CERN Accelerating science

Leading diagrams giving rise to LQ pair production at \muc{}. The top row shows direct pair production from muon collisions, while the bottom row shows possible contributions from VBF-like diagrams, where the gauge bosons are to be understood as arising collinear radiation from the radiation beam and the remanant particle is unobserved. (See Sec.~\ref{subsec:SP} for more details.) Except for the top-right diagram, all the other ones only depend on the electroweak gauge couplings.

Leading diagrams giving rise to LQ pair production at \muc{}. The top row shows direct pair production from muon collisions, while the bottom row shows possible contributions from VBF-like diagrams, where the gauge bosons are to be understood as arising collinear radiation from the radiation beam and the remanant particle is unobserved. (See Sec.~\ref{subsec:SP} for more details.) Except for the top-right diagram, all the other ones only depend on the electroweak gauge couplings.

Leading diagrams giving rise to LQ pair production at \muc{}. The top row shows direct pair production from muon collisions, while the bottom row shows possible contributions from VBF-like diagrams, where the gauge bosons are to be understood as arising collinear radiation from the radiation beam and the remanant particle is unobserved. (See Sec.~\ref{subsec:SP} for more details.) Except for the top-right diagram, all the other ones only depend on the electroweak gauge couplings.

Leading diagrams giving rise to LQ pair production at \muc{}. The top row shows direct pair production from muon collisions, while the bottom row shows possible contributions from VBF-like diagrams, where the gauge bosons are to be understood as arising collinear radiation from the radiation beam and the remanant particle is unobserved. (See Sec.~\ref{subsec:SP} for more details.) Except for the top-right diagram, all the other ones only depend on the electroweak gauge couplings.

An example ``barking dog'' diagram with one intermediate LQ leading to the same final states as in Fig.~\ref{fig:diag_pairprod} (left), as well as representative diagrams leading to the same final state as the PP signal in the SM (center and right). The distinct topologies of SM and LQ contribution to these final states gives rise to different kinematic observables that we can cut on.

An example ``barking dog'' diagram with one intermediate LQ leading to the same final states as in Fig.~\ref{fig:diag_pairprod} (left), as well as representative diagrams leading to the same final state as the PP signal in the SM (center and right). The distinct topologies of SM and LQ contribution to these final states gives rise to different kinematic observables that we can cut on.

An example ``barking dog'' diagram with one intermediate LQ leading to the same final states as in Fig.~\ref{fig:diag_pairprod} (left), as well as representative diagrams leading to the same final state as the PP signal in the SM (center and right). The distinct topologies of SM and LQ contribution to these final states gives rise to different kinematic observables that we can cut on.

Normalized distributions of the invariant mass for particle-antiparticle pairs in the SM background (gray shaded) and for LQ PP signals. We use $\beta_L^{32}=0.1$ in all the figures. The left two panels show the $m_{bb}$ distribution, while the right two panels show the $m_{\mu\mu}$ (top) and $m_{\tau\tau}$ (bottom) distributions. The upper two panels correspond to flavor scenario 1, with $bb\mu \mu$ final states, while the bottom two panels correspond to flavor scenario 3, with $b b\tau \tau$ final states. The histograms motivate cuts on $m_{bb}$ for improving the signal-to-background ratio; see the text for further details.

Normalized distributions of the invariant mass for particle-antiparticle pairs in the SM background (gray shaded) and for LQ PP signals. We use $\beta_L^{32}=0.1$ in all the figures. The left two panels show the $m_{bb}$ distribution, while the right two panels show the $m_{\mu\mu}$ (top) and $m_{\tau\tau}$ (bottom) distributions. The upper two panels correspond to flavor scenario 1, with $bb\mu \mu$ final states, while the bottom two panels correspond to flavor scenario 3, with $b b\tau \tau$ final states. The histograms motivate cuts on $m_{bb}$ for improving the signal-to-background ratio; see the text for further details.

Normalized distributions of the invariant mass for particle-antiparticle pairs in the SM background (gray shaded) and for LQ PP signals. We use $\beta_L^{32}=0.1$ in all the figures. The left two panels show the $m_{bb}$ distribution, while the right two panels show the $m_{\mu\mu}$ (top) and $m_{\tau\tau}$ (bottom) distributions. The upper two panels correspond to flavor scenario 1, with $bb\mu \mu$ final states, while the bottom two panels correspond to flavor scenario 3, with $b b\tau \tau$ final states. The histograms motivate cuts on $m_{bb}$ for improving the signal-to-background ratio; see the text for further details.

Normalized distributions of the invariant mass for particle-antiparticle pairs in the SM background (gray shaded) and for LQ PP signals. We use $\beta_L^{32}=0.1$ in all the figures. The left two panels show the $m_{bb}$ distribution, while the right two panels show the $m_{\mu\mu}$ (top) and $m_{\tau\tau}$ (bottom) distributions. The upper two panels correspond to flavor scenario 1, with $bb\mu \mu$ final states, while the bottom two panels correspond to flavor scenario 3, with $b b\tau \tau$ final states. The histograms motivate cuts on $m_{bb}$ for improving the signal-to-background ratio; see the text for further details.

Plot of the PP cross section at $\sqrt{s} = 14\,\textrm{TeV}$ as a function of the LQ mass for several values of $\beta_L^{32}$, normalized by the branching ratio of the LQ. The solid curves show the direct $\mu^+\mu^-$ cross section while the dashed curve shows the VBF-induced process computed using the effective photon approximation (see the diagrams on the bottom row of Fig.~\ref{fig:diag_pairprod}). The dashed gray line indicates the $\sqrt{s}/2$ threshold. For couplings $\beta_L^{32} \lesssim 0.2$ the production cross section is dominated by the electroweak production for all different masses.

Contour plots of the 95\% CL (dashed) and 5$\sigma$ discovery (solid) for pair production of LQ at $\sqrt{s}=3,14$ TeV. We show the reach for flavor scenario 1 (left) and flavor scenario 3 (right). In the gray region, the LQ lifetime is longer than $\Lambda_{\mathrm{QCD}}^{-1}$ and non-perturbative hadronization effects will have to be included for a more accurate result. For sufficiently small couplings the production cross section is dominated by the electroweak production and the bounds become independent of the LQ coupling to the muons.

Contour plots of the 95\% CL (dashed) and 5$\sigma$ discovery (solid) for pair production of LQ at $\sqrt{s}=3,14$ TeV. We show the reach for flavor scenario 1 (left) and flavor scenario 3 (right). In the gray region, the LQ lifetime is longer than $\Lambda_{\mathrm{QCD}}^{-1}$ and non-perturbative hadronization effects will have to be included for a more accurate result. For sufficiently small couplings the production cross section is dominated by the electroweak production and the bounds become independent of the LQ coupling to the muons.

Diagrams leading to single production of LQs. A vector boson from $\mu^+$($\mu^-$) collides with $\mu^-$($\mu^+$) through different channels producing a down-type quark and a LQ.

Diagrams leading to single production of LQs. A vector boson from $\mu^+$($\mu^-$) collides with $\mu^-$($\mu^+$) through different channels producing a down-type quark and a LQ.

Diagrams leading to single production of LQs. A vector boson from $\mu^+$($\mu^-$) collides with $\mu^-$($\mu^+$) through different channels producing a down-type quark and a LQ.

Normalized distributions of the angular distance, $\Delta R$ between the $b$-pair (left) and of the pseudorapidity of the $\mu^+$ in single production. The SM background is shown as a gray, shaded histogram while the colored curves show the LQ signal for several values of the LQ mass. The histograms motivate some cuts on $\Delta R_{bb}$ and $\eta_\mu$.

Normalized distributions of the angular distance, $\Delta R$ between the $b$-pair (left) and of the pseudorapidity of the $\mu^+$ in single production. The SM background is shown as a gray, shaded histogram while the colored curves show the LQ signal for several values of the LQ mass. The histograms motivate some cuts on $\Delta R_{bb}$ and $\eta_\mu$.

SP cross section normalized by the branching ratio of the LQ for the $U_1$ at a COM energy of 3 TeV (left) and 14 TeV (right) for flavor scenario 1. The cross section strongly depends on the coupling to muons and the LQ mass. For $m_{\mathrm{LQ}} \leq \sqrt{s}$, where the LQs can be produced on-shell, the cross section scales like $(\beta^{32}_L)^2$, and it scales as $(\beta^{32}_L)^4$ for higher masses.

SP cross section normalized by the branching ratio of the LQ for the $U_1$ at a COM energy of 3 TeV (left) and 14 TeV (right) for flavor scenario 1. The cross section strongly depends on the coupling to muons and the LQ mass. For $m_{\mathrm{LQ}} \leq \sqrt{s}$, where the LQs can be produced on-shell, the cross section scales like $(\beta^{32}_L)^2$, and it scales as $(\beta^{32}_L)^4$ for higher masses.

Contour plots of the 95\% CL (dashed) and 5$\sigma$ discovery (solid) for single LQ production at $\sqrt{s}=3, 14$ TeV. We show the reach for flavor scenario 1 with one muon in the final state (left), and flavor scenario 3 with a tau in the final state (right). In the gray region, the LQ lifetime is longer than $\Lambda_{\mathrm{QCD}}^{-1}$ and non-perturbative hadronization effects will have to be included for a more accurate result.

Contour plots of the 95\% CL (dashed) and 5$\sigma$ discovery (solid) for single LQ production at $\sqrt{s}=3, 14$ TeV. We show the reach for flavor scenario 1 with one muon in the final state (left), and flavor scenario 3 with a tau in the final state (right). In the gray region, the LQ lifetime is longer than $\Lambda_{\mathrm{QCD}}^{-1}$ and non-perturbative hadronization effects will have to be included for a more accurate result.

Contribution to DY dijet production from LQ exchange (left) and SM (right). We can use the interference of these two diagrams to look for the LQ signal.

Contribution to DY dijet production from LQ exchange (left) and SM (right). We can use the interference of these two diagrams to look for the LQ signal.

Distribution of DY events in $\eta$ for two different values of LQ mass and its coupling to $\mu_L$ and $b_L$ ($\beta_L^{32}$). We use $\sqrt{s} = 3$~TeV for generating these results. We observe that SM distribution (gray) can be significantly different from the LQ model prediction, which is a consequence of different SM and LQ diagram topologies. We use these different distributions to search for the LQ signal in this channel.

Distribution of DY events in $\eta$ for two different values of LQ mass and its coupling to $\mu_L$ and $b_L$ ($\beta_L^{32}$). We use $\sqrt{s} = 3$~TeV for generating these results. We observe that SM distribution (gray) can be significantly different from the LQ model prediction, which is a consequence of different SM and LQ diagram topologies. We use these different distributions to search for the LQ signal in this channel.

The $95\%$ CL exclusion bound (dashed) and the $5\sigma$ discovery (solid) reach of the DY interference channel with $\sqrt{s} = 3, 14$ TeV. In calculating these bounds we neglected the systematic uncertainties. We also use 10 bins in $\eta$ for the final be jets. The DY channel bounds only depend on the $\beta^{32}$ couplings, thus are the same across the four scenarios of Tab.~\ref{tab:flavor_structure}.

The $5\sigma$ discovery reach of the all channels at $\sqrt{s} = 3$ TeV. Any LQ model in the region to the left or above the red lines can be discovered by the corresponding channel. We show the results for all flavor scenarios presented in Tab.~\ref{tab:flavor_structure}. The final state we search for in the scenarios 1 and 2 (3 and 4) is $\mu b \bar{b}$ ($\tau b \bar{b}$). The DY interference bounds are the same across different scenarios, while the single and pair production can change between the scenarios of top or on the bottom row. Additionally, for flavor scenarios 2 and 4, we include the contours corresponding to the central value of the $R_K$ anomaly. We find that the parameter space explaining this anomaly is completely covered with our proposed searches. The PP channel can cover the low LQ mass of the parameter space, while the DY interference and single production probing the higher masses; the former can probe LQ masses far beyond the intrinsic reach of the collider.

The $5\sigma$ discovery reach of the all channels at $\sqrt{s} = 3$ TeV. Any LQ model in the region to the left or above the red lines can be discovered by the corresponding channel. We show the results for all flavor scenarios presented in Tab.~\ref{tab:flavor_structure}. The final state we search for in the scenarios 1 and 2 (3 and 4) is $\mu b \bar{b}$ ($\tau b \bar{b}$). The DY interference bounds are the same across different scenarios, while the single and pair production can change between the scenarios of top or on the bottom row. Additionally, for flavor scenarios 2 and 4, we include the contours corresponding to the central value of the $R_K$ anomaly. We find that the parameter space explaining this anomaly is completely covered with our proposed searches. The PP channel can cover the low LQ mass of the parameter space, while the DY interference and single production probing the higher masses; the former can probe LQ masses far beyond the intrinsic reach of the collider.

The $5\sigma$ discovery reach of the all channels at $\sqrt{s} = 3$ TeV. Any LQ model in the region to the left or above the red lines can be discovered by the corresponding channel. We show the results for all flavor scenarios presented in Tab.~\ref{tab:flavor_structure}. The final state we search for in the scenarios 1 and 2 (3 and 4) is $\mu b \bar{b}$ ($\tau b \bar{b}$). The DY interference bounds are the same across different scenarios, while the single and pair production can change between the scenarios of top or on the bottom row. Additionally, for flavor scenarios 2 and 4, we include the contours corresponding to the central value of the $R_K$ anomaly. We find that the parameter space explaining this anomaly is completely covered with our proposed searches. The PP channel can cover the low LQ mass of the parameter space, while the DY interference and single production probing the higher masses; the former can probe LQ masses far beyond the intrinsic reach of the collider.

The $5\sigma$ discovery reach of the all channels at $\sqrt{s} = 3$ TeV. Any LQ model in the region to the left or above the red lines can be discovered by the corresponding channel. We show the results for all flavor scenarios presented in Tab.~\ref{tab:flavor_structure}. The final state we search for in the scenarios 1 and 2 (3 and 4) is $\mu b \bar{b}$ ($\tau b \bar{b}$). The DY interference bounds are the same across different scenarios, while the single and pair production can change between the scenarios of top or on the bottom row. Additionally, for flavor scenarios 2 and 4, we include the contours corresponding to the central value of the $R_K$ anomaly. We find that the parameter space explaining this anomaly is completely covered with our proposed searches. The PP channel can cover the low LQ mass of the parameter space, while the DY interference and single production probing the higher masses; the former can probe LQ masses far beyond the intrinsic reach of the collider.

Same as Fig.~\ref{fig:combined3} but for $\sqrt{s} = 14$ TeV. Any LQ model in the region to the left or above the purple lines can be discovered by their corresponding channel.

Same as Fig.~\ref{fig:combined3} but for $\sqrt{s} = 14$ TeV. Any LQ model in the region to the left or above the purple lines can be discovered by their corresponding channel.

Same as Fig.~\ref{fig:combined3} but for $\sqrt{s} = 14$ TeV. Any LQ model in the region to the left or above the purple lines can be discovered by their corresponding channel.

Same as Fig.~\ref{fig:combined3} but for $\sqrt{s} = 14$ TeV. Any LQ model in the region to the left or above the purple lines can be discovered by their corresponding channel.

Diagrams for the tree-level LQ contributions to the $R_K^{(*)}$ anomaly (left) and $B_s \rightarrow \mu^+\mu^-$ (right). The two contributions are related via crossing symmetry.

Diagrams for the tree-level LQ contributions to the $R_K^{(*)}$ anomaly (left) and $B_s \rightarrow \mu^+\mu^-$ (right). The two contributions are related via crossing symmetry.

Contours showing the $5\sigma$ discovery reach of a $\sqrt{s} = 3$ or $14\,\textrm{TeV}$ muon collider via pair production for several values of the modified gauge coupling, governed by $\tilde{\kappa}_U$ (see Eq.~\eqref{eq:u1_lag}). The solid, dashed, and dotted lines indicate the reach with $\tilde{\kappa}_U = 0.0$, $0.5$, and $1.0$, respectively.

Contours showing the $5\sigma$ discovery reach of a $\sqrt{s} = 3$ or $14\,\textrm{TeV}$ muon collider via pair production for several values of the modified gauge coupling, governed by $\tilde{\kappa}_U$ (see Eq.~\eqref{eq:u1_lag}). The solid, dashed, and dotted lines indicate the reach with $\tilde{\kappa}_U = 0.0$, $0.5$, and $1.0$, respectively.