Direct Search for Dark Matter Axions Excluding ALP Cogenesis in the 63-67 micro-eV Range, with The ORGAN Experiment

The nature of dark matter remains one of the major unsolved problems in physics and astronomy with precise cosmological measurements indicating that it accounts for 85% of all the matter in the Universe [1, 2]. In this work we undertake a direct search for one of the prime candidates, the dark matter axion, in a well-motivated mass range [10, 11].

Axions are hypothetical, massive spin-0 particles that were first postulated as a result of an elegant solution to the strong CP problem in quantum chromodynamics [5, 6, 7]. The weakly interacting nature of axions, combined with theoretical predictions and early-Universe production mechanisms before or after inflation [8, 9, 10, 11, 12, 13, 14, 18, 19, 17, 18, 19, 20, 21, 22] simultaneously make them a compelling dark matter candidate. To directly detect the dark matter axion we may use a resonant cavity haloscope, which exploits the predicted axion two-photon coupling [23, 24]. Under this coupling, axions can convert to photons by interaction with another photon via the inverse Primakoff effect. In a typical haloscope experiment, a strong DC magnetic field is used to create a source of virtual photons for axions to interact with, producing real photons at a frequency corresponding to the rest mass of the axion, $m_{a}$ [23, 24], with some contribution from the axion velocity. In a typical haloscope, a resonant cavity with a suitable mode geometry is employed to capture these axion-converted photons, and the axion signal is read out with a low noise amplification chain.

The received signal power in such an experiment, due to axion-photon conversion on resonance with the cavity, in the limit $Q_{L}\ll Q_{a}$ can be expressed as,

Here, the axion two-photon coupling strength $g_{a\gamma\gamma}$, local dark matter density $\rho_{a}\approx 0.45\,\mathrm{GeV/cm^{3}}$ (assumed to be all axions) and $m_{a}$ are parameters set by nature. However, parameters controllable by the experimentalist include the magnetic field strength $B_{0}$, cavity volume $V$, mode-dependent form factor $C$ and loaded quality factor $Q_{L}=Q_{0}/(1+\beta)$, where $Q_{0}$ and $\beta$ denote the unloaded quality factor and receiver coupling strength respectively. Another controllable parameter is the system noise temperature ($T_{S}$) of the receiver, which represents the random Nyquist noise in the system in terms of the equivalent effective temperature. To minimise these fluctuations, and to enable use of a superconducting solenoidal magnet, a dilution refrigerator is typically used. Furthermore, since the axion mass and its coupling to photons are a priori unknown, experiments must tune (or scan) the haloscope resonant frequency, $\nu_{c}$ to match the axion frequency, $\nu_{a}\approx m_{a}c^{2}/h$. The searchable value of the axion mass in theory may span many orders of magnitude, however current models and astrophysical constraints suggest that the axion mass lies in the $\mu\textrm{eV}-\textrm{meV}$ region, for example the SMASH model predicts $50\leq m_{a}\leq 200\,\mu\textrm{eV}$[10, 11]. In addition recent QCD lattice simulations also favour $40\leq m_{a}\leq 180\,\mu\textrm{eV}$, with indications that the mass is close to $65\pm 6\,\mu eV$ ($14.2-17.2$ GHz) [25], of which the mass range scanned in this experiment is a subset. However, since again the axion mass is unknown, experiments are required to span the largest possible axion mass range, to maximize the prospects for discovery. As such, the relevant figure of merit for axion haloscopes is the allowable rate of frequency scanning [19], given by [26]

Here, $k_{B}$ is Boltzmann’s constant and $Q_{a}\sim 10^{6}$ is the expected signal quality factor due to the axion kinetic energy distribution, most commonly cited as a Maxwell-Boltzmann distribution in the case of an isothermal, virialized halo [27, 28]. The axion-photon coupling is parameterised by $g_{\gamma}$, a dimensionless model-dependent number taking a value of $-0.97$ and 0.36 in two benchmark QCD axion models, the Kim-Shifman-Vainshtein-Zakharov (KSVZ) and the Dine-Fisher-Srednicki-Zhitnisky (DFSZ) models respectively [12, 13, 14, 15, 16]. So far, only a handful of experiments have reached KSVZ sensitivity [34, 35, 36, 37], and only one experiment, the Axion Dark Matter eXperiment (ADMX) has reached the weaker DFSZ sensitivity [38, 25, 24].

Although most axion experiments target the QCD axion model bands, recent theoretical work suggests more general ALP (Axion-Like Particle) models are possible. For example, cogenesis, which predicts a much stronger axion-photon coupling as a consequence of adding ALPs to the standard model in the early universe to simultaneously explain the observed baryon and dark matter densities [17, 18, 19]. Another example is the recent work on photophilic and photophobic axions, which shows that the parameter space for QCD axions may be much wider than conventional KSVZ and DFSZ axion models suggest [41, 20].

The Oscillating Resonant Group AxioN Experiment (ORGAN) is a microwave cavity haloscope hosted at the University of Western Australia (UWA), which aims to search for axions in the $62-207\,\mu\textrm{eV}$ ($15-50\,\textrm{GHz}$) mass region. The ORGAN run plan consists of several phases over different regions in the $15-50\,\textrm{GHz}$ parameter space, with the first 26.5 GHz path-finding run already complete [42]. We present the results of Phase 1a (schematic shown in Fig. 1), which scans for axion masses in the $15.28-16.23$ GHz ($63-67\,\mu$eV) region of axion-photon coupling parameter space using a tunable $\textrm{TM}_{010}$-based copper conducting-rod resonator. This initial phase of ORGAN serves to test the ALP cogenesis model, operating at a physical temperature $\sim 5.2\textrm{K}$ in a 11.5 T magnetic field, and utilising the best available low-noise High Electron Mobility Transistor (HEMT) amplifiers. Whilst this experiment is capable of placing sensitive limits on axion-photon coupling in its own right, it also serves as a path-finder for future ORGAN phases, which aim to reach the QCD KSVZ and DFSZ model bands.

Compared to lower frequency axion haloscopes, the disadvantage of the cavity resonator approach at the SMASH frequencies of interest is the necessarily small volume, which is of the order of the cube of the axion Compton wavelength, while the scan rate (Eqn. 2) is proportional to the volume squared. This presents a significant challenge for haloscopes going forward into the higher mass ranges. We are pursuing various parallel lines of research and development to mitigate this issue, and achieve high sensitivity in the region of interest.

In the supplementary material we detail a path for the cavity resonator technique to be extended to reach KSVZ and DFSZ in the higher mass range. Subsequent stages of ORGAN will utilise the Phase 1a infrastructure as a test bed for various technologies and techniques required to attain this sensitivity, such as GHz single photon counting [9, 44, 45], novel cavity designs utilising dielectric boosted sensitivity [2, 1], and utilising multiple cavities simultaneously [48]. Other experiments which target this mass range, such as MADMAX [49] and ALPHA [50] use other strategies to mitigate this problem, but are both currently in research and development.

Using Eqn. 1 and inserting typical values for our Phase 1a detector, we find $P_{\textrm{signal}}\simeq 2.3\times 10^{-25}\,(3.1\times 10^{-26})$ W for a $64\,\mu$eV KSVZ (DFSZ) axion. The total system noise referred to the receiver input is a function of the physical cavity temperature $T_{C}$, the total added noise from the amplifier chain $T_{A}$, and the detuning from resonance $\Delta=(\nu-\nu_{c})/\Delta\nu_{c}$, where $\Delta\nu_{c}$ denotes the cavity linewidth. When the cavity and first amplifier are directly coupled with no isolation, $T_{S}$ can be expressed as [51],

For our parameters, the total system noise temperature is orders of magnitude greater in power than that from axion conversion at DFSZ sensitivity. However, the power generated by a cogenesis ALP is many orders of magnitude greater than the KSVZ or DFSZ axion, we calculate $P_{\textrm{signal}}\simeq 8.5\times 10^{-21}$ W at $64\,\mu$eV, which is of similar order to the system noise in the ORGAN-Phase 1a experiment. To improve our ability to resolve any signal above these fluctuations, we must average many measurements to improve the signal-to-noise ratio (SNR). For a total integration time $\tau$, the maximum achievable SNR is given by the Dicke radiometer equation: (4), where $\Delta\nu_{a}$ is the expected axion linewidth.

ORGAN-Phase 1a was run for $\sim 2.5$ weeks in September 2021 and a further week in January 2022, where typical parameters for the TM₀₁₀ mode include, $Q_{L}\simeq 3500$, $C\simeq 0.4$ and $\beta$ between 0.2 and 3. This initial phase was designed as the simplest implementation of the experiment with equipment on hand, the setup of which is shown in Fig. 1. The cavity is coupled directly to the amplifier to minimize losses, and instead of measuring the readout antenna coupling in situ during the experiment, we opted to set the coupling statically at room temperature, and characterise it at as a function of mode frequency, at cryogenic temperatures on separate, dedicated runs directly before and after the data-taking run. The average deviation in $\beta$ between the ‘before data-taking’ and ’after data-taking’ coupling characterisation runs amounts to $10.1\%$, with a standard deviation of $7.7\%$. This verifies that we have a good understanding of the coupling, without the need to measure it in situ. Our experiment consists of a 32 mm inner diameter copper cavity that houses a 16 mm diameter copper tuning rod, which at a cavity height of 80 mm, gives $V\sim 48$ mL. The tuning rod was machined so that 0.2 mm gaps between the lid and the rod were present at either end of the rod, thus ensuring smooth tuning at cryogenic temperatures.

The coupling was set so that $\beta\simeq 2$ was reached at the operating temperature over as much of the target frequency range as possible. Since we had good knowledge of the coupling, with relative changes verified in situ by measuring the change in transmission spectrum, the integration time at each cavity step was varied between 45 and 210 minutes depending on the value, so that cogenesis ALPs could be searched for, or excluded over the entire accessible region.

The readout chain, as shown in Fig. 1, consisted of a vector network analyzer (VNA) that measured (and later utilized) the frequency response of the TM₀₁₀ mode in transmission, a cryogenic pre-amplifer, a directional coupler and a down-conversion stage, which utilised a local oscillator (LO) coupled to an IQ-mixer and 90 degree hybrid coupler. This down-mixing stage achieved image-rejection of the noisy, amplifier-only sideband, giving us the best possible $T_{S}$. A 250 MS/s digitizer (NI-5761R) was used to sample the output of the hybrid coupler, and the digital data was processed in real time on a field-programmable gate array (FPGA; Xilinx Kintex-7, NI-7935R). A zero-dead-time, hybrid superheterodyne-FFT spectrum analyzer was implemented on the FPGA, which generated a 26,214 point, 12.5-MHz-wide spectrum centered at 45.1 MHz, with bin width $\Delta\nu_{b}\approx 477$ Hz. Frequency tuning was achieved by rotating the off-axis rod with an Attocube ANR240 piezoelectric stepper motor, and steps between successive cavity positions were defined as a fraction of the cavity linewidth. A mode map of angular position versus frequency was made prior to data taking (see Fig. 2), and converted the required frequency step $\sim\Delta\nu_{c}/5$, to stepper motor steps.

During the total $\sim 3.5$ weeks of data taking, 597 resonant frequencies were scanned, amounting to a search window of $\sim 700$ MHz between $15.28-16.23$ GHz. Some of the data could not be used due to mode-mixing between the axion-sensitive TM₀₁₀ mode and intruding transverse electric (TE) modes, which arises as a result of the longitudinal symmetry-breaking due to assembly tolerance in the axial position of the tuning rod [52]. Mode interactions created forbidden frequency ranges between $15.58-15.61$ GHz, $15.65-15.69$ GHz and $15.96-16.15$ GHz, reducing the duty cycle of our search to $\sim 74\%$. These regions will be probed in future, more sensitive iterations of the ORGAN experiment. At each cavity position, $Q_{L}$, $\nu_{c}$, and $\Delta\nu_{c}$ were extracted from transmission measurements, so that the LO frequency could be set to $\nu_{c}-45.1$ MHz, thus placing the centre of the mode at the centre of the intermediate frequency (IF) window. Although the relatively high IF prevents unwanted spurious noise sources that are common at lower frequencies (IF $\leq$ 10 MHz), there were in fact inescapable, large noise spikes at 40 and 50 MHz due to the device’s onboard 10 MHz oscillator, and so we restrict the analysis region to be between $\sim 41.2-48.8$ MHz.

We follow the HAYSTAC analysis procedure [53], which builds upon the pioneering work of [22]. The first step is spectrum baseline removal, where the frequency dependent baseline is a combination of the cavity thermal noise and the variable noise and gain of the readout chain. The broadband baseline of each spectrum can be removed using a Savitsky-Golay (SG) filter, which is a digital low-pass filter. The parameters of the SG filter must be chosen so that the passband is flat over large spectral scales, comparable to the baseline, whilst also maximising stop band attenuation over smaller spectral scales, comparable to the axion signal width. As outlined by [53], the imperfect stop band attenuation of the SG filter induces small negative correlations between neighbouring bins of the same spectrum, and attenuates signals on small spectral scales, like an axion. This effect can be simulated and thus accounted for, but it requires knowledge of the full covariance matrix (see supplementary material).

Once filtered, the spectra are rescaled according to their axion sensitivity and then vertically combined using a maximum likelihood (ML) weighted sum of contributing spectra to maximize the SNR. As noted, the expected axion signal is thought to have $Q_{a}\sim 10^{6}$, hence for ORGAN, a 15.6 GHz axion would have a linewidth $\Delta\nu_{a}\sim 15.6\,\textrm{kHz}\sim 32\Delta\nu_{b}$. Therefore we must horizontally combine bins from the vertically combined spectra so that the resulting “grand spectrum” bin width $\Delta\nu_{g}$ is $\sim\Delta\nu_{a}$. Additionally, the expected Maxwell-Boltzmann axion lineshape allows us to further enhance our sensitivity to potential axion signals by optimally filtering sets of 32 consecutive contributing bins according to this lineshape.

The excess power in the kth grand bin is denoted by $\delta^{g}_{k}$, and in the absence of correlations the resulting normalized distribution $\delta^{g}_{k}/\sigma^{g}_{k}$ is expected to have a standard normal distribution. However, as shown in Fig. 3, the width of the grand spectrum distribution is reduced to $\xi^{g}=0.97$, which is a direct result of the negative correlations induced by the imperfect stop-band attention of the SG filter. These negative correlations are accounted for through simulation (details given in the supplementary material), which allows us to place axion exclusion limits in a statistical manner, avoiding Monte Carlo simulations.

We place bin-by-bin exclusion limits on axion-photon coupling by assuming a constant target SNR and re-scaling the sensitivity of each grand bin accordingly [53]. To avoid rescans (which have been shown to have a negligible impact on sensitivity [53]) , we set the candidate threshold at the maximum normalized power excess, $4.6\sigma$, which corresponds to a target SNR of 6.245$\sigma$ at 95$\%$ confidence. As shown in Fig. 4, we have surpassed the limits set by CAST by over an order of magnitude and excluded ALP-cogenesis over most of the frequency range between $15.28-16.23$ GHz ($63-67\,\mu$eV), with the assumption that axions make up the total local dark matter density.

ORGAN is the first haloscope experiment to probe axions beyond 10.4 GHz ($43\,\mu$eV) [56], into the Ku microwave band, and we have set the most sensitive limits to date on axion-photon coupling in this high-frequency region despite the unfavourable sensitivity scaling. We have detailed the operations and design of our first tunable cavity, with future plans to explore the entire $15-50$ GHz parameter space at QCD model band coupling, with further details given in the supplementary material. Development of quantum readout circuits required to reach this goal, such as GHz single photon counters, is ongoing.

Supplementary Information for
“Direct Search for Dark Matter Axions Excluding ALP Cogenesis in the 63-67 micro-eV Range, with The ORGAN Experiment”