CERN Accelerating science

Potential QCD axion mass range explored by efforts described in this white paper. The green bars indicate running experiments in the QCD region, red indicate proposals that utilize the axion-photon coupling, and blue indicates proposal utilizing alternative couplings.

Illustration of Axion DM structure in the modern Universe from the scale of the cosmic web (lower left panel) to the mean axion field as may be observed by a terrestrial search (right panels). Each panel represents a view of axion DM structure at a different scale, with each of the four left panels showing the axion density in orange. The cosmic web (lower left) shows the clustering behavior of DM halos and surrounding gases. The MW (upper left) is surrounded by a halo with virial radius at least on order of magnitude larger than the Galaxy. The inner Solar System and the region immediately surrounding the Earth (middle panels) may contain axion structures beyond the diffuse component, including mini-halos and Bose stars and their tidal streams, axions bound to compact objects such as the Earth and Sun, and axion strings. The axion field as viewed by a terrestrial search (right panels) can be characterized by its coherence properties over time and the structure of its spectra. Amplitudes of sub-structures in the frequency spectra were chosen for illustrative purposes and are not necessarily indicative of a feature's expected prominence. The cosmic web image is a snapshot of gas shocks (blue) and DM density (orange) from the Illustris TNG Collaboration's TNG100-1 simulation~\cite{Springel:2017tpz}. The upper left panel contains an artist's conception of the MW's spiral structure as informed by NASA's Spitzer Space Telescope, with image credit to NASA/JPL-Caltech/R. Hurt (SSC/Caltech)~\cite{SpitzerMWimage}.

Cavity diagrams for Run 1A-C (Run 1D will use one tuning rod in a single cavity), Run 2A, and ADMX-EFR.

Predicted signal and background rates for SQuAD along with sensitivity obtained when averaging over $10^3$~s integration time per cavity tuning. For demonstrated experimental parameters, DFSZ sensitivity is obtained for frequencies up to 30~GHz.

Axion parameter space showing the dimensionless axion-photon coupling constant $C_{a\gamma}$ as a function of the axion mass, $m_a$, with various bounds. This dimensionless coupling is defined so that it is O(1) for models which solve the strong CP problem regardless of the axion mass. The axion mass gives the frequency at which the field oscillates, typically corresponding to the microwave regime (roughly 10 GHz). Haloscope experiments looking for dark matter are shown in grey, the limit from the CAST helioscope looking for solar axions is shown in blue and astrophysical limits are shown in green. The extended QCD axion model band is shown in yellow, with traditional KSVZ and DFSZ models shown as black lines. The region to be explored by ALPHA is shown in purple, covering a significant portion of well-motivated parameter space. This projection assumes a plasma haloscope with quality factor Q=5000 inside a 13 Tesla, 50 cm bore solenoid magnet using quantum limited detection running for three years.

MADMAX Prototype design. The axion-induced radiation from the booster (left) containing $20$ discs of \SI{30}{\centi\metre} diameter is collected by the focusing mirror and antenna. It will be operated in the MORPURGO magnet at CERN, offering a \SI{1.6}{\tesla} dipole field (right).

MADMAX Prototype design. The axion-induced radiation from the booster (left) containing $20$ discs of \SI{30}{\centi\metre} diameter is collected by the focusing mirror and antenna. It will be operated in the MORPURGO magnet at CERN, offering a \SI{1.6}{\tesla} dipole field (right).

Left: Ray-tracing simulation of photons (yellow lines) emitted by the BREAD cylindrical barrel reflector and focused by the parabolic surface to a focus. Reproduced from Ref.~\cite{BREAD:2021tpx}. Right: ADMX-EFR and the large-scale BREAD experiment will be hosted side-by-side in a former MRI magnet.

Left: Ray-tracing simulation of photons (yellow lines) emitted by the BREAD cylindrical barrel reflector and focused by the parabolic surface to a focus. Reproduced from Ref.~\cite{BREAD:2021tpx}. Right: ADMX-EFR and the large-scale BREAD experiment will be hosted side-by-side in a former MRI magnet.

Projected sensitivity for BREAD by photosensor technology (thick lines) in axion coupling vs.\ mass plane. Different assumptions on exposure time and sensor noise equivalent power (NEP) are displayed in the legend. Reproduced from Ref.~\cite{BREAD:2021tpx}.

The projected sensitivities for \DMRL, \DMRm, and \DMRG. The \DMR program aims to probe the QCD axion below $1\,\mu\mathrm{eV}$. This assumes scan times of 3 years for \DMRL, 5 years for \DMRm, and 5 years for \DMRG.

Left Top: Diagram of the \abra detector used for the Run 3 results. A $\sim$ 10\,cm-scale 1\,T toroidal magnet (blue) drives the axion induced magnetic field (purple lines) which is screened by the cylindrical pickup (green). The detector is enclosed within a superconducting shield. Left Bottom: Schematic of the broadband readout. The axion effective current (blue) drives a flux through the inductive pickup (green), which is inductively coupled to a SQUID readout in flux lock mode and monitored. Right: 95\% CL exclusion limits from Runs 1 and 3 of the \abra prototype. Figures from~\cite{Salemi2021a}.

Left Top: Diagram of the \abra detector used for the Run 3 results. A $\sim$ 10\,cm-scale 1\,T toroidal magnet (blue) drives the axion induced magnetic field (purple lines) which is screened by the cylindrical pickup (green). The detector is enclosed within a superconducting shield. Left Bottom: Schematic of the broadband readout. The axion effective current (blue) drives a flux through the inductive pickup (green), which is inductively coupled to a SQUID readout in flux lock mode and monitored. Right: 95\% CL exclusion limits from Runs 1 and 3 of the \abra prototype. Figures from~\cite{Salemi2021a}.

Left Top: Diagram of the \abra detector used for the Run 3 results. A $\sim$ 10\,cm-scale 1\,T toroidal magnet (blue) drives the axion induced magnetic field (purple lines) which is screened by the cylindrical pickup (green). The detector is enclosed within a superconducting shield. Left Bottom: Schematic of the broadband readout. The axion effective current (blue) drives a flux through the inductive pickup (green), which is inductively coupled to a SQUID readout in flux lock mode and monitored. Right: 95\% CL exclusion limits from Runs 1 and 3 of the \abra prototype. Figures from~\cite{Salemi2021a}.

The SHAFT experiment and projected sensitivity~\cite{Gramolin2021}. (a) Schematic of a single detection channel. Two permeable toroids are independently magnetized by injecting current into a magnetizing coil wrapped around each toroid. (b) The circuit model that shows the axion-induced flux~$\Phi_a$ coupling into the pickup coil (inductance $L_p$). The pickup coil is coupled to the SQUID magnetic flux sensor (SQ) via twisted pair leads (inductance $L_{\rm tp}$) and input coil (inductance $L_{\rm in}$). The SQUID is operated in the flux-locked-loop mode, with feedback resistance $R_f$. The feedback voltage $V$ was digitized and recorded by the data acquisition system (DAQ). (c) The SHAFT experimental schematic. The apparatus contains four permeable toroids, shown such that the top and bottom channels are magnetized in opposite directions, to make use of phase-sensitive systematic rejection. The experiment operates at 4.2~K in a liquid helium bath cryostat. (d) Published limits set by the first-generation SHAFT search are shown in blue~\cite{Gramolin2021}. Target sensitivity of next-generation SHAFT search is shown in red.

The SHAFT experiment and projected sensitivity~\cite{Gramolin2021}. (a) Schematic of a single detection channel. Two permeable toroids are independently magnetized by injecting current into a magnetizing coil wrapped around each toroid. (b) The circuit model that shows the axion-induced flux~$\Phi_a$ coupling into the pickup coil (inductance $L_p$). The pickup coil is coupled to the SQUID magnetic flux sensor (SQ) via twisted pair leads (inductance $L_{\rm tp}$) and input coil (inductance $L_{\rm in}$). The SQUID is operated in the flux-locked-loop mode, with feedback resistance $R_f$. The feedback voltage $V$ was digitized and recorded by the data acquisition system (DAQ). (c) The SHAFT experimental schematic. The apparatus contains four permeable toroids, shown such that the top and bottom channels are magnetized in opposite directions, to make use of phase-sensitive systematic rejection. The experiment operates at 4.2~K in a liquid helium bath cryostat. (d) Published limits set by the first-generation SHAFT search are shown in blue~\cite{Gramolin2021}. Target sensitivity of next-generation SHAFT search is shown in red.

(Left) A schematic of the heterodyne/upconversion experimental setup of Sec.~\ref{sec:heterodyne} (taken from~\cite{Berlin:2019ahk}). In an SRF cavity, a pump mode photon of frequency $\omega_0 \sim \text{GHz}$ is converted by axion dark matter into a nearly degenerate photon of frequency $\omega_1 = \omega_0 + m_a$. (Right) The projected sensitivity of a superconducting upconversion setup. As three representative examples, we show the projected sensitivity of a 50L prototype, a $1 \ \text{m}^3$ setup, as well as a futuristic experiment with a total instrumented volume of $5 \ \text{m}^3$. See text for additional details. Regions motivated by the QCD axion and dark matter produced by the misalignment mechanism are also shown as orange and blue bands, respectively.

(Left) A schematic of the heterodyne/upconversion experimental setup of Sec.~\ref{sec:heterodyne} (taken from~\cite{Berlin:2019ahk}). In an SRF cavity, a pump mode photon of frequency $\omega_0 \sim \text{GHz}$ is converted by axion dark matter into a nearly degenerate photon of frequency $\omega_1 = \omega_0 + m_a$. (Right) The projected sensitivity of a superconducting upconversion setup. As three representative examples, we show the projected sensitivity of a 50L prototype, a $1 \ \text{m}^3$ setup, as well as a futuristic experiment with a total instrumented volume of $5 \ \text{m}^3$. See text for additional details. Regions motivated by the QCD axion and dark matter produced by the misalignment mechanism are also shown as orange and blue bands, respectively.

The CASPEr experimental schematic and CASPEr-e projected sensitivity. (a) The CASPEr experimental schematic, showing the nuclear spin ensemble whose spin states are split by the applied bias field $B_0$. When this splitting is resonant with the axion-like dark matter Compton frequency $\omega_a$, the ensemble magnetization $M$ is tilted and undergoes precession that is detected by an inductively-coupled sensor. (b) CASPEr-e projected sensitivity, showing the published limits (blue) and the sensitivity of the search with a 5~mm sample (blue dashed line)~\cite{Aybas2021a}. The red line shows the quantum spin projection noise-limited sensitivity of a CASPEr-e search with a 30~cm sample. The green region is excluded by constraints on excess cooling of SN1987A~\cite{Graham:2013AxionDM,Chang2018a,PDG2019}. The QCD axion is in the purple band, whose width shows theoretical uncertainty~\cite{Graham:2013AxionDM}.

(left) Setup: a sprocket-shaped source mass is rotated so its ``teeth'' pass near an NMR sample at its resonant frequency. (right) Projected reach for monopole-dipole axion mediated interactions. The band bounded by the red (dark) solid line and dashed line denotes the limit set by transverse magnetization noise, depending on achieved $T_2$. Current constraints and expectations for the QCD axion also are shown, adapted from Refs. \cite{arvanitaki2014resonantly,romalis2018,OHare:2020wah}.

{\it (left:)} BabyIAXO and IAXO sensitivity~\cite{IAXO:2019mpb}, compared with the QCD axion (yellow) band and other current (solid) and future (shaded) experimental limits. BabyIAXO (IAXO) will improve sensitivity to $g_{a\gamma}$ by a factor of 5 (20) for the wide mass range up to 0.25\,eV, and are the only experiments with sensitivity to high-mass ($ > 10^{-3}$\,eV) QCD axions. The lower dotted line refers to an optimized IAXO+ configuration. {\it (right:)} Illustration of the IAXO instrument~\cite{IAXOLoI2013,BabyIAXOCDR}. IAXO will consist of a superconducting toroid magnet with eight custom X-ray telescopes that focus the reconverted photons onto ultra-low background detectors.

Constraints on low-mass axions, primarily from high-energy astrophysical probes using X-ray and $\gamma$-ray data. Astrophysical bounds are shown in shades of green whereas experimental (haloscope/helioscope) bounds are shown in shades of red. We also mark the upper bound on ALP dark matter from Ref.~\cite{Arias:2012az} with a dashed black line. The experimental bounds shown in this range are from CAST~\cite{Andriamonje:2007ew,CAST:2017uph}, SHAFT~\cite{Gramolin2021}, ABRA~\cite{Ouellet:2018beu,Salemi:2021gck}, ADMX~\cite{Asztalos2010,Du:2018uak,ADMX:2019uok,ADMX:2021abc}, ADMX SLIC~\cite{Crisosto:2019fcj}, RBF~\cite{DePanfilis}, UF~\cite{Hagmann}, and CAPP~\cite{Lee:2020cfj,Jeong:2020cwz,CAPP:2020utb}. The astrophysical bounds shown are from: searches using Fermi-LAT data on extragalactic supernovae $\gamma$-rays~\cite{Meyer:2020vzy}, NGC1275~\cite{Fermi-LAT:2016nkz}, and for the decay of the diffuse supernova ALP background~\cite{Calore:2021hhn,Calore:2020tjw}. NuSTAR observations of super star clusters~\cite{Dessert:2020lil} and Betelgeuse~\cite{Xiao:2020pra}. Chandra observations of M87~\cite{Marsh:2017yvc}, NGC1275~\cite{Reynolds:2019uqt}, and Hydra-A~\cite{Wouters:2013hua}. HESS analysis of PKS 2155-304~\cite{HESS:2013udx}. HAWC observations of TeV blazars~\cite{Jacobsen:2022swa}. Constraints from nearby magnetic white dwarfs observed via X-ray (Chandra)~\cite{Dessert:2021bkv} and polarisation signals~\cite{Dessert:2022yqq}. Gamma rays from SN1987A~\cite{Payez:2014xsa}, and ARGO-YBJ+Fermi observations of the cluster Mrk 421~\cite{Li:2020pcn}. Finally we also show projections for constraints (green dashed lines) from the supernova distance ladder~\cite{Buen-Abad:2020zbd} and if a 10~$M_\odot$ SN occurred around the galactic centre and was observed by Fermi~\cite{Meyer:2016wrm}. A word of caution should be made about the differing statistical methodologies, and levels of assumption in deriving these bounds---original references should always be consulted when attempting a detailed comparison. Plotting scripts and limit data available at Ref.~\cite{ciaran_o_hare_2020_3932430}.

Current and projected constraints on the axion-electron coupling $g_{aee}$ demonstrating the landscape is dominated currently by the stellar cooling bounds across the majority of the mass range, the bound shown here is from the red giants (RG) in the globular cluster $\omega$Centauri~\cite{Capozzi:2020cbu} (though other derived bounds are comparable). We also show the LUX bound on solar axions~\cite{LUX:2017glr} and the solar luminosity bound~\cite{Gondolo:2008dd}. The only competitive constraints on DM axions exist for $m_a\gtrsim 100$~eV, where underground recoil searches like XENON1T~\cite{XENON:2019gfn,XENON:2020rca,VanTilburg:2020jvl}, PandaX~\cite{PandaX:2017ock}, DARWIN~\cite{DARWIN:2016hyl}, LZ~\cite{LZ:2021xov}, and semiconductors~\cite{EDELWEISS:2018tde,Bloch:2016sjj}, can set bounds, before they are superseded by the non-observation of X-rays from the one-electron-loop decay to two photons~\cite{Ferreira:2022egk}. Plotting scripts and limit data available at Ref.~\cite{ciaran_o_hare_2020_3932430}.

(Left) Evolution of peak fields and bore sizes available from superconducting magnets in recent years. (Right) Magnetic field profile for a 1 Tesla peak spilt toroidal magnet design. The strongest field leakage occurs not only in the gap region, but also in between individual magnet coils. The superconducting elements of this experiment will be placed within 10 mm of the coils/gap region while the field strength falls below 100 mT

(Left) Evolution of peak fields and bore sizes available from superconducting magnets in recent years. (Right) Magnetic field profile for a 1 Tesla peak spilt toroidal magnet design. The strongest field leakage occurs not only in the gap region, but also in between individual magnet coils. The superconducting elements of this experiment will be placed within 10 mm of the coils/gap region while the field strength falls below 100 mT

Layout of design challenges and potential R\&D avenues to pursue. Enhancing the detection volume can take several general design paths. Multicell cavities can be used in a frequency locked configuration (such as what is being pursed by ADMX-G2 and ADMX-EFR) or in a frequency multiplexed configuration. Multicell cavities consist of geometries in which effective cavities communicate through irises.

Current (opaque) and projected (transparent) constraints on the axion-photon coupling. All existing constraints are described in the preceeding sections. The estimated sensitivities of several proposed and in-construction haloscopes are shown including (from low to high masses, roughly): DANCE~\cite{Michimura:2019qxr}, ADBC~\cite{Liu:2018icu}, aLIGO~\cite{Nagano:2019rbw}, SRF cavity~\cite{Berlin:2020vrk}, WISPLC~\cite{Zhang:2021bpa}, DM-Radio~\cite{DMRadio}, FLASH~\cite{Alesini:2017ifp}, ADMX~\cite{Stern:2016bbw}, ALPHA~\cite{Lawson:2019brd}, MADMAX~\cite{Beurthey:2020yuq}, ORGAN~\cite{McAllister:2017lkb}, BRASS~\cite{BRASS}, BREAD~\cite{BREAD:2021tpx}, TOORAD~\cite{Schutte-Engel:2021bqm}, and LAMPOST~\cite{Baryakhtar:2018doz}. We also show projections for IAXO~\cite{Shilon:2013xma} and ALPS-II~\cite{Ortiz:2020tgs}. Finally, we have displayed forecasted sensitivity to heavy dark matter ALP decays to X-rays using eROSITA~\cite{Dekker:2021bos} and THESEUS~\cite{Thorpe-Morgan:2020rwc}, as well as a projection for a Fermi-LAT observation of a galactic supernova~\cite{Meyer:2016wrm}. Plotting scripts and data available at Ref.~\cite{ciaran_o_hare_2020_3932430}.