PASSAT: Particle Accelerator helioScopes for Slim Axion-like-particle deTection

Walter M. Bonivento, ∗ Doojin Kim, 3, † and Kuver Sinha ‡ Istituto Nazionale di Fisica Nucleare, Sezione di Cagliari, Cittadella Universitaria di Monserrato, Monserrato (CA), Italy Department of Physics, University of Arizona, Tucson, AZ 85721, USA Mitchell Institute for Fundamental Physics and Astronomy, Department of Physics and Astronomy, Texas A&M University, College Station, TX 77843, USA Department of Physics and Astronomy, University of Oklahoma, Norman, OK 73019, USA


I. INTRODUCTION AND MOTIVATIONS
The QCD axion [1][2][3] and more general pseudo-scalar axion-like-particles (ALPs), which are ubiquitous in string theory [4,5], are a major focus of searches for physics beyond the Standard Model (SM). The experimental ecosystem investigating these particles is vast and rich. The techniques often rely on the ALP-photon coupling: where g aγγ is the coupling between ALP (henceforth denoted by a) and the SM photon and where F µν (F µν ) is the usual field (dual field) strength tensor of the photon. ALPs can convert to photons and vice versa in the presence of an external magnetic field, leading to experiments based on the axion haloscope and the axion helioscope [6][7][8]. On the other hand, photon regeneration (light shining through wall, LSW) experiments [9] attempt to actively produce ALPs with a high-intensity laser beam applied in a magnetic field, followed by detecting the produced photons via ALP-photon conversion. We refer to Ref. [10] for a recent review of these topics. In contrast, particle accelerator-based experiments have so far been proposed to search for heavy (i.e., MeV -GeV-scale) ALPs, since they are relatively shortlived and their decay point is not much displaced from their production point. Examples include NA62 [11], SHiP [12], FASER [13,14], and SeaQuest [15]. In such experiments, an ALP is first produced in the target/dump material and subsequently decays to photons in the decay volume. As the ALP mass is lowered, it exits the decay volume without decaying and these experiments lose their sensitivity. We refer to [16][17][18][19] for recent theoretical studies on ALP searches.
The purpose of this paper is to point out that if the ALP enters a region with a transverse magnetic field after being produced at the target, then a beam dump becomes sensitive to very light ALPs (see Figure 1). This is because the ALP is no longer required to decay; rather, the ALP converts to a photon which can be detected. If the length traversed by the ALP is shorter than the associated oscillation length, the conversion is coherent and a net probability of conversion can be obtained as a function of the ALP-photon coupling. The predicted photon signal is a product of the ALP production cross section at the target material and its conversion probability as it subsequently traverses the magnetic field.
Dubbed Particle Accelerator helioScopes for Slim Axion-like-particle deTection (PASSAT), our proposal thus combines the principle of the axion helioscope with traditional ALP production in beam dumps. From the perspective of a traditional helioscope, the Sun is replaced by the target material as the source of ALPs; from the perspective of a traditional beam dump experiment, the ALP decay process is replaced by the ALP conversion process.
While its expected reach cannot rival that of the CAST helioscope, PASSAT outperforms other searches for laboratory-produced ALPs. We stress that it is important to pursue laboratory-based experiments to probe the ALP parameter space, even in regimes that are constrained by helioscopes and astrophysical sources. As pointed out in the aftermath of the PVLAS signal [20], there are many assumptions that lie behind constraints given by solar helioscopes (we choose [21][22][23] among the many papers that make this point). The environmental conditions for the production of ALPs inside the Sun or in stars are very different from those in laboratories. The coupling g aγγ or the mass m a can depend on a host of environmental parameters, such as the temperature, matter density, or plasma frequency, as well as the momentum transfer at the ALP-photon vertex. Thus, laboratorybased searches, apart from being complementary to astrophysical searches, are also more conservative.
We begin our work by discussing ALP production and conversion at PASSAT, and then apply the resulting formalism to several implementations in past, current, and future experimental facilities to obtain an initial estimate of the expected performance. We first reinterpret existing data from the NOMAD experiment [24] in light of PASSAT. We then discuss the possible future implementation of PASSAT at CERN, combining two components: (i) a permanent fixed target complex composed of the beam line and target infrastructure from the proposed Beam Dump Facility (BDF) [25] and the muon shield component from the SHiP detector [26] (ii) followed by the CAST [27] or BabyIAXO [28] magnets, together with some new detectors. In each case, we provide the experimental parameters and the projected sensitivities, including the future potential of upgrading LHC-like magnets up to 20 T, as projected by studies related to the FCC-hh collider.

II. ALP PRODUCTION AND CONVERSION
In this section, we calculate the expected number of events N ex from ALP production via the Primakoff process at the target followed by its conversion to a photon in the magnetic field. The quantity N ex is simply given as where N POT is the total number of protons on target (POT) and σ γ→all is the cross section for photon-nucleus scattering which is dominated by photon conversion to an electron-positron pair in the nuclear fields. For the photon energies of our interest, we have σ γ→all ≈ 1.2 × 10 4 mb in Molybdenum and σ γ→all ≈ 1.4 × 10 2 mb in Beryllium [29]. P a→γ stands for the probability of ALPto-photon conversion when an ALP travels distance L in a magnetic field B: where the product of the second and third factors is the form factor reflecting the coherence of the conversion. In the relativistic limit and in vacuum, q is given by The integrand in Eq. (2) describes the differential ALP production cross section via the Primakoff process convoluted with a differential photon number density profile n γ , in ALP energy E a and its outgoing angle θ a from the beam axis. This is given by where φ denotes the angle in the transverse plane between the incoming photon and the outgoing ALP and σ γN is the cross section for the Primakoff process. We note that n γ is a function over the photon transverse momentum p T and we have substituted the E γ dependence in n γ with E a in the collinear limit, i.e., E a ≈ E γ . In the massless (or ultra relativistic) ALP limit, the σ γN is approximately of the form [16,19] where α and Z are the fine structure constant and the atomic number of target material, respectively, and where t = −(p γ − p a ) 2 is given by We follow Ref. [16] and choose the Helm form factor as F (|t|) which is assumed to be vanishing for |t|R 1 > 4.49: where s = 0.9 fm, Θ(x) is the Heaviside step function, and j 1 is the spherical Bessel function of the first kind. Here R 1 is parametrized according to Ref. [30], i.e., R 1 = (1.23A 1/3 − 0.6) 2 + 2.18 fm with A being the atomic mass number of target material.
We finally turn to the photon number density profile n γ . In principle, the precise determination of n γ requires a full detector-level simulation. However, in this first study, we opt to take a (semi-)analytic approach, based on an empirical model. This enables us to perform rapid estimates, essentially as a proof of principle.
Since the ALPs under consideration are sufficiently light, the dominant photon source is the decay of mesons (e.g., π 0 , η). Production of mesons through high-energy proton beams on target is elegantly parametrized by the so-called BMPT model [31] whose fits were tuned with p-Beryllium target collision data. In the limit of negligible transverse momenta of mesons, we find that the differential production cross section of say, a charged pion has the form of where E beam denotes the particle beam energy. We assume that the functional behavior of the above spectrum describes the differential π 0 number density dN π /dE π . Our parameter choices (c α , c β , c γ ) for π ± are (3.45, 1.57, 0.517) [31]. We further assume that N π is normalized to 4 for E beam = 400 GeV considering the measurement data in Ref. [32] and the simulation study in Ref. [17]. The pion energy E π and the photon energy E γ in the laboratory frame are related by the following Lorentz transformation, where E * γ (= m π /2) and θ * γ are the photon energy and the photon emission angle in the pion rest frame, respectively, and where the pion boost factor contains E π dependence such that γ π = E π /m π . Since typical pions are highly boosted, γ 2 π − 1 ≈ γ π so that we have The density of p 2 T , w(p 2 T ), can be calculated from the density of cos θ * γ , w(cos θ * γ ), that is, Here w(cos θ * γ ) = 1/2 as only the forward-moving photon contributes to the final estimate out of the two decay products. Taking the collinear limit E a ≈ E γ again, therefore, we find where the Jacobian factor can be readily computed from Eq. (11).

III. REINTERPRETATION OF PAST EXPERIMENTS
We first discuss the NOMAD experiment since it has experimental data and possesses the main features of PASSAT, a fact that was not appreciated in the past. The ALP search at NOMAD [24] assumes that a fraction of the photons produced by a proton beam on the Beryllium target enters the horn region where they are converted to ALPs. These ALPs are subsequently reconverted back to photons in the NOMAD spectrometer. The underlying principle is the LSW class of experiments, with the laser replaced by a beam dump. Like a LSW experiment, it requires two conversion stages in two separate regions with magnetic fields: first from photons to ALPs, and then ALPs back to photons.
Motivated by the idea of PASSAT applied to NOMAD, we instead focus on the ALPs directly created in the target, jettisoning the first phase of photon to ALP conversion. ALPs directly produced in the target by the Primakoff process will subsequently be converted back to photons in the magnetic field region of the NOMAD spectrometer. The distance between the target and the detector is 835 m, and in the conversion region a 0.4 T magnetic field is applied for a length L = 7.5 m. The width×height of the magnetic field region is 3.5 × 3.5 m 2 .
We take a circular area of radius 1.75 m instead of the square cross section for convenience of calculation. The produced ALPs should reach the photon detector without being absorbed in other parts of experimental facility. This imposes a maximum allowed value of θ a , given approximately by the ratio of radius of cross-sectional area A to the entire distance between the target and the (γray) detector (see also Table I) Table I.

IV. POSSIBLE NEW EXPERIMENTS
As far as future experiments are concerned, we propose to recycle the magnets from CAST or BabyIAXO experiments, after they are decommissioned, and locate them at the BDF complex, possibly after its first use with the SHiP experiment. The BDF project, which is currently in its planning phase, will be housed in the North Area of CERNs Prevessin site and utilize the 400 GeV Super Proton Synchrotron (SPS) proton beam. This component will provide the beam line and target infrastructure. It is to this component that the muon shield from SHiP will be added, forming the BDF-SHiP complex.
The conceptual design of the experimental setup that we are envisioning is depicted in Figure 2. The BDF/SHiP module includes the proton beam, target complex, and active muon shield. In our study we assume that the beam energy is 400 GeV and the target in the core of the shower is Molybdenum (which is contained in TZM alloy) like BDF for purposes of illustration. The produced ALPs traverse the muon shield area and enter the bore of CAST/BabyIAXO where the ALP-photon conversion occurs.
We note that the iron-filled active muon shield area itself comes with a 50 m-long transverse magnetic field region of approximately 1.8 T. Some ALPs may convert to photons in the magnetic field in the shield area, but such photons will be quickly absorbed to the material. We thus neglect any contribution to the final photon count arising from conversions in the muon shield area. A fraction ∼ 10 −7 of incident ALPs are lost due to conversion in the muon shield in this manner.
We make a few comments on the input parameters required to calculate the final expected number of pho-tons. Firstly, POT is expected to be 2 × 10 20 in five years. Secondly, when calculating the maximum angular acceptances, the length of the muon shield area should be taken into account; for example, θ max a for the BabyIAXO case is 0.5/(50 + 10) ≈ 8.3 mrad. The values of the magnetic field and lengths of the different conversion modules are tabulated in Table I. Finally, we note that the photon detectors in the CAST/BabyIAXO experiments are designed to be sensitive to X-ray. For our purpose, the detector is replaced by a γ-ray photon detector (e.g., calorimeter).

V. EXPERIMENTAL SENSITIVITIES
From Eq. (2), the expected number of events can be obtained by integrating the differential cross section in Eq. (5) over E a , θ a , φ and p 2 T . Firstly, in all our sensitivity calculations, we impose the requirement that E a > 50 GeV. Given the fact that the produced mesons are forward-directed and not much transverse [31], this implies that the momenta of incoming photons and in turn their parent mesons along the beam axis dominate so significantly that one can neglect their transverse momentum. In other words, we restrict our initial estimates to the phase space where the negligible transverse momentum approximation and the limit of ultra relativistic mesons are sufficiently valid. The unconsidered phase space can provide an additional contribution to the signal sensitivities of interest, and therefore, our estimate here may be understood as being rather conservative. We will perform a dedicated study including full experimental setup details and the (significant) cascade factor of showering in future work [34].
The photons from ALP conversion in the magnetic field should reach the photon detector without being absorbed in other parts of experimental facility, giving a maximum angular acceptance θ a for each benchmark experiment, summarized in Table I. φ simply ranges from 0 to π. Finally, p 2 T spans 0 to m 2 π /4. Since we are restricted to E a > 50 GeV, the full p T range is within their angular acceptance. However, the angular acceptance for CAST is somewhat limited, so we consider p 2 T ∈ (0, 36 2 ) MeV 2 in the corresponding calculation.
The curves in Figure 3 display our estimate of the experimental sensitivity and existing bounds from various laboratory-produced ALP search experiments in the plane of m a and g aγγ . We first estimate the exclusion limit that the NOMAD experiment would reach with existing data. With a 450 GeV proton beam on the Beryllium target and 1.08 × 10 19 POT, no significant excess has been observed over the expected neutrino background 272 ± 18 events [24] which can occur in the preshower region or in the upstream region. We consider E a ≈ E γ ranging 50 GeV to 140 GeV, while conservatively assuming that all expected background events are relevant to this energy range. The limit is computed at 90% C.L. for a given background assumption and its statistical un- Expected experimental sensitivity that can be achieved by PASSAT with CAST (blue lines) and BabyIAXO (red lines) magnets, in the plane of ALP mass ma and the associated photon coupling gaγγ. The NOMAD ALP search in [24] is reinterpreted in terms of PASSAT as the experiment possesses the main features of PASSAT, and the black solid line shows the resulting limit. Dashed lines are the corresponding sensitivities with prospective B of 20 T for CAST-PASSAT and BabyIAXO-PASSAT. The current bounds summarized in Ref. [18] are from existing laboratory-produced ALP searches. The prospective limits are estimated by 90% C.L. under the assumptions of 10 (negligible) background events for BabyIAXO-PASSAT (CAST-PASSAT) and 2×10 20 POT. The NOMAD case is calculated with the expected number of background events reported in [24], being normalized to 1.08 × 10 19 POT.
certainty. 1 The result is shown by the black-solid curve in Figure 3. The red-shaded region denotes the bounds published by the NOMAD Collaboration, assuming a LSW interpretation. We see that NOMAD-PASSAT constrains a wider range of parameter space, not only covering the existing NOMAD bound but exploring up to g aγγ ∼ 10 −4 GeV −1 for m a 0.1 keV.
When it comes to the other possible experiments, we assume that 400 GeV of CERN SPS proton beam is incident on a Molybdenum target with specifications similar to those of the target adopted in the BDF project, as mentioned earlier. We include the contribution from the η meson decay, simply assuming that the expected number of photons is roughly 1/10 of the π 0 meson case [17,32], although the experimental sensitivities are not much affected by this inclusion. Again, the limits 1 Since the Beryllium target in NOMAD is as thin as 100 mm, some fraction of incident protons may not scatter in the target but traverse towards the downstream dump area. We here take a rather simple analysis scheme, not distinguishing ALPs produced at the target with those produced at the downstream complex, which is beyond the scope of this study.

VI. CONSIDERATIONS ON BACKGROUND
At the expected proton beam intensities at the BDF, there will still be a large flux of muons coming out of the active muon shield. Therefore, to suppress background from charged particles and possible neutral particles at the exit point of the shield, a set of properly optimized veto detectors will be needed. To avoid interactions in the bore region of the CAST/BabyIAXO module some level of vacuum could also be needed.
There will be an irreducible background arising from ν e elastic scattering (ES) events, mostly coming from the decays of charmed particles in the beam dump, inside the photon detector. We attempt an order of magnitude estimate here based on previous related studies that can be found in [26] and subsequent documents for the 9,600 kg neutrino detector of the SHiP experiment. The number of ES found there can be scaled to what is expected in PASSAT from the detector mass ratio. We assume for PASSAT a calorimeter made of (i) an electromagnetic section with appropriate longitudinal segmentation for selecting interactions in the first four radiation lengths, in order to keep high efficiency on signal photons and good angular resolution and (ii) a hadronic section aiming at rejecting deep inelastic scattering events. Assuming that the neutrino flux is uniformly incident on the calorimeter, the expected number of ES events at BabyIAXO-PASSAT would be 17, obtained as follows: 800 (the number of background events for a dark matter search with electron scattering in [26]) × 200 (weight of a 4X 0 lead calorimeter of BabyIAXO magnet area) / 9, 600 ≈ 17. The requirement of E a ≈ E γ > 50 GeV further reduces 80% − 90% of the ES background [26]. In this analysis we conservatively assume 10 background events for BabyIAXO-PASSAT. On the other hand, for CAST-PASSAT we assume negligible background as the associated cross sectional area A is much smaller, implying an even more suppressed neutrino flux entering the calorimeter.
Our analysis results with CAST and BabyIAXO magnets are exhibited by the blue and red solid curves, respectively, in Figure 3. We clearly see that all of the benchmark experiments promoted to PASSAT show equally good capabilities and allow for probing a substantially broader range of parameter space than explored by past laboratory-produced ALP searches.
Beyond m a ≈ 0.01 − 0.1 keV, the associated oscillation length of the produced ALP becomes shorter than L and the conversion mechanism becomes non-coherent, resulting in a rising sensitivity line. We further show the expected experimental sensitivities with a prospec-tive higher magnetic field of 20 T, 2 by the dashed but same color-coded lines. BabyIAXO (CAST) can accomplish sizable (mild) improvements in the sensitivities as B is increased by an order of magnitude (a factor of ∼ 2). We caution the reader that although not depicted in our figure, the sensitivity curves should terminate when they encounter the traditional beam dump constraint regions (solid orange), since the ALPs are expected to decay before they can convert.
It should be stressed that, in contrast to other proposed experiments at beam dumps looking for New Physics particles decaying to neutral particles only, such as [35] and [36], for PASSAT it is possible to determine the background directly from the data, by running with the magnet current switched off. It is reasonable that the data acquisition can include periods with current on and off for equal duration. This will also allow us to optimize the setup and evaluate its feasibility at the beginning of the experiment.

VII. CONCLUSIONS AND OUTLOOK
We have proposed a novel method to search for ALPs at particle accelerator experiments. Our results suggest that PASSAT should probe a wide range of parameter space that none of the laboratory-produced ALP search experiments have ever explored. In particular, the ex-pected experimental sensitivity covers regions explored by the CAST helioscope experiment, providing a conservative and complementary probe. The experimental sensitivity also extends into regions that are currently solely constrained by astrophysical observations (e.g., HB stars).
Finally, we emphasize that the idea of PASSAT can be implemented at other facilities and beam lines (e.g., electron beam dumps). We reserve these topics for future work.