo>˜</mo></mover><mn>2</mn><mn>0</mn></msubsup></mrow></semantics></math>, (<b>e</b>) <math display="inline"><semantics><mrow><msubsup><mover accent="true"><mi>χ</mi><mo>˜</mo></mover><mn>1</mn><mo>+</mo></msubsup><msubsup><mover accent="true"><mi>χ</mi><mo>˜</mo></mover><mn>4</mn><mn>0</mn></msubsup></mrow></semantics></math> and (<b>f</b>) <math display="inline"><semantics><mrow><msubsup><mover accent="true"><mi>χ</mi><mo>˜</mo></mover><mn>1</mn><mo>+</mo></msubsup><msubsup><mover accent="true"><mi>χ</mi><mo>˜</mo></mover><mn>3</mn><mn>0</mn></msubsup></mrow></semantics></math> from Isajet 7.88 [<a href="#B35-symmetry-15-01475" class="html-bibr">35</a>] for the model line introduced in the text.</p>
Full article ">Figure 4
<p>Distribution in <math display="inline"><semantics><mrow><msub><mi>m</mi><mi>T</mi></msub><mrow><mo>(</mo><msub><mi>τ</mi><mi>h</mi></msub><mo>,</mo><mrow><mfrac bevelled="true"><mi>E</mi><mi>T</mi></mfrac></mrow></mrow></mrow></semantics></math> from <math display="inline"><semantics><mrow><mi>p</mi><mi>p</mi><mo>→</mo><msup><mi>H</mi><mo>±</mo></msup><mrow><mo>(</mo><mo>→</mo><mi>τ</mi><mi>ν</mi><mo>)</mo></mrow><mo>+</mo><mi>t</mi><mo>+</mo><mi>X</mi></mrow></semantics></math> followed by the decay <math display="inline"><semantics><mrow><mi>τ</mi><mo>→</mo><mi>h</mi><mi>a</mi><mi>d</mi><mi>r</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>+</mo><mrow><mfrac bevelled="true"><mi>E</mi><mi>T</mi></mfrac></mrow></mrow></semantics></math>. We also show dominant SM backgrounds.</p>
Full article ">Figure 5
<p>Distribution in <math display="inline"><semantics><mrow><msub><mi>m</mi><mi>T</mi></msub><mrow><mo>(</mo><mo>ℓ</mo><mo>,</mo><mrow><mfrac bevelled="true"><mi>E</mi><mi>T</mi></mfrac></mrow><mo>)</mo></mrow></mrow></semantics></math> from <math display="inline"><semantics><mrow><mi>p</mi><mi>p</mi><mo>→</mo><msup><mi>H</mi><mo>±</mo></msup><mrow><mo>(</mo><mi>τ</mi><mi>ν</mi><mo>)</mo></mrow><mo>+</mo><mi>t</mi><mo>+</mo><mi>X</mi></mrow></semantics></math> followed by <math display="inline"><semantics><mrow><mi>τ</mi><mo>→</mo><mo>ℓ</mo><mo>+</mo><mrow><mfrac bevelled="true"><mi>E</mi><mi>T</mi></mfrac></mrow></mrow></semantics></math> decay. We also show dominant SM backgrounds.</p>
Full article ">Figure 6
<p>Distribution in <math display="inline"><semantics><mrow><msub><mi>m</mi><mi>T</mi></msub><mrow><mo>(</mo><msub><mi>τ</mi><mi>h</mi></msub><mo>,</mo><mrow><mfrac bevelled="true"><mi>E</mi><mi>T</mi></mfrac></mrow><mo>)</mo></mrow></mrow></semantics></math> from <math display="inline"><semantics><mrow><mi>p</mi><mi>p</mi><mo>→</mo><msup><mi>H</mi><mo>±</mo></msup><mi>t</mi><mo>+</mo><mi>X</mi></mrow></semantics></math> followed by <math display="inline"><semantics><mrow><msup><mi>H</mi><mo>±</mo></msup><mo>→</mo><msub><mi>τ</mi><mi>h</mi></msub><mo>+</mo><mrow><mfrac bevelled="true"><mi>E</mi><mi>T</mi></mfrac></mrow></mrow></semantics></math> decay and also <math display="inline"><semantics><mrow><mi>t</mi><mo>→</mo><mi>b</mi><mo>ℓ</mo><msub><mi>ν</mi><mo>ℓ</mo></msub></mrow></semantics></math> decay. We also show dominant SM backgrounds.</p>
Full article ">Figure 7
<p>In (<b>a</b>) (upper), we show the <math display="inline"><semantics><mrow><mn>5</mn><mi>σ</mi></mrow></semantics></math> discovery region of the <math display="inline"><semantics><msub><mi>m</mi><mi>A</mi></msub></semantics></math> vs. <math display="inline"><semantics><mrow><mo>tan</mo><mi>β</mi></mrow></semantics></math> plane for <math display="inline"><semantics><mrow><mi>p</mi><mi>p</mi><mo>→</mo><msup><mi>H</mi><mo>±</mo></msup><mi>t</mi><mo>+</mo><mi>X</mi></mrow></semantics></math> followed by <math display="inline"><semantics><mrow><mi>τ</mi><mo>→</mo><mo>ℓ</mo><mo>+</mo><mrow><mfrac bevelled="true"><mi>E</mi><mi>T</mi></mfrac></mrow></mrow></semantics></math> decay for HL-LHC with 3000 fb<math display="inline"><semantics><msup><mrow/><mrow><mo>−</mo><mn>1</mn></mrow></msup></semantics></math>. In (<b>b</b>) (lower), we plot the corresponding 95% CL exclusion region. The region above the dashed blue curve is excluded by ATLAS searches for <math display="inline"><semantics><mrow><mi>H</mi><mo>/</mo><mi>A</mi><mo>→</mo><mi>τ</mi><mi>τ</mi></mrow></semantics></math> events.</p>
Full article ">Figure 7 Cont.
<p>In (<b>a</b>) (upper), we show the <math display="inline"><semantics><mrow><mn>5</mn><mi>σ</mi></mrow></semantics></math> discovery region of the <math display="inline"><semantics><msub><mi>m</mi><mi>A</mi></msub></semantics></math> vs. <math display="inline"><semantics><mrow><mo>tan</mo><mi>β</mi></mrow></semantics></math> plane for <math display="inline"><semantics><mrow><mi>p</mi><mi>p</mi><mo>→</mo><msup><mi>H</mi><mo>±</mo></msup><mi>t</mi><mo>+</mo><mi>X</mi></mrow></semantics></math> followed by <math display="inline"><semantics><mrow><mi>τ</mi><mo>→</mo><mo>ℓ</mo><mo>+</mo><mrow><mfrac bevelled="true"><mi>E</mi><mi>T</mi></mfrac></mrow></mrow></semantics></math> decay for HL-LHC with 3000 fb<math display="inline"><semantics><msup><mrow/><mrow><mo>−</mo><mn>1</mn></mrow></msup></semantics></math>. In (<b>b</b>) (lower), we plot the corresponding 95% CL exclusion region. The region above the dashed blue curve is excluded by ATLAS searches for <math display="inline"><semantics><mrow><mi>H</mi><mo>/</mo><mi>A</mi><mo>→</mo><mi>τ</mi><mi>τ</mi></mrow></semantics></math> events.</p>
Full article ">Figure 8
<p>Distribution in <math display="inline"><semantics><mrow><mi>m</mi><mo>(</mo><mi>t</mi><mi>b</mi><mo>)</mo></mrow></semantics></math> from <math display="inline"><semantics><mrow><mi>p</mi><mi>p</mi><mo>→</mo><msup><mi>H</mi><mo>±</mo></msup><mi>t</mi><mo>+</mo><mi>X</mi></mrow></semantics></math> followed by <math display="inline"><semantics><mrow><msup><mi>H</mi><mo>±</mo></msup><mo>→</mo><mi>t</mi><mi>b</mi></mrow></semantics></math> decay. These events include a top-jet tagged by HEPTopTagger2. We also show dominant SM backgrounds.</p>
Full article ">Figure 9
<p>Distribution in <math display="inline"><semantics><mrow><mi>m</mi><mo>(</mo><mi>t</mi><mi>b</mi><mo>)</mo></mrow></semantics></math> from <math display="inline"><semantics><mrow><mi>p</mi><mi>p</mi><mo>→</mo><msup><mi>H</mi><mo>±</mo></msup><mi>t</mi><mo>+</mo><mi>X</mi></mrow></semantics></math> followed by <math display="inline"><semantics><mrow><msup><mi>H</mi><mo>±</mo></msup><mo>→</mo><mi>t</mi><mi>b</mi></mrow></semantics></math> decay, but no fat jet tagged as top by HEPTopTagger2. We also show dominant SM backgrounds.</p>
Full article ">Figure 10
<p>Distribution in <math display="inline"><semantics><mrow><mi>m</mi><mo>(</mo><mi>t</mi><mi>b</mi><mo>)</mo></mrow></semantics></math> from <math display="inline"><semantics><mrow><mi>p</mi><mi>p</mi><mo>→</mo><msup><mi>H</mi><mo>±</mo></msup><mi>t</mi><mo>+</mo><mi>X</mi></mrow></semantics></math> followed by <math display="inline"><semantics><mrow><msup><mi>H</mi><mo>±</mo></msup><mo>→</mo><mi>t</mi><mi>b</mi></mrow></semantics></math> decay, a fat jet tagged as a top-jet by HEPTopTagger2, and an isolated lepton from the decay of one of the top quarks. We also show dominant SM backgrounds.</p>
Full article ">Figure 11
<p>Distribution in <math display="inline"><semantics><mrow><mi>m</mi><mo>(</mo><mi>t</mi><mi>b</mi><mo>)</mo></mrow></semantics></math> from <math display="inline"><semantics><mrow><mi>p</mi><mi>p</mi><mo>→</mo><msup><mi>H</mi><mo>±</mo></msup><mi>t</mi><mo>+</mo><mi>X</mi></mrow></semantics></math> followed by <math display="inline"><semantics><mrow><msup><mi>H</mi><mo>±</mo></msup><mo>→</mo><mi>t</mi><mi>b</mi></mrow></semantics></math> decay. We also require that there is no fat jet tagged as a top-jet by HEPTopTagger2 but that there is an isolated lepton from the decay of one of the top quarks. We also show dominant SM backgrounds.</p>
Full article ">Figure 12
<p>In (<b>a</b>), we plot the <math display="inline"><semantics><mrow><mn>5</mn><mi>σ</mi></mrow></semantics></math> discovery region of the <math display="inline"><semantics><msub><mi>m</mi><mi>A</mi></msub></semantics></math> vs. <math display="inline"><semantics><mrow><mo>tan</mo><mi>β</mi></mrow></semantics></math> plane for <math display="inline"><semantics><mrow><mi>p</mi><mi>p</mi><mo>→</mo><msup><mi>H</mi><mo>±</mo></msup><mi>t</mi><mo>+</mo><mi>X</mi></mrow></semantics></math> followed by <math display="inline"><semantics><mrow><msup><mi>H</mi><mo>±</mo></msup><mo>→</mo><mi>t</mi><mi>b</mi></mrow></semantics></math> decay for HL-LHC with 3000 fb<math display="inline"><semantics><msup><mrow/><mrow><mo>−</mo><mn>1</mn></mrow></msup></semantics></math>. In (<b>b</b>), we plot the corresponding 95% CL exclusion region. The dashed blue line shows the boundary of the region excluded at the 95% confidence level in Ref. [<a href="#B44-symmetry-15-01475" class="html-bibr">44</a>].</p>
Full article ">Figure 13
<p>Plot of charged Higgs production cross-section times <math display="inline"><semantics><mrow><mi>B</mi><mi>F</mi><mo>(</mo><msup><mi>H</mi><mo>±</mo></msup><mo>→</mo><mi>S</mi><mi>U</mi><mi>S</mi><mi>Y</mi><mo>)</mo></mrow></semantics></math> in fb in the <math display="inline"><semantics><msub><mi>m</mi><mi>A</mi></msub></semantics></math> vs. <math display="inline"><semantics><mrow><mo>tan</mo><mi>β</mi></mrow></semantics></math> plane for the <math display="inline"><semantics><mrow><msubsup><mi>m</mi><mi>h</mi><mn>125</mn></msubsup><mrow><mo>(</mo><mi>nat</mi><mo>)</mo></mrow></mrow></semantics></math> scenario.</p>
Full article ">Figure 14
<p>Plot of <math display="inline"><semantics><mrow><mn>5</mn><mi>σ</mi></mrow></semantics></math> discovery projections for heavy SUSY Higgs boson searches at HL-LHC in the <math display="inline"><semantics><msub><mi>m</mi><mi>A</mi></msub></semantics></math> vs. <math display="inline"><semantics><mrow><mo>tan</mo><mi>β</mi></mrow></semantics></math> plane for the <math display="inline"><semantics><mrow><msubsup><mi>m</mi><mi>h</mi><mn>125</mn></msubsup><mrow><mo>(</mo><mi>nat</mi><mo>)</mo></mrow></mrow></semantics></math> scenario.</p>
Full article ">Figure 15
<p>Plot of 95% CL exclusion projections for heavy SUSY Higgs boson searches at HL-LHC in the <math display="inline"><semantics><msub><mi>m</mi><mi>A</mi></msub></semantics></math> vs. <math display="inline"><semantics><mrow><mo>tan</mo><mi>β</mi></mrow></semantics></math> plane for the <math display="inline"><semantics><mrow><msubsup><mi>m</mi><mi>h</mi><mn>125</mn></msubsup><mrow><mo>(</mo><mi>nat</mi><mo>)</mo></mrow></mrow></semantics></math> scenario.</p>
Full article ">
25 pages, 473 KiB  
Article
Octonion Internal Space Algebra for the Standard Model
by Ivan Todorov
Universe 2023, 9(5), 222; https://doi.org/10.3390/universe9050222 - 6 May 2023
Cited by 6 | Viewed by 1577
Abstract
This paper surveys recent progress in our search for an appropriate internal space algebra for the standard model (SM) of particle physics. After a brief review of the existing approaches, we start with the Clifford algebras involving operators of left multiplication by octonions. [...] Read more.
This paper surveys recent progress in our search for an appropriate internal space algebra for the standard model (SM) of particle physics. After a brief review of the existing approaches, we start with the Clifford algebras involving operators of left multiplication by octonions. A central role is played by a distinguished complex structure that implements the splitting of the octonions O=CC3, which reflect the lepton-quark symmetry. Such a complex structure on the 32-dimensional space S of C10 Majorana spinors is generated by the C6(C10) volume form, ω6=γ1γ6, and is left invariant by the Pati–Salam subgroup of Spin(10), GPS=Spin(4)×Spin(6)/Z2. While the Spin(10) invariant volume form ω10=γ1γ10 of C10 is known to split S on a complex basis into left and right chiral (semi)spinors, P=12(1iω6) is interpreted as the projector on the 16-dimensional particle subspace (which annihilates the antiparticles).The standard model gauge group appears as the subgroup of GPS that preserves the sterile neutrino (which is identified with the Fock vacuum). The Z2-graded internal space algebra A is then included in the projected tensor product APC10P=C4C60. The Higgs field appears as the scalar term of a superconnection, an element of the odd part C41 of the first factor. The fact that the projection of C10 only involves the even part C60 of the second factor guarantees that the color symmetry remains unbroken. As an application, we express the ratio mHmW of the Higgs to the W boson masses in terms of the cosine of the theoretical Weinberg angle. Full article
(This article belongs to the Section Mathematical Physics)
21 pages, 2683 KiB  
Review
A Concise Review on Some Higgs-Related New Physics Models in Light of Current Experiments
by Lei Wang, Jin Min Yang, Yang Zhang, Pengxuan Zhu and Rui Zhu
Universe 2023, 9(4), 178; https://doi.org/10.3390/universe9040178 - 4 Apr 2023
Cited by 9 | Viewed by 2228
Abstract
The Higgs boson may serve as a portal to new physics beyond the standard model (BSM), which is implied by the theoretical naturalness or experimental anomalies. This review aims to briefly survey some typical Higgs-related BSM models. First, for the theories to solve [...] Read more.
The Higgs boson may serve as a portal to new physics beyond the standard model (BSM), which is implied by the theoretical naturalness or experimental anomalies. This review aims to briefly survey some typical Higgs-related BSM models. First, for the theories to solve the hierarchy problem, the two exemplary theories, the low energy supersymmetry (focusing on the minimal supersymmetric model) and the little Higgs theory, are discussed. For the phenomenological models without addressing the hierarchy problem, we choose the two-Higgs-doublet models (2HDMs) to emphatically elucidate their phenomenological power in explaining current measurements of muon g2, the W-boson mass and the dark matter (DM) data. For the singlet extensions, which are motivated by the cosmic phase transition and the DM issue, we illustrate the singlet-extended standard model (xSM) and the singlet-extended 2HDM (2HDM+S), emphasizing the vacuum stability. In the decade since the discovery of the Higgs boson, these theories have remained the typical candidates of new physics, which will be intensively studied in future theoretical and experimental research. Full article
Show Figures

Figure 1

Figure 1
<p>A sketch map showing that the Higgs sector may serve as a portal to BSM physics implied by the naturalness, the experimental anomalies from the muon <math display="inline"><semantics> <mrow> <mi>g</mi> <mo>−</mo> <mn>2</mn> </mrow> </semantics></math> or <span class="html-italic">W</span>-mass, the cosmic phase transition and DM.</p>
Full article ">Figure 2
<p>The scatter plots showing the mass of the SM-like Higgs boson versus the stop mass in the MSSM. The SM upper and lower bounds are from the requirement of vacuum stability and non-triviality for the UV cut-off scale around TeV [<a href="#B49-universe-09-00178" class="html-bibr">49</a>].</p>
Full article ">Figure 3
<p>The scatter plots jointly explaining at <math display="inline"><semantics> <mrow> <mn>2</mn> <mi>σ</mi> </mrow> </semantics></math> level the muon <math display="inline"><semantics> <mrow> <mi>g</mi> <mo>−</mo> <mn>2</mn> </mrow> </semantics></math> reported by the FNAL and the <span class="html-italic">W</span>-boson mass measured by the CDF II as well as providing the correct DM relic density under direct detection limits. This figure is taken from our previous work [<a href="#B27-universe-09-00178" class="html-bibr">27</a>].</p>
Full article ">Figure 4
<p>The scatter plots explaining at <math display="inline"><semantics> <mrow> <mn>2</mn> <mi>σ</mi> </mrow> </semantics></math> level the muon <math display="inline"><semantics> <mrow> <mi>g</mi> <mo>−</mo> <mn>2</mn> </mrow> </semantics></math> reported by the FNAL, with the higgsino (<math display="inline"><semantics> <mi>μ</mi> </semantics></math> in the range of 100–400 GeV) as the lightest super particle satisfying the <math display="inline"><semantics> <mrow> <mn>2</mn> <mi>σ</mi> </mrow> </semantics></math> upper bound of the DM relic density and the direct detection limits. This figure is taken from our previous work [<a href="#B79-universe-09-00178" class="html-bibr">79</a>].</p>
Full article ">Figure 5
<p>The MSSM parameter space explaining both anomalies of the muon <math display="inline"><semantics> <mrow> <mi>g</mi> <mo>−</mo> <mn>2</mn> </mrow> </semantics></math> reported by the FNAL and the electron <math display="inline"><semantics> <mrow> <mi>g</mi> <mo>−</mo> <mn>2</mn> </mrow> </semantics></math> from the Berkeley experiment [<a href="#B89-universe-09-00178" class="html-bibr">89</a>]. This figure is taken from our previous work [<a href="#B85-universe-09-00178" class="html-bibr">85</a>].</p>
Full article ">Figure 6
<p>The LHT parameter space allowed by the Planck DM relic density and the CMS Higgs data at the <math display="inline"><semantics> <mrow> <mn>2</mn> <mi>σ</mi> </mrow> </semantics></math> level, projected on the plane of the spin-independent scattering cross-section off the nucleon versus the heavy photon mass. The best point is with minimal <math display="inline"><semantics> <msup> <mi>χ</mi> <mn>2</mn> </msup> </semantics></math> value for the CMS Higgs data and with the relic density closest to the measured central value. This figure is taken from our previous work [<a href="#B143-universe-09-00178" class="html-bibr">143</a>].</p>
Full article ">Figure 7
<p>Scatter plots of the parameter space of the 2HDM with <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>−</mo> <mi>τ</mi> </mrow> </semantics></math> LFV interactions: the dark squares (light bullets) satisfy the data of the muon <math display="inline"><semantics> <mrow> <mi>g</mi> <mo>−</mo> <mn>2</mn> </mrow> </semantics></math> and the <span class="html-italic">W</span>-boson mass at the <math display="inline"><semantics> <mrow> <mn>2</mn> <mi>σ</mi> </mrow> </semantics></math> level with (without) the constraints of <math display="inline"><semantics> <mi>τ</mi> </semantics></math>-decays. This figure is taken from our previous work [<a href="#B30-universe-09-00178" class="html-bibr">30</a>].</p>
Full article ">Figure 8
<p>The likely shapes of the Higgs potential at the early hot universe and the cold universe.</p>
Full article ">Figure 9
<p>An illustrative diagram of effective potential developing as the temperature is dropping for the xSM, using a benchmark point taken from our previous work [<a href="#B211-universe-09-00178" class="html-bibr">211</a>].</p>
Full article ">Figure 10
<p>The xSM parameter space excluded by checking the thermal history of the universe, taken from our previous work [<a href="#B211-universe-09-00178" class="html-bibr">211</a>].</p>
Full article ">Figure 11
<p>The dilution factor <span class="html-italic">d</span> versus the mass parameter <math display="inline"><semantics> <msub> <mi>m</mi> <mn>12</mn> </msub> </semantics></math> for the 2HDM+S, taken from our previous work [<a href="#B217-universe-09-00178" class="html-bibr">217</a>]. The DM density is diluted by the electroweak FOPT to <math display="inline"><semantics> <mrow> <mn>1</mn> <mo>/</mo> <mi>d</mi> </mrow> </semantics></math>.</p>
Full article ">
30 pages, 493 KiB  
Article
Dark Energy Is the Cosmological Quantum Vacuum Energy of Light Particles—The Axion and the Lightest Neutrino
by Héctor J. de Vega and Norma G. Sanchez
Universe 2023, 9(4), 167; https://doi.org/10.3390/universe9040167 - 30 Mar 2023
Cited by 3 | Viewed by 2246
Abstract
We uncover the general mechanism and the nature of today’s dark energy (DE). This is only based on well-known quantum physics and cosmology. We show that the observed DE today originates from the cosmological quantum vacuum of light particles, which provides a continuous [...] Read more.
We uncover the general mechanism and the nature of today’s dark energy (DE). This is only based on well-known quantum physics and cosmology. We show that the observed DE today originates from the cosmological quantum vacuum of light particles, which provides a continuous energy distribution able to reproduce the data. Bosons give positive contributions to the DE, while fermions yield negative contributions. As usual in field theory, ultraviolet divergences are subtracted from the physical quantities. The subtractions respect the symmetries of the theory, and we normalize the physical quantities to be zero for the Minkowski vacuum. The resulting finite contributions to the energy density and the pressure from the quantum vacuum grow as loga(t), where a(t) is the scale factor, while the particle contributions dilute as 1/a3(t), as it must be for massive particles. We find the explicit dark energy equation of state of today to be P=w(z)H: it turns to be slightly w(z)<1 with w(z) asymptotically reaching the value 1 from below. A scalar particle can produce the observed dark energy through its quantum cosmological vacuum provided that (i) its mass is of the order of 103 eV = 1 meV, (ii) it is very weakly coupled, and (iii) it is stable on the time scale of the age of the universe. The axion vacuum thus appears as a natural candidate. The neutrino vacuum (especially the lightest mass eigenstate) can give negative contributions to the dark energy. We find that w(z=0) is slightly below 1 by an amount ranging from (1.5×103) to (8×103) and we predict the axion mass to be in the range between 4 and 5 meV. We find that the universe will expand in the future faster than the de Sitter universe as an exponential in the square of the cosmic time. Dark energy today arises from the quantum vacuum of light particles in FRW cosmological space-time in an analogous way to the Casimir vacuum effect of quantum fields in Minkowski space-time with non-trivial boundary conditions. Full article
(This article belongs to the Special Issue Quantum Physics including Gravity: Highlights and Novelties)
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Figure 1

Figure 1
<p>The equation of state <span class="html-italic">w(z)</span> vs. the redshift <span class="html-italic">z</span> for the three cases explicitly calculated in this paper: (i) [full line] No neutrino contribution to the dark energy and the scalar mass <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>3.96</mn> </mrow> </semantics></math> meV. (ii) [broken line] A Majorana neutrino with mass <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>3.2</mn> </mrow> </semantics></math> meV and the scalar mass <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>4.35</mn> </mrow> </semantics></math> meV. (iii) [dotted line] A Dirac neutrino with mass <math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>3.2</mn> </mrow> </semantics></math> meV and the scalar mass <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>4.66</mn> </mrow> </semantics></math> meV. (See the discussion in <a href="#sec9-universe-09-00167" class="html-sec">Section 9</a>.) In all three cases, <math display="inline"><semantics> <mrow> <mi>w</mi> <mo>&lt;</mo> <mo>−</mo> <mn>1</mn> </mrow> </semantics></math> by less than <math display="inline"><semantics> <mrow> <mn>1</mn> <mo>%</mo> </mrow> </semantics></math>.</p>
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22 pages, 1233 KiB  
Article
Detecting Heavy Neutral SUSY Higgs Bosons Decaying to Sparticles at the High-Luminosity LHC
by Howard Baer, Vernon Barger, Xerxes Tata and Kairui Zhang
Symmetry 2023, 15(2), 548; https://doi.org/10.3390/sym15020548 - 18 Feb 2023
Cited by 5 | Viewed by 1924
Abstract
In supersymmetry (SUSY) models with low electroweak naturalness (natSUSY), which have been suggested to be the most likely version of SUSY to emerge from the string landscape, higgsinos are expected at the few hundred GeV scale, whilst electroweak gauginos inhabit the TeV scale. [...] Read more.
In supersymmetry (SUSY) models with low electroweak naturalness (natSUSY), which have been suggested to be the most likely version of SUSY to emerge from the string landscape, higgsinos are expected at the few hundred GeV scale, whilst electroweak gauginos inhabit the TeV scale. For TeV-scale heavy neutral SUSY Higgs bosons H and A, as currently required by LHC searches, the dominant decay modes of H,A are gaugino plus higgsino provided these decays are kinematically open. The light higgsinos decay to soft particles, so are largely invisible, whilst the gauginos decay to W, Z or h plus missing transverse energy (ET). Thus, we examine the viability of H,AW+ET, Z+ET and h+ET signatures at the high luminosity LHC (HL-LHC) in light of large standard model (SM) backgrounds from (mainly) tt¯, VV and Vh production (where V=W,Z). We also examine whether these signal channels can be enhanced over backgrounds by requiring the presence of an additional soft lepton from the decays of the light higgsinos. We find significant regions in the vicinity of mA12 TeV of the mA vs. tanβ plane, which can be probed at the high luminosity LHC, using these dominant signatures by HL-LHC at 5σ and at the 95% confidence level (CL). Full article
(This article belongs to the Special Issue Supersymmetry with Higgs Bosons Research)
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Figure 1
<p>The total cross section for (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>p</mi> <mi>p</mi> <mo>→</mo> <mi>H</mi> </mrow> </semantics></math> and (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>p</mi> <mi>p</mi> <mo>→</mo> <mi>A</mi> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <msqrt> <mi>s</mi> </msqrt> <mo>=</mo> <mn>14</mn> </mrow> </semantics></math> TeV using the SusHi code [<a href="#B60-symmetry-15-00548" class="html-bibr">60</a>].</p>
Full article ">Figure 1 Cont.
<p>The total cross section for (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>p</mi> <mi>p</mi> <mo>→</mo> <mi>H</mi> </mrow> </semantics></math> and (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>p</mi> <mi>p</mi> <mo>→</mo> <mi>A</mi> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <msqrt> <mi>s</mi> </msqrt> <mo>=</mo> <mn>14</mn> </mrow> </semantics></math> TeV using the SusHi code [<a href="#B60-symmetry-15-00548" class="html-bibr">60</a>].</p>
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<p>Branching fractions for <span class="html-italic">H</span> to (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>b</mi> <mover accent="true"> <mi>b</mi> <mo>¯</mo> </mover> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>τ</mi> <mover accent="true"> <mi>τ</mi> <mo>¯</mo> </mover> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <msubsup> <mover accent="true"> <mi>χ</mi> <mo>˜</mo> </mover> <mn>1</mn> <mo>±</mo> </msubsup> <msubsup> <mover accent="true"> <mi>χ</mi> <mo>˜</mo> </mover> <mn>2</mn> <mo>∓</mo> </msubsup> </mrow> </semantics></math>, (<b>d</b>) <math display="inline"><semantics> <mrow> <msubsup> <mover accent="true"> <mi>χ</mi> <mo>˜</mo> </mover> <mn>1</mn> <mn>0</mn> </msubsup> <msubsup> <mover accent="true"> <mi>χ</mi> <mo>˜</mo> </mover> <mn>4</mn> <mn>0</mn> </msubsup> </mrow> </semantics></math>, (<b>e</b>) <math display="inline"><semantics> <mrow> <msubsup> <mover accent="true"> <mi>χ</mi> <mo>˜</mo> </mover> <mn>2</mn> <mn>0</mn> </msubsup> <msubsup> <mover accent="true"> <mi>χ</mi> <mo>˜</mo> </mover> <mn>4</mn> <mn>0</mn> </msubsup> </mrow> </semantics></math> and (<b>f</b>) <math display="inline"><semantics> <mrow> <msubsup> <mover accent="true"> <mi>χ</mi> <mo>˜</mo> </mover> <mn>1</mn> <mn>0</mn> </msubsup> <msubsup> <mover accent="true"> <mi>χ</mi> <mo>˜</mo> </mover> <mn>3</mn> <mn>0</mn> </msubsup> </mrow> </semantics></math> from Isajet 7.88 [<a href="#B38-symmetry-15-00548" class="html-bibr">38</a>].</p>
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<p>Branching fractions for <span class="html-italic">A</span> to (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>b</mi> <mover accent="true"> <mi>b</mi> <mo>¯</mo> </mover> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>τ</mi> <mover accent="true"> <mi>τ</mi> <mo>¯</mo> </mover> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <msubsup> <mover accent="true"> <mi>χ</mi> <mo>˜</mo> </mover> <mn>1</mn> <mo>±</mo> </msubsup> <msubsup> <mover accent="true"> <mi>χ</mi> <mo>˜</mo> </mover> <mn>2</mn> <mo>∓</mo> </msubsup> </mrow> </semantics></math>, (<b>d</b>) <math display="inline"><semantics> <mrow> <msubsup> <mover accent="true"> <mi>χ</mi> <mo>˜</mo> </mover> <mn>1</mn> <mn>0</mn> </msubsup> <msubsup> <mover accent="true"> <mi>χ</mi> <mo>˜</mo> </mover> <mn>4</mn> <mn>0</mn> </msubsup> </mrow> </semantics></math>, (<b>e</b>) <math display="inline"><semantics> <mrow> <msubsup> <mover accent="true"> <mi>χ</mi> <mo>˜</mo> </mover> <mn>2</mn> <mn>0</mn> </msubsup> <msubsup> <mover accent="true"> <mi>χ</mi> <mo>˜</mo> </mover> <mn>4</mn> <mn>0</mn> </msubsup> </mrow> </semantics></math> and (<b>f</b>) <math display="inline"><semantics> <mrow> <msubsup> <mover accent="true"> <mi>χ</mi> <mo>˜</mo> </mover> <mn>1</mn> <mn>0</mn> </msubsup> <msubsup> <mover accent="true"> <mi>χ</mi> <mo>˜</mo> </mover> <mn>3</mn> <mn>0</mn> </msubsup> </mrow> </semantics></math> from Isajet 7.88 [<a href="#B38-symmetry-15-00548" class="html-bibr">38</a>].</p>
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<p>Distribution in <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mi>T</mi> </msub> <mrow> <mo>(</mo> <mo>ℓ</mo> <mo>,</mo> <mrow> <mfrac bevelled="true"> <mi>E</mi> <mi>T</mi> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>p</mi> <mi>p</mi> <mo>→</mo> <mi>H</mi> <mo>,</mo> <mi>A</mi> <mo>→</mo> <mi>W</mi> <mo>+</mo> <mrow> <mfrac bevelled="true"> <mi>E</mi> <mi>T</mi> </mfrac> </mrow> </mrow> </semantics></math> events. We show two signal distributions (dashed) along with dominant SM backgrounds (not stacked).</p>
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<p>Distribution in <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mrow> <mi>c</mi> <mi>T</mi> </mrow> </msub> <mrow> <mo>(</mo> <mo>ℓ</mo> <mover accent="true"> <mo>ℓ</mo> <mo>¯</mo> </mover> <mo>,</mo> <mrow> <mfrac bevelled="true"> <mi>E</mi> <mi>T</mi> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>p</mi> <mi>p</mi> <mo>→</mo> <mi>H</mi> <mo>,</mo> <mi>A</mi> <mo>→</mo> <mi>Z</mi> <mo>+</mo> <mrow> <mfrac bevelled="true"> <mi>E</mi> <mi>T</mi> </mfrac> </mrow> </mrow> </semantics></math> with <math display="inline"><semantics> <mrow> <mi>Z</mi> <mo>→</mo> <msup> <mo>ℓ</mo> <mo>+</mo> </msup> <msup> <mo>ℓ</mo> <mo>−</mo> </msup> </mrow> </semantics></math> decay events at <math display="inline"><semantics> <mrow> <msqrt> <mi>s</mi> </msqrt> <mo>=</mo> <mn>14</mn> </mrow> </semantics></math> TeV. We show two signal distributions (dashed) along with dominant SM backgrounds (not stacked).</p>
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<p>Distribution in <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mrow> <mi>c</mi> <mi>T</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>b</mi> <mover accent="true"> <mi>b</mi> <mo>¯</mo> </mover> <mo>,</mo> <mrow> <mfrac bevelled="true"> <mi>E</mi> <mi>T</mi> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>p</mi> <mi>p</mi> <mo>→</mo> <mi>H</mi> <mo>,</mo> <mi>A</mi> <mo>→</mo> <mi>h</mi> <mo>+</mo> <mrow> <mfrac bevelled="true"> <mi>E</mi> <mi>T</mi> </mfrac> </mrow> </mrow> </semantics></math> with <math display="inline"><semantics> <mrow> <mi>h</mi> <mo>→</mo> <mi>b</mi> <mover accent="true"> <mi>b</mi> <mo>¯</mo> </mover> </mrow> </semantics></math> decay events at <math display="inline"><semantics> <mrow> <msqrt> <mi>s</mi> </msqrt> <mo>=</mo> <mn>14</mn> </mrow> </semantics></math> TeV. We show two signal distributions (dashed) along with dominant SM backgrounds (not stacked).</p>
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<p>Distribution in <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mrow> <mi>c</mi> <mi>T</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>L</mi> <mi>R</mi> <mi>j</mi> <mo>,</mo> <mrow> <mfrac bevelled="true"> <mi>E</mi> <mi>T</mi> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>p</mi> <mi>p</mi> <mo>→</mo> <mi>H</mi> <mo>,</mo> <mi>A</mi> <mo>→</mo> <mi>L</mi> <mi>R</mi> <mi>j</mi> <mo>+</mo> <mo>ℓ</mo> <mo>+</mo> <mrow> <mfrac bevelled="true"> <mi>E</mi> <mi>T</mi> </mfrac> </mrow> </mrow> </semantics></math> events at <math display="inline"><semantics> <mrow> <msqrt> <mi>s</mi> </msqrt> <mo>=</mo> <mn>14</mn> </mrow> </semantics></math> TeV. We show two signal distributions (dashed) along with dominant SM backgrounds (not stacked).</p>
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<p>Distribution in <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mrow> <mi>c</mi> <mi>T</mi> </mrow> </msub> <mrow> <mo>(</mo> <mn>3</mn> <mo>ℓ</mo> <mo>,</mo> <mrow> <mfrac bevelled="true"> <mi>E</mi> <mi>T</mi> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>p</mi> <mi>p</mi> <mo>→</mo> <mi>H</mi> <mo>,</mo> <mi>A</mi> <mo>→</mo> <mn>3</mn> <mo>ℓ</mo> <mo>+</mo> <mrow> <mfrac bevelled="true"> <mi>E</mi> <mi>T</mi> </mfrac> </mrow> </mrow> </semantics></math> events at <math display="inline"><semantics> <mrow> <msqrt> <mi>s</mi> </msqrt> <mo>=</mo> <mn>14</mn> </mrow> </semantics></math> TeV. We show two signal distributions (dashed) along with dominant SM backgrounds (not stacked).</p>
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<p>Distribution in <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mrow> <mi>c</mi> <mi>T</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>b</mi> <mi>b</mi> <mo>ℓ</mo> <mo>,</mo> <mrow> <mfrac bevelled="true"> <mi>E</mi> <mi>T</mi> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>p</mi> <mi>p</mi> <mo>→</mo> <mi>H</mi> <mo>,</mo> <mi>A</mi> <mo>→</mo> <mi>b</mi> <mi>b</mi> <mo>ℓ</mo> <mo>+</mo> <mrow> <mfrac bevelled="true"> <mi>E</mi> <mi>T</mi> </mfrac> </mrow> </mrow> </semantics></math> events at <math display="inline"><semantics> <mrow> <msqrt> <mi>s</mi> </msqrt> <mo>=</mo> <mn>14</mn> </mrow> </semantics></math> TeV. We show two signal distributions (dashed) along with dominant SM backgrounds (not stacked).</p>
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<p>In frame (<b>a</b>), we plot the HL-LHC <math display="inline"><semantics> <mrow> <mn>5</mn> <mi>σ</mi> </mrow> </semantics></math> discovery contours for <math display="inline"><semantics> <mrow> <mi>H</mi> <mo>,</mo> <mi>A</mi> <mo>→</mo> <mi>b</mi> <mi>b</mi> <mo>+</mo> <mrow> <mfrac bevelled="true"> <mi>E</mi> <mi>T</mi> </mfrac> </mrow> </mrow> </semantics></math> events with <math display="inline"><semantics> <mrow> <msqrt> <mi>s</mi> </msqrt> <mo>=</mo> <mn>14</mn> </mrow> </semantics></math> TeV and 3000 fb<sup>−1</sup>. In frame (<b>b</b>), we plot the corresponding 95% CL exclusion limit. In frame (<b>c</b>), we plot the <math display="inline"><semantics> <mrow> <mn>5</mn> <mi>σ</mi> </mrow> </semantics></math> discovery reach via the combined <math display="inline"><semantics> <mrow> <mi>b</mi> <mi>b</mi> <mo>+</mo> <mrow> <mfrac bevelled="true"> <mi>E</mi> <mi>T</mi> </mfrac> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>ℓ</mo> <mover accent="true"> <mo>ℓ</mo> <mo>¯</mo> </mover> <mo>+</mo> <mrow> <mfrac bevelled="true"> <mi>E</mi> <mi>T</mi> </mfrac> </mrow> </mrow> </semantics></math> channels. In (<b>d</b>), we plot the corresponding 95% CL exclusion. In (<b>e</b>), we show the <math display="inline"><semantics> <mrow> <mn>5</mn> <mi>σ</mi> </mrow> </semantics></math> contour combining all six discovery channels, while in (<b>f</b>) we plot the 95% CL exlusion limits from all six channels combined. The region above the dashed contour in the frames in the right-hand column is excluded at the 95%CL by ATLAS, although in the <math display="inline"><semantics> <msubsup> <mi>m</mi> <mi>h</mi> <mn>125</mn> </msubsup> </semantics></math> scenario, the <span class="html-italic">H</span> and <span class="html-italic">A</span> essentially decay only via SM modes.</p>
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31 pages, 3206 KiB  
Article
Recent Cross-Section Measurements of Top-Quark Pair Production in Association with Gauge Bosons
by Joshuha Thomas-Wilsker
Universe 2023, 9(1), 39; https://doi.org/10.3390/universe9010039 - 6 Jan 2023
Viewed by 1734
Abstract
This article reviews recent cross-section measurements of tt¯ production in association with a photon, W or Z boson at the Large Hadron Collider (LHC). All measurements reviewed use proton–proton (pp) datasets collected by the ATLAS and CMS experiments between 2016 and [...] Read more.
This article reviews recent cross-section measurements of tt¯ production in association with a photon, W or Z boson at the Large Hadron Collider (LHC). All measurements reviewed use proton–proton (pp) datasets collected by the ATLAS and CMS experiments between 2016 and 2018 from collisions at a centre-of-mass energy of 13 TeV during the LHC Run 2. Differential and inclusive cross-section measurements are discussed along with the constraints on the effective field theory operators accessible through each process. Finally, we discuss the potential for measurements of these processes at future colliders. Full article
(This article belongs to the Special Issue Top Quark at the New Physics Frontier)
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Figure 1

Figure 1
<p>Leading-order Feynman diagram for gluon-gluon top-pair production (<math display="inline"><semantics> <mrow> <mi>gg</mi> <mo>→</mo> <mi mathvariant="normal">t</mi> <mover accent="true"> <mi mathvariant="normal">t</mi> <mo>¯</mo> </mover> </mrow> </semantics></math>) in association with a boson (X).</p>
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<p>ATLAS control regions [<a href="#B11-universe-09-00039" class="html-bibr">11</a>].</p>
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<p>ATLAS signal regions [<a href="#B11-universe-09-00039" class="html-bibr">11</a>].</p>
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<p>CMS signal regions [<a href="#B10-universe-09-00039" class="html-bibr">10</a>].</p>
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<p>Comparison of normalised unfolded particle- and parton-level distribution of the transverse momentum of the Z boson in observed data from ATLAS [<a href="#B11-universe-09-00039" class="html-bibr">11</a>] with Theoretical expectations obtained from different generators: Sherpa 2.2.1 [<a href="#B17-universe-09-00039" class="html-bibr">17</a>] generator at NLO QCD accuracy using either multi-leg or inclusive setups and MG5_aMC@NLO [<a href="#B18-universe-09-00039" class="html-bibr">18</a>] at NLO QCD accuracy interfaced with either the Pythia [<a href="#B19-universe-09-00039" class="html-bibr">19</a>] or Herwig [<a href="#B20-universe-09-00039" class="html-bibr">20</a>] parton shower models.</p>
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<p>Comparison of normalised unfolded parton−level distribution of the transverse momentum of the Z boson in observed data from CMS [<a href="#B10-universe-09-00039" class="html-bibr">10</a>] with Theoretical expectations obtained from different generators: Sherpa 2.2.1 generator at NLO QCD accuracy using either multi-leg or inclusive setups and MG5_aMC@NLO at NLO QCD accuracy interfaced with either the Pythia or Herwig parton shower models.</p>
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<p>Two−dimensional scan of <math display="inline"><semantics> <msub> <mi>c</mi> <mrow> <mi>t</mi> <mi>Z</mi> </mrow> </msub> </semantics></math> with <math display="inline"><semantics> <msubsup> <mi>c</mi> <mrow> <mi>t</mi> <mi>Z</mi> </mrow> <mrow> <mo>[</mo> <mi>I</mi> <mo>]</mo> </mrow> </msubsup> </semantics></math> and <math display="inline"><semantics> <msub> <mi>c</mi> <mrow> <mi>Φ</mi> <mi>t</mi> </mrow> </msub> </semantics></math> with <math display="inline"><semantics> <msub> <mi>c</mi> <mrow> <mover accent="true"> <mi>Φ</mi> <mo>¯</mo> </mover> <mi>Q</mi> </mrow> </msub> </semantics></math> Wilson coefficients [<a href="#B10-universe-09-00039" class="html-bibr">10</a>].</p>
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<p>Post−fit distributions of the EFT neural networks in the <math display="inline"><semantics> <mrow> <mi mathvariant="normal">t</mi> <mover accent="true"> <mi mathvariant="normal">t</mi> <mo>¯</mo> </mover> <mi mathvariant="normal">Z</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mi>tZq</mi> </semantics></math> signal regions from [<a href="#B22-universe-09-00039" class="html-bibr">22</a>]. The top row shows the 5D discriminant while the bottom row shows the discriminant trained to target the effects of the <math display="inline"><semantics> <msub> <mi>c</mi> <mrow> <mi>t</mi> <mi>Z</mi> </mrow> </msub> </semantics></math> operator. The middle ratio plot demonstrates the data/MC agreement, while the lower ratio demonstrates the increasing impact on the yields in each bin from larger WC values.</p>
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<p>95% CL confidence intervals for the 1D and 5D fits in [<a href="#B22-universe-09-00039" class="html-bibr">22</a>].</p>
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<p>95% CL confidence intervals for the 2D fits in [<a href="#B22-universe-09-00039" class="html-bibr">22</a>].</p>
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<p>Leading-order (top left) and next-to-leading-order (top right and bottom) Feynman diagram for the <math display="inline"><semantics> <mrow> <mi mathvariant="normal">t</mi> <mover accent="true"> <mi mathvariant="normal">t</mi> <mo>¯</mo> </mover> <mi mathvariant="normal">W</mi> </mrow> </semantics></math> process. The last diagram is an example of the sub-leading electroweak corrections.</p>
Full article ">Figure 12
<p>Measurements of the inclusive <math display="inline"><semantics> <mrow> <mi mathvariant="normal">t</mi> <mover accent="true"> <mi mathvariant="normal">t</mi> <mo>¯</mo> </mover> <mi mathvariant="normal">W</mi> </mrow> </semantics></math> cross−section [<a href="#B41-universe-09-00039" class="html-bibr">41</a>]. The combined result is shown with a breakdown of the measurement obtained in the different dilepton and tri−lepton channels, as well as the measurement obtained in the different lepton flavour categories of the dilepton channel. The black inner error bar indicates the statistical uncertainty, while the green outer error bar represents the full systematic plus statistical uncertainty. The measurements are compared with two SM predictions. The prediction shown by the black line is from Ref. [<a href="#B31-universe-09-00039" class="html-bibr">31</a>] while the prediction represented by the red line comes from Ref. [<a href="#B29-universe-09-00039" class="html-bibr">29</a>] and includes FxFx predictions. The central lines of these two vertical lines represent the nominal prediction, while the band represents the combined uncertainty from the scale and PDF theory variations in the calculation.</p>
Full article ">Figure 13
<p>Contours showing the <math display="inline"><semantics> <mrow> <mn>68</mn> <mo>%</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mn>95</mn> <mo>%</mo> </mrow> </semantics></math> CL intervals from the likelihood fit in which the <math display="inline"><semantics> <mrow> <mi mathvariant="normal">t</mi> <mover accent="true"> <mi mathvariant="normal">t</mi> <mo>¯</mo> </mover> <msup> <mi mathvariant="normal">W</mi> <mo>+</mo> </msup> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi mathvariant="normal">t</mi> <mover accent="true"> <mi mathvariant="normal">t</mi> <mo>¯</mo> </mover> <msup> <mi mathvariant="normal">W</mi> <mo>−</mo> </msup> </mrow> </semantics></math> processes are measured simultaneously as independent parameters [<a href="#B41-universe-09-00039" class="html-bibr">41</a>]. The best fit value of the fit is indicated by the black cross, with the theory prediction from Ref. [<a href="#B31-universe-09-00039" class="html-bibr">31</a>] shown by the red cross. The theory prediction included is without the FxFx jet merging.</p>
Full article ">Figure 14
<p>Negative log−likelihood scan for values of the ratio of <math display="inline"><semantics> <mrow> <mi mathvariant="normal">t</mi> <mover accent="true"> <mi mathvariant="normal">t</mi> <mo>¯</mo> </mover> <msup> <mi mathvariant="normal">W</mi> <mo>+</mo> </msup> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi mathvariant="normal">t</mi> <mover accent="true"> <mi mathvariant="normal">t</mi> <mo>¯</mo> </mover> <msup> <mi mathvariant="normal">W</mi> <mo>−</mo> </msup> </mrow> </semantics></math> cross-sections. The best fit value is found at the minimum of the curve, while the dashed horizontal lines represent the CL limits [<a href="#B41-universe-09-00039" class="html-bibr">41</a>]. The red line and hatched band represent the central value and total uncertainty of the theory prediction without the FxFx merging in Ref. [<a href="#B31-universe-09-00039" class="html-bibr">31</a>].</p>
Full article ">Figure 15
<p>Leading-order Feynman diagram for the <math display="inline"><semantics> <mrow> <mi mathvariant="normal">t</mi> <mover accent="true"> <mi mathvariant="normal">t</mi> <mo>¯</mo> </mover> <mi>γ</mi> </mrow> </semantics></math> process. Each diagram demonstrates a different production mechanism for the high energy photon in the process.</p>
Full article ">Figure 16
<p>Leading-order Feynman diagram for the <math display="inline"><semantics> <mrow> <mi>tW</mi> <mi>γ</mi> </mrow> </semantics></math> process. Red gauge boson lines represent W bosons while blue gauge boson lines represent photons [<a href="#B49-universe-09-00039" class="html-bibr">49</a>].</p>
Full article ">Figure 17
<p>Inclusive <math display="inline"><semantics> <mrow> <mi mathvariant="normal">t</mi> <mover accent="true"> <mi mathvariant="normal">t</mi> <mo>¯</mo> </mover> <mi>γ</mi> </mrow> </semantics></math> production cross-section measurements by ATLAS in leptonic channels [<a href="#B46-universe-09-00039" class="html-bibr">46</a>]. The NLO prediction from theory is shown in the dashed vertical line, with the uncertainty shown in the beige band. The measured values in data are represented by the black points, where the associated total and statistical uncertainties are shown in the red and blue lines, respectively. Results in each of the different lepton flavour channels are also shown.</p>
Full article ">Figure 18
<p>Inclusive <math display="inline"><semantics> <mrow> <mi mathvariant="normal">t</mi> <mover accent="true"> <mi mathvariant="normal">t</mi> <mo>¯</mo> </mover> <mi>γ</mi> </mrow> </semantics></math> production cross−section measurements by CMS in the single−lepton channel [<a href="#B47-universe-09-00039" class="html-bibr">47</a>]. Results are also shown for the individual lepton flavour channels.</p>
Full article ">Figure 19
<p>Inclusive <math display="inline"><semantics> <mrow> <mi mathvariant="normal">t</mi> <mover accent="true"> <mi mathvariant="normal">t</mi> <mo>¯</mo> </mover> <mi>γ</mi> </mrow> </semantics></math> production cross-section measurements by CMS in the dilepton channel [<a href="#B48-universe-09-00039" class="html-bibr">48</a>]. Results are also shown for both the combined measurement and the breakdown for the individual dilepton channels.</p>
Full article ">Figure 20
<p>Differential <math display="inline"><semantics> <mrow> <mi mathvariant="normal">t</mi> <mover accent="true"> <mi mathvariant="normal">t</mi> <mo>¯</mo> </mover> <mi>γ</mi> </mrow> </semantics></math> production cross-section measurements by CMS in the single-lepton channel [<a href="#B47-universe-09-00039" class="html-bibr">47</a>]. Results are also shown as a function of the transverse momentum of the photon at particle level.</p>
Full article ">Figure 21
<p>Distribution of the absolute production cross-section of <math display="inline"><semantics> <mrow> <mi mathvariant="normal">t</mi> <mover accent="true"> <mi mathvariant="normal">t</mi> <mo>¯</mo> </mover> <mi>γ</mi> </mrow> </semantics></math> in the dilepton channel as a function of the <math display="inline"><semantics> <msub> <mi>p</mi> <mi>T</mi> </msub> </semantics></math> of the photon, as measured by the CMS experiment [<a href="#B48-universe-09-00039" class="html-bibr">48</a>]. Observed data unfolded to particle level is compared with the predicted distribution from the Madgraph generator with two different parton shower models. Theoretical uncertainties evaluated using the Pythia 8 prediction are shown in the shaded grey bands.</p>
Full article ">Figure 22
<p>Normalised differential cross-section as a function of the photon transverse momentum [<a href="#B46-universe-09-00039" class="html-bibr">46</a>]. Unfolded distributions are compared with predictions using the <math display="inline"><semantics> <mrow> <mi>MG</mi> <msub> <mn>5</mn> <mi mathvariant="normal">a</mi> </msub> <mi>MC</mi> <mo>+</mo> <mi>Pythia</mi> <mn>8</mn> </mrow> </semantics></math> together with up and down variations of the <math display="inline"><semantics> <mrow> <mi>Pythia</mi> <mn>8</mn> <mi mathvariant="normal">A</mi> <mn>14</mn> </mrow> </semantics></math> tune parameters, the <math display="inline"><semantics> <mrow> <mi>MG</mi> <msub> <mn>5</mn> <mi mathvariant="normal">a</mi> </msub> <mi>MC</mi> <mo>+</mo> <mi>Herwig</mi> <mn>7</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>POWHEG</mi> <mo>+</mo> <mi>Pythia</mi> <mn>8</mn> </mrow> </semantics></math> <math display="inline"><semantics> <mrow> <mi mathvariant="normal">t</mi> <mover accent="true"> <mi mathvariant="normal">t</mi> <mo>¯</mo> </mover> </mrow> </semantics></math> where the photon radiation is modelled in the parton shower.</p>
Full article ">Figure 23
<p>Distribution of the absolute production cross−section of <math display="inline"><semantics> <mrow> <mi mathvariant="normal">t</mi> <mover accent="true"> <mi mathvariant="normal">t</mi> <mo>¯</mo> </mover> <mi>γ</mi> </mrow> </semantics></math> in the <math display="inline"><semantics> <mrow> <mo>e</mo> <mi>μ</mi> </mrow> </semantics></math> channel as a function of the <math display="inline"><semantics> <msub> <mi>p</mi> <mi>T</mi> </msub> </semantics></math> of the photon, as measured by the ATLAS experiment [<a href="#B49-universe-09-00039" class="html-bibr">49</a>]. Observed data unfolded to parton level is compared with the predicted distribution from the theoretical prediction from [<a href="#B50-universe-09-00039" class="html-bibr">50</a>,<a href="#B51-universe-09-00039" class="html-bibr">51</a>]. The systematic and statistical uncertainties are shown in the grey bands.</p>
Full article ">Figure 24
<p>Best fit values for the explored EFT Wilson coefficients by CMS in the single−lepton channel [<a href="#B47-universe-09-00039" class="html-bibr">47</a>]. Both the 1D and 2D scans are shown.</p>
Full article ">Figure 25
<p>Distributions of the observed (solid line) and expected (dashed line) negative log-likelihood difference from the best fit value for the one-dimensional and two-dimensional scans of the studied Wilson coefficients. The results are obtained from the fit to data using the photon <math display="inline"><semantics> <msub> <mi>p</mi> <mi>T</mi> </msub> </semantics></math> distribution. The plots shown here are from the combination of the single lepton and dilepton analyses [<a href="#B48-universe-09-00039" class="html-bibr">48</a>].</p>
Full article ">Figure 26
<p>Comparison of observed 95% CL intervals for the two Wilson coefficients, <math display="inline"><semantics> <msub> <mi>c</mi> <mrow> <mi>t</mi> <mi>Z</mi> </mrow> </msub> </semantics></math> (<b>upper panel</b>) and <math display="inline"><semantics> <msub> <mi>c</mi> <mrow> <mi>t</mi> <mi>Z</mi> <mi>I</mi> </mrow> </msub> </semantics></math> (<b>lower panel</b>) from CMS measurements of: <math display="inline"><semantics> <mrow> <mi mathvariant="normal">t</mi> <mover accent="true"> <mi mathvariant="normal">t</mi> <mo>¯</mo> </mover> <mo>Z</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi mathvariant="normal">t</mi> <mover accent="true"> <mi mathvariant="normal">t</mi> <mo>¯</mo> </mover> <mi>γ</mi> </mrow> </semantics></math> single lepton, <math display="inline"><semantics> <mrow> <mi mathvariant="normal">t</mi> <mover accent="true"> <mi mathvariant="normal">t</mi> <mo>¯</mo> </mover> <mi>γ</mi> </mrow> </semantics></math> dilepton. The results are shown from the one-dimensional scans, i.e., all other Wilson coefficients have values set to zero. The dashed lines indicate the results from the combination with the single−lepton channel. In the case of the global fit and the <math display="inline"><semantics> <mrow> <mi mathvariant="normal">t</mi> <mover accent="true"> <mi mathvariant="normal">t</mi> <mo>¯</mo> </mover> <mo>Z</mo> <mo>+</mo> <mi>t</mi> <mi>Z</mi> <mi>q</mi> </mrow> </semantics></math>, the solid lines represent the result where all Wilson coefficients are fixed to zero, whereas the dashed lines show the results from the marginalised limits. The tightest constraint to date on these Wilson coefficients comes from the combination of the <math display="inline"><semantics> <mrow> <mi mathvariant="normal">t</mi> <mover accent="true"> <mi mathvariant="normal">t</mi> <mo>¯</mo> </mover> <mi>γ</mi> </mrow> </semantics></math> single lepton and dilepton channels [<a href="#B48-universe-09-00039" class="html-bibr">48</a>].</p>
Full article ">Figure 27
<p>Comparison of expected 95% confidence intervals on Wilson coefficients for dimension-six operators affecting top-quark production and decay measurements using the LHC Run 2 dataset and the HL-LHC dataset [<a href="#B59-universe-09-00039" class="html-bibr">59</a>]. Only linear terms proportional to <math display="inline"><semantics> <msup> <mi>Λ</mi> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </semantics></math> are accounted for in the dependence of the observables on the Wilson coefficients. The solid bars show the constraint of from the single parameter fits, while the translucent bars show the marginalised constraints from the global fit.</p>
Full article ">Figure 28
<p>Comparison of expected 95% confidence intervals combining data from the HL-LHC with data from several proposed lepton collider experiments [<a href="#B59-universe-09-00039" class="html-bibr">59</a>]. <math display="inline"><semantics> <mrow> <mi>q</mi> <mover> <mi>q</mi> <mo>¯</mo> </mover> <mi mathvariant="normal">t</mi> <mover> <mi mathvariant="normal">t</mi> <mo>¯</mo> </mover> </mrow> </semantics></math> and <math display="inline"><semantics> <msub> <mi>C</mi> <mrow> <mi>t</mi> <mi>G</mi> </mrow> </msub> </semantics></math> coefficients are not shown in the figure as <math display="inline"><semantics> <mrow> <msup> <mi>e</mi> <mo>+</mo> </msup> <msup> <mi>e</mi> <mo>−</mo> </msup> </mrow> </semantics></math> collider measurements provide no additional sensitivity; however, all operators are included in the global fit. The solid bars show the constraint of from the single parameter fits, while the translucent bars show the marginalised constraints from the global fit. N.B. label HL-LHC+CC refers to the addition of FCC results.</p>
Full article ">
16 pages, 6091 KiB  
Article
Two-Real-Singlet-Model Benchmark Planes
by Tania Robens
Symmetry 2023, 15(1), 27; https://doi.org/10.3390/sym15010027 - 22 Dec 2022
Cited by 9 | Viewed by 1350
Abstract
In this manuscript, I briefly review the Benchmark Planes in the Two-Real-Singlet Model (TRSM), a model that enhances the Standard Model (SM) scalar sector by two real singlets that obey a Z2Z2 symmetry. In this model, all fields [...] Read more.
In this manuscript, I briefly review the Benchmark Planes in the Two-Real-Singlet Model (TRSM), a model that enhances the Standard Model (SM) scalar sector by two real singlets that obey a Z2Z2 symmetry. In this model, all fields acquire a vacuum expectation value, such that the model contains in total three CP-even neutral scalars that can interact with each other. All interactions with SM-like particles are inherited from the SM-like doublet via mixing. I remind the readers of the previously proposed benchmark planes and briefly discuss possible production at future Higgs factories, as well as regions in a more generic scan of the model. For these, I also discuss the use of the W-boson mass as a precision observable to determine allowed/excluded regions in the models’ parameter space. This work is an extension of a white paper submitted to the Snowmass process. Full article
Show Figures

Figure 1

Figure 1
<p>Benchmark planes for asymmetric production and decay, <math display="inline"><semantics> <mrow> <mi>p</mi> <mspace width="0.166667em"/> <mi>p</mi> <mspace width="0.166667em"/> <mo>→</mo> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mn>3</mn> </msub> <mspace width="0.166667em"/> <mo>→</mo> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mn>1</mn> </msub> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mn>2</mn> </msub> </mrow> </semantics></math>, for various assignments of the 125 GeV resonance. <b>Top row</b>: BP1, where <math display="inline"><semantics> <mrow> <msub> <mi>h</mi> <mn>3</mn> </msub> <mspace width="0.166667em"/> <mo>≡</mo> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mn>125</mn> </msub> </mrow> </semantics></math>. Production cross-sections are close to the SM production here, of around <math display="inline"><semantics> <mrow> <mo>∼</mo> <mn>4</mn> <mspace width="0.166667em"/> <mi>pb</mi> </mrow> </semantics></math> at 13 TeV. The branching ratio to <math display="inline"><semantics> <mrow> <msub> <mi>h</mi> <mn>1</mn> </msub> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mn>2</mn> </msub> </mrow> </semantics></math> is shown in the two-dimensional mass plane. <b>Middle and bottom rows</b>: BPs 2 and 3, where <math display="inline"><semantics> <mrow> <msub> <mi>h</mi> <mrow> <mn>2</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mspace width="0.166667em"/> <mo>≡</mo> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mn>125</mn> </msub> </mrow> </semantics></math>, respectively. <b>Left</b>: Production cross-sections at a 13 TeV LHC. <b>Right</b>: Branching ratios of the <math display="inline"><semantics> <mrow> <msub> <mi>h</mi> <mn>1</mn> </msub> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mn>2</mn> </msub> </mrow> </semantics></math> state as a function of the free light scalar mass. The slashed/hatched/dotted regions on the benchmark planes are excluded from comparison with data via <tt>HiggsBounds</tt>/<tt>HiggsSignals</tt>, the requirement that the potential must be bounded from below, and unitarity constraints. Partially taken from [<a href="#B13-symmetry-15-00027" class="html-bibr">13</a>].</p>
Full article ">Figure 2
<p>Benchmark planes for symmetric production and decay, <math display="inline"><semantics> <mrow> <mi>p</mi> <mspace width="0.166667em"/> <mi>p</mi> <mspace width="0.166667em"/> <mo>→</mo> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mi>i</mi> </msub> <mspace width="0.166667em"/> <mo>→</mo> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mi>j</mi> </msub> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mi>j</mi> </msub> </mrow> </semantics></math>, for various assignments of the 125 GeV resonance. <b>Top/middle/bottom rows</b>: BPs 4/5/6, where <math display="inline"><semantics> <mrow> <msub> <mi>h</mi> <mrow> <mn>3</mn> <mo>/</mo> <mn>2</mn> <mo>/</mo> <mn>1</mn> </mrow> </msub> <mspace width="0.166667em"/> <mo>≡</mo> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mn>125</mn> </msub> </mrow> </semantics></math>. <b>Left</b>: Production cross-sections at a 13 TeV LHC. <b>Right</b>: Branching ratios of the <math display="inline"><semantics> <mrow> <msub> <mi>h</mi> <mi>j</mi> </msub> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mi>j</mi> </msub> </mrow> </semantics></math> state as a function of the lighter free scalar mass. Branching ratios for BP4 and 5 are identical; therefore, only one plot is displayed here. The slashed/dotted regions on the benchmark planes are excluded from comparison with data via <tt>HiggsBounds</tt>/<tt>HiggsSignals</tt>, and unitarity constraints. Partially taken from [<a href="#B13-symmetry-15-00027" class="html-bibr">13</a>].</p>
Full article ">Figure 2 Cont.
<p>Benchmark planes for symmetric production and decay, <math display="inline"><semantics> <mrow> <mi>p</mi> <mspace width="0.166667em"/> <mi>p</mi> <mspace width="0.166667em"/> <mo>→</mo> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mi>i</mi> </msub> <mspace width="0.166667em"/> <mo>→</mo> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mi>j</mi> </msub> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mi>j</mi> </msub> </mrow> </semantics></math>, for various assignments of the 125 GeV resonance. <b>Top/middle/bottom rows</b>: BPs 4/5/6, where <math display="inline"><semantics> <mrow> <msub> <mi>h</mi> <mrow> <mn>3</mn> <mo>/</mo> <mn>2</mn> <mo>/</mo> <mn>1</mn> </mrow> </msub> <mspace width="0.166667em"/> <mo>≡</mo> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mn>125</mn> </msub> </mrow> </semantics></math>. <b>Left</b>: Production cross-sections at a 13 TeV LHC. <b>Right</b>: Branching ratios of the <math display="inline"><semantics> <mrow> <msub> <mi>h</mi> <mi>j</mi> </msub> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mi>j</mi> </msub> </mrow> </semantics></math> state as a function of the lighter free scalar mass. Branching ratios for BP4 and 5 are identical; therefore, only one plot is displayed here. The slashed/dotted regions on the benchmark planes are excluded from comparison with data via <tt>HiggsBounds</tt>/<tt>HiggsSignals</tt>, and unitarity constraints. Partially taken from [<a href="#B13-symmetry-15-00027" class="html-bibr">13</a>].</p>
Full article ">Figure 3
<p>The expected exclusion region for the full integrated luminosity of the HL-LHC, <math display="inline"><semantics> <mrow> <mn>3000</mn> <mspace width="3.33333pt"/> <msup> <mrow> <mi>fb</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>, through final states <span class="html-italic">other</span> than <math display="inline"><semantics> <mrow> <mi>p</mi> <mi>p</mi> <mo>→</mo> <msub> <mi>h</mi> <mn>1</mn> </msub> <msub> <mi>h</mi> <mn>1</mn> </msub> <msub> <mi>h</mi> <mn>1</mn> </msub> </mrow> </semantics></math> as explained in the main text. Points with green circles are expected to be excluded by <math display="inline"><semantics> <mrow> <mi>Z</mi> <mi>Z</mi> </mrow> </semantics></math> final states, with red circles by <math display="inline"><semantics> <mrow> <msub> <mi>h</mi> <mn>1</mn> </msub> <msub> <mi>h</mi> <mn>1</mn> </msub> </mrow> </semantics></math> and with blue circles by <math display="inline"><semantics> <mrow> <msup> <mi>W</mi> <mo>+</mo> </msup> <msup> <mi>W</mi> <mo>−</mo> </msup> </mrow> </semantics></math>. The <math display="inline"><semantics> <mrow> <msup> <mi>W</mi> <mo>+</mo> </msup> <msup> <mi>W</mi> <mo>−</mo> </msup> </mrow> </semantics></math> analysis excludes only very few points on the parameter space and therefore appears infrequently in the figure. The points <b>A</b>–<b>I</b> that we have considered in our analysis of <math display="inline"><semantics> <mrow> <mi>p</mi> <mi>p</mi> <mo>→</mo> <msub> <mi>h</mi> <mn>1</mn> </msub> <msub> <mi>h</mi> <mn>1</mn> </msub> <msub> <mi>h</mi> <mn>1</mn> </msub> </mrow> </semantics></math> are shown in black circles overlaid on top of the circles indicating the exclusion. The two cut-out white regions near <math display="inline"><semantics> <mrow> <msub> <mi>M</mi> <mn>2</mn> </msub> <mo>∼</mo> <mn>130</mn> </mrow> </semantics></math> GeV and <math display="inline"><semantics> <mrow> <msub> <mi>M</mi> <mn>2</mn> </msub> <mo>∼</mo> <mn>170</mn> </mrow> </semantics></math> GeV will remain viable at the end of the HL-LHC. Taken from [<a href="#B43-symmetry-15-00027" class="html-bibr">43</a>].</p>
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<p>Reinterpretation of a <math display="inline"><semantics> <mrow> <mn>36</mn> <mspace width="0.166667em"/> <msup> <mrow> <mi>fb</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> CMS search for di-Higgs production via a heavy resonance using the 4 b final state. The exclusion line uses the results obtained in [<a href="#B44-symmetry-15-00027" class="html-bibr">44</a>]. Points to the right and above the red contour are excluded. The slashed regions on the benchmark planes are excluded from comparison with data via <tt>HiggsBounds</tt>/<tt>HiggsSignals</tt>. Taken from [<a href="#B46-symmetry-15-00027" class="html-bibr">46</a>].</p>
Full article ">Figure 5
<p>Expected (<b>left</b>) and observed (<b>right</b>) <math display="inline"><semantics> <mrow> <mn>95</mn> <mo>%</mo> </mrow> </semantics></math> confidence limits for the <math display="inline"><semantics> <mrow> <mi>p</mi> <mspace width="0.166667em"/> <mi>p</mi> <mspace width="0.166667em"/> <mo>→</mo> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mn>3</mn> </msub> <mspace width="0.166667em"/> <mo>→</mo> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mn>2</mn> </msub> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mn>1</mn> </msub> </mrow> </semantics></math> search, with subsequent decays into <math display="inline"><semantics> <mrow> <mi>b</mi> <mover accent="true"> <mi>b</mi> <mo>¯</mo> </mover> <mi>b</mi> <mover accent="true"> <mi>b</mi> <mo>¯</mo> </mover> </mrow> </semantics></math>. For both models, maximal mass regions up to <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mn>3</mn> </msub> <mo>∼</mo> </mrow> </semantics></math> 1.4 TeV, <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mn>2</mn> </msub> <mo>∼</mo> </mrow> </semantics></math> 140 GeV can be excluded. Figure taken from [<a href="#B11-symmetry-15-00027" class="html-bibr">11</a>].</p>
Full article ">Figure 6
<p>Expected (<b>left</b>) and observed (<b>right</b>) <math display="inline"><semantics> <mrow> <mn>95</mn> <mo>%</mo> </mrow> </semantics></math> confidence limits for the <math display="inline"><semantics> <mrow> <mi>p</mi> <mspace width="0.166667em"/> <mi>p</mi> <mspace width="0.166667em"/> <mo>→</mo> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mn>3</mn> </msub> <mspace width="0.166667em"/> <mo>→</mo> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mn>2</mn> </msub> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mn>1</mn> </msub> </mrow> </semantics></math> search, with subsequent decays into <math display="inline"><semantics> <mrow> <mi>b</mi> <mover accent="true"> <mi>b</mi> <mo>¯</mo> </mover> <mi>γ</mi> <mi>γ</mi> </mrow> </semantics></math>. Depending on the model, maximal mass regions up to <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mn>3</mn> </msub> <mo>∼</mo> </mrow> </semantics></math> 800 GeV, <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mn>2</mn> </msub> <mo>∼</mo> </mrow> </semantics></math> 400 GeV can be excluded. Figure taken from [<a href="#B12-symmetry-15-00027" class="html-bibr">12</a>].</p>
Full article ">Figure 7
<p>Leading order production cross-sections for <math display="inline"><semantics> <mrow> <mi>Z</mi> <mspace width="0.166667em"/> <mi>h</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>h</mi> <mspace width="0.166667em"/> <msub> <mi>ν</mi> <mo>ℓ</mo> </msub> <mspace width="0.166667em"/> <msub> <mover accent="true"> <mi>ν</mi> <mo>¯</mo> </mover> <mo>ℓ</mo> </msub> </mrow> </semantics></math> production at an <math display="inline"><semantics> <mrow> <msup> <mi>e</mi> <mo>+</mo> </msup> <mspace width="0.166667em"/> <msup> <mi>e</mi> <mo>−</mo> </msup> </mrow> </semantics></math> collider with a COM energy of 240 GeV (<b>left</b>) and 250 GeV (<b>right</b>) using Madgraph5 for an SM-like scalar h. The contribution of <math display="inline"><semantics> <mrow> <mi>Z</mi> <mspace width="0.166667em"/> <mi>h</mi> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <msub> <mi>ν</mi> <mo>ℓ</mo> </msub> <mspace width="0.166667em"/> <msub> <mover accent="true"> <mi>ν</mi> <mo>¯</mo> </mover> <mo>ℓ</mo> </msub> <mspace width="0.166667em"/> <mi>h</mi> </mrow> </semantics></math> using a factorized approach for the Z decay is also shown. Taken from [<a href="#B8-symmetry-15-00027" class="html-bibr">8</a>].</p>
Full article ">Figure 8
<p>Production cross-sections for <math display="inline"><semantics> <mrow> <mi>Z</mi> <msub> <mi>h</mi> <mrow> <mn>2</mn> <mo>/</mo> <mn>3</mn> </mrow> </msub> </mrow> </semantics></math> in BPs 4 and 5, respectively, at a 250 GeV Higgs factory.</p>
Full article ">Figure 9
<p>Available parameter space in the TRSM, with one (high–low) or two (low–low) masses lighter than 125 GeV. <b>Left</b>: light scalar mass and mixing angle, with <math display="inline"><semantics> <mrow> <mo form="prefix">sin</mo> <mi>α</mi> <mspace width="0.166667em"/> <mo>=</mo> <mspace width="0.166667em"/> <mn>0</mn> </mrow> </semantics></math> corresponding to complete decoupling. <b>Right</b>: available parameter space in the <math display="inline"><semantics> <mfenced separators="" open="(" close=")"> <msub> <mi>M</mi> <mn>1</mn> </msub> <mo>,</mo> <mspace width="0.166667em"/> <msub> <mi>M</mi> <mn>2</mn> </msub> </mfenced> </semantics></math> plane, with color coding denoting the rescaling parameter <math display="inline"><semantics> <mrow> <mo form="prefix">sin</mo> <mi>α</mi> </mrow> </semantics></math> for the lighter scalar <math display="inline"><semantics> <msub> <mi>h</mi> <mn>1</mn> </msub> </semantics></math>. Within the green triangle, <math display="inline"><semantics> <mrow> <msub> <mi>h</mi> <mn>125</mn> </msub> <mspace width="0.166667em"/> <mo>→</mo> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mn>2</mn> </msub> <msub> <mi>h</mi> <mn>1</mn> </msub> <mspace width="0.166667em"/> <mo>→</mo> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mn>1</mn> </msub> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mn>1</mn> </msub> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mn>1</mn> </msub> </mrow> </semantics></math> decays are kinematically allowed. Taken from [<a href="#B8-symmetry-15-00027" class="html-bibr">8</a>].</p>
Full article ">Figure 10
<p>Allowed (red) and excluded (green) regions in the <math display="inline"><semantics> <mfenced separators="" open="(" close=")"> <msub> <mi>M</mi> <mn>3</mn> </msub> <mo>;</mo> <mrow> <mo>|</mo> <msub> <mi>κ</mi> <mn>3</mn> </msub> <mo>|</mo> </mrow> </mfenced> </semantics></math> plane for the “high–low” dataset, where <math display="inline"><semantics> <mrow> <msub> <mi>M</mi> <mn>3</mn> </msub> <mspace width="0.166667em"/> <mo>≳</mo> <mspace width="0.166667em"/> <msub> <mi>M</mi> <mn>125</mn> </msub> </mrow> </semantics></math>. Regions roughly above <math display="inline"><semantics> <mrow> <msub> <mi>M</mi> <mn>3</mn> </msub> <mspace width="0.166667em"/> <mo>≳</mo> <mspace width="0.166667em"/> <mn>200</mn> <mspace width="0.166667em"/> <mi>GeV</mi> <mo>,</mo> <mspace width="0.166667em"/> <mrow> <mo>|</mo> <msub> <mi>κ</mi> <mn>3</mn> </msub> <mo>|</mo> </mrow> <mspace width="0.166667em"/> <mo>≳</mo> <mspace width="0.166667em"/> <mn>0.15</mn> </mrow> </semantics></math> can be excluded requiring a maximal 2 <math display="inline"><semantics> <mi>σ</mi> </semantics></math> discrepancy between prediction and experimentally allowed value.</p>
Full article ">Figure 11
<p>Maximal production cross-section for Higgs-strahlung for scalars of masses ≠ 125 GeV in the TRSM for points passing all discussed constraints. Production cross-sections depend on the parameter point and can reach up to 30 fb.</p>
Full article ">Figure 12
<p>Production cross sections for <math display="inline"><semantics> <mrow> <msup> <mi>e</mi> <mo>+</mo> </msup> <msup> <mi>e</mi> <mo>−</mo> </msup> <mspace width="0.166667em"/> <mo>→</mo> <mspace width="0.166667em"/> <mi>Z</mi> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mspace width="0.166667em"/> <mo>→</mo> <mspace width="0.166667em"/> <mi>Z</mi> <mspace width="0.166667em"/> <mi>X</mi> <mspace width="0.166667em"/> <mi>X</mi> </mrow> </semantics></math>, with <math display="inline"><semantics> <mrow> <mi>X</mi> <mspace width="0.166667em"/> <mo>≡</mo> <mspace width="0.166667em"/> <mi>b</mi> </mrow> </semantics></math> (magenta) and <math display="inline"><semantics> <msub> <mi>h</mi> <mn>1</mn> </msub> </semantics></math> (blue). Points from all data sets are included. Cross sections can reach up to 20 fb. In the low mass region, also <math display="inline"><semantics> <mrow> <mi>X</mi> <mspace width="0.166667em"/> <mo>≡</mo> <mspace width="0.166667em"/> <mi>τ</mi> <mo>,</mo> <mi>c</mi> </mrow> </semantics></math> final states can become important (not shown here).</p>
Full article ">Figure 13
<p>Production cross-sections for <math display="inline"><semantics> <mrow> <msup> <mi>e</mi> <mo>+</mo> </msup> <msup> <mi>e</mi> <mo>−</mo> </msup> <mspace width="0.166667em"/> <mo>→</mo> <mspace width="0.166667em"/> <mi>Z</mi> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mn>3</mn> </msub> <mspace width="0.166667em"/> <mo>→</mo> <mspace width="0.166667em"/> <mi>Z</mi> <mspace width="0.166667em"/> <mi>X</mi> <mspace width="0.166667em"/> <mi>X</mi> </mrow> </semantics></math>, with <math display="inline"><semantics> <mrow> <mi>X</mi> <mspace width="0.166667em"/> <mo>≡</mo> <mspace width="0.166667em"/> <mi>b</mi> </mrow> </semantics></math> (magenta), <math display="inline"><semantics> <msub> <mi>h</mi> <mn>1</mn> </msub> </semantics></math> (blue), and <span class="html-italic">W</span> (green). Points from all data sets are included. Cross-sections can reach up to ∼12 fb.</p>
Full article ">Figure 14
<p>Production cross-sections for <math display="inline"><semantics> <mrow> <msup> <mi>e</mi> <mo>+</mo> </msup> <msup> <mi>e</mi> <mo>−</mo> </msup> <mspace width="0.166667em"/> <mo>→</mo> <mspace width="0.166667em"/> <mi>Z</mi> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mrow> <mn>2</mn> <mo>/</mo> <mn>3</mn> </mrow> </msub> <mspace width="0.166667em"/> <mo>→</mo> <mspace width="0.166667em"/> <mi>Z</mi> <mspace width="0.166667em"/> <mi>X</mi> <mspace width="0.166667em"/> <mi>X</mi> </mrow> </semantics></math>, with <math display="inline"><semantics> <mrow> <mi>X</mi> <mspace width="0.166667em"/> <mo>≡</mo> <mspace width="0.166667em"/> <msub> <mi>h</mi> <mn>1</mn> </msub> </mrow> </semantics></math>, in the <math display="inline"><semantics> <mfenced separators="" open="(" close=")"> <msub> <mi>M</mi> <mn>1</mn> </msub> <mo>,</mo> <mspace width="0.166667em"/> <msub> <mi>M</mi> <mrow> <mn>2</mn> <mo>/</mo> <mn>3</mn> </mrow> </msub> </mfenced> </semantics></math> plane. Color coding refers to the <math display="inline"><semantics> <mrow> <msub> <mo form="prefix">log</mo> <mn>10</mn> </msub> <mfenced separators="" open="[" close="]"> <mi>σ</mi> <mo>/</mo> <mi>fb</mi> </mfenced> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>Z</mi> <msub> <mi>h</mi> <mn>1</mn> </msub> <msub> <mi>h</mi> <mn>1</mn> </msub> </mrow> </semantics></math> production. Maximal cross-sections are around 20 fb.</p>
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16 pages, 588 KiB  
Article
Implications of W-Boson Mass Anomaly for Atomic Parity Violation
by Hoang Bao Tran Tan and Andrei Derevianko
Atoms 2022, 10(4), 149; https://doi.org/10.3390/atoms10040149 - 9 Dec 2022
Cited by 14 | Viewed by 1971
Abstract
We consider the implications of the recent measurement of the W-boson mass MW=80,433.5±9.4MeV/c2 for atomic parity violation experiments. We show that the change in MW shifts the Standard Model prediction for the 133 [...] Read more.
We consider the implications of the recent measurement of the W-boson mass MW=80,433.5±9.4MeV/c2 for atomic parity violation experiments. We show that the change in MW shifts the Standard Model prediction for the 133Cs nuclear weak charge to QW(133Cs)=73.11(1), i.e., by 8.5σ from its current value, and the proton weak charge by 2.7%. The shift in QW(133Cs) ameliorates the tension between existing determinations of its value and motivates more accurate atomic theory calculations, while the shift in QW(p) inspires next-generation atomic parity violation experiments with hydrogen. Using our revised value for QW(133Cs), we also readjust constraints on parameters of physics beyond the Standard Model. Finally, we reexamine the running of the electroweak coupling for the new W boson mass. Full article
Show Figures

Figure 1

Figure 1
<p>(Color online) Comparison between the <math display="inline"><semantics> <msup> <mrow/> <mn>133</mn> </msup> </semantics></math>Cs nuclear weak charge as predicted by the Standard Model (SM) with the mass of the <span class="html-italic">W</span> boson being <math display="inline"><semantics> <mrow> <msub> <mi>M</mi> <mi>W</mi> </msub> <mo>=</mo> <mn>80.357</mn> <mspace width="0.166667em"/> <mrow> <mi>GeV</mi> <mo>/</mo> <msup> <mi mathvariant="normal">c</mi> <mn>2</mn> </msup> </mrow> </mrow> </semantics></math> [<a href="#B82-atoms-10-00149" class="html-bibr">82</a>] (blue band), the SM with <math display="inline"><semantics> <mrow> <msub> <mi>M</mi> <mi>W</mi> </msub> <mo>=</mo> <mn>80.433</mn> <mspace width="0.166667em"/> <mrow> <mi>GeV</mi> <mo>/</mo> <msup> <mi mathvariant="normal">c</mi> <mn>2</mn> </msup> </mrow> </mrow> </semantics></math> [<a href="#B33-atoms-10-00149" class="html-bibr">33</a>] (pink band), and <math display="inline"><semantics> <msup> <mrow/> <mn>133</mn> </msup> </semantics></math>Cs APV experiment [<a href="#B1-atoms-10-00149" class="html-bibr">1</a>] with different calculations for the <math display="inline"><semantics> <msup> <mrow/> <mn>133</mn> </msup> </semantics></math>Cs atomic structure factor (red and blue points).</p>
Full article ">Figure 2
<p>(Color online) Running of <math display="inline"><semantics> <mrow> <mo form="prefix">sin</mo> <msub> <mover accent="true"> <mi>θ</mi> <mo>^</mo> </mover> <mi>W</mi> </msub> </mrow> </semantics></math> predicted by the Standard Model (SM) with the mass of the <span class="html-italic">W</span> boson being <math display="inline"><semantics> <mrow> <msub> <mi>M</mi> <mi>W</mi> </msub> <mo>=</mo> <mn>80.357</mn> <mspace width="0.166667em"/> <mrow> <mi>GeV</mi> <mo>/</mo> <msup> <mi mathvariant="normal">c</mi> <mn>2</mn> </msup> </mrow> </mrow> </semantics></math> [<a href="#B82-atoms-10-00149" class="html-bibr">82</a>] (blue line) and the SM with the new value <math display="inline"><semantics> <mrow> <msub> <mi>M</mi> <mi>W</mi> </msub> <mo>=</mo> <mn>80.433</mn> <mspace width="0.166667em"/> <mrow> <mi>GeV</mi> <mo>/</mo> <msup> <mi mathvariant="normal">c</mi> <mn>2</mn> </msup> </mrow> </mrow> </semantics></math> [<a href="#B33-atoms-10-00149" class="html-bibr">33</a>] (red line). Results of several low-energy parity-violating lepton scattering experiments, as well as <span class="html-italic">Z</span>-pole measurements are also presented. The points P2 and SoLID are projected values from MESA’s P2 experiment [<a href="#B116-atoms-10-00149" class="html-bibr">116</a>] and Jefferson Lab’s SoLID experiment [<a href="#B117-atoms-10-00149" class="html-bibr">117</a>]. For clarity, the Tevatron and LHC results have been horizontally shifted.</p>
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6 pages, 266 KiB  
Communication
W-Boson Mass Anomaly as a Manifestation of Spontaneously Broken Additional SU(2) Global Symmetry on a New Fundamental Scale
by Sergey Afonin
Universe 2022, 8(12), 627; https://doi.org/10.3390/universe8120627 - 28 Nov 2022
Cited by 8 | Viewed by 1122
Abstract
Recently, the CDF Collaboration has announced a new precise measurement of the W-boson mass MW that deviates from the Standard Model (SM) prediction by 7σ. The discrepancy in MW is about ΔW ≃ 70 MeV and is [...] Read more.
Recently, the CDF Collaboration has announced a new precise measurement of the W-boson mass MW that deviates from the Standard Model (SM) prediction by 7σ. The discrepancy in MW is about ΔW ≃ 70 MeV and is probably caused by a beyond the SM physics. Within a certain scenario of extension of the SM, we obtain the relation ΔW3α8πMW ≃ 70 MeV, where α is the electromagnetic fine structure constant. The main conjecture is the appearance of longitudinal components of the W-bosons as the Goldstone bosons of a spontaneously broken additional SU(2) global symmetry at distances much smaller than the electroweak symmetry breaking scale rEWSB. We argue that within this scenario, the masses of charged Higgs scalars can obtain an electromagnetic radiative contribution which enhances the observed value of MW± with respect to the usual SM prediction. Our relation for ΔW follows from the known one-loop result for the corresponding effective Coleman–Weinberg potential in combination with the Weinberg sum rules. Full article
(This article belongs to the Special Issue Research on Physics beyond the Standard Model)
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