Searching for energetic cosmic axions in a laboratory experiment: testing the PVLAS anomaly

Astrophysical sources of energetic gamma rays provide the right conditions for maximal mixing between (pseudo)scalar (axion-like) particles and photons if their coupling is as strong as suggested by the PVLAS claim. This is independent of whether or not the axion interaction is standard at all energies or becomes supressed in the extreme conditions of the stellar interior. The flux of such particles through the Earth could be observed using a metre long, Tesla strength superconducting solenoid thus testing the axion interpretation of the PVLAS anomaly. The rate of events in CAST caused by axions from the Crab pulsar is also estimated for the PVLAS-favoured parameters.

Recently, the PVLAS experiment has reported an observation of a rotation of the plane of polarization of a laser beam passing through magnetic field [1] which was claimed to be compatible with the existence of a new (pseudo)scalar particle with a mass of m ∼ 10 −3 eV and an inverse coupling to photon M ∼ 10 5 GeV. This is unexpected since experiments such as CAST [2] have seemingly ruled out this region of parameter space. Some authors have tried to explain this discrepancy by suggesting alternative models for the pseudoscalar in which its effective coupling to photons is suppressed in the extreme conditions of the stellar interior [3]. Alternative explanations of the effect by means of particles carrying very small electric charge [4] are disfavoured [5] by preliminary PVLAS data and severely constrained (if not ruled out) by the limits on the millicharged particles [6]. Note that the quantitative results of the CAST experiment depend on the model of the solar interior while the PVLAS claim is based on relatively low statistics. Doubts have also been raised over the latter result due to possible systematic experimental effects from the rotation of the magnet [7]. The apparent discrepancy between the two experiments calls for more model-independent tests both in laboratory experiments [5,8] and in gamma-ray astronomy [9,10,11]. Here we suggest that if new axion-like particles exist which have a coupling to two photons as strong as that suggested by the PVLAS claim, there should be a flux of these particles through the Earth coming from conversion of energetic gamma-rays emitted by astrophysical sources to axions in the magnetic fields of the sources themselves. Since the conditions (temperature, density and average momentum transfer) in such typical sources are much closer to those in the laboratory rather than the stellar interior, this flux is guaranteed in any model which explains the PVLAS result with a new (pseudo)scalar. We argue that this flux can be detected in a laboratory experiment by using a superconducting solenoid surrounded by an electromagnetic calorimeter.
For definiteness, let us consider the Lagrangian density of the photon-pseudoscalar system 1 , where F µν is the electromagnetic stress tensor and F µν = ǫ µνρλ F ρλ its dual, a the pseudoscalar (axion) field, m the axion mass and M is its inverse coupling to the photon field. The coupling of the photon and pseudoscalar fields in this way means that a photon has a finite probability of mixing with its opposite polarisation and with the pseudoscalar in the presence of an external magnetic field [12,13,14]. The probability of the a → γ oscillation after traveling the distance L in the constant magnetic field with perpendicular component B is , n e is the electron density, m e is the electron mass, α is the fine-structure constant and ω is the photon (axion) energy.
The discussion of Ref. [10], based upon the Hillas plot presented there, suggests that for the PVLAS-favoured parameters, the maximal mixing between photons and axions takes place inside the source for most of the astrophysical objects which emit gamma rays. This fact does not depend on details of the emission mechanism and on the models of the source; it is based entirely on the information about the geometrical size of the objects and the magnetic fields in their outer regions, obtained from astronomical observations. This maximal mixing means that if the flux F γ of gamma rays is detected from the source, it should be inevitably accompanied by a flux F a = F γ /2 of axions of the same energy, if such strongly coupled axions exist (the factor 1/2 is due to complete mixing between two photon and one axion polarizations).
Let us concentrate first on the gamma rays with energies E 10 keV and estimate the contribution of various astrophysical sources to the axion flux. The signal at these energies would be dominated by pulsars and gamma-ray bursts since other sources, e.g. active galactic nuclei, contribute only at high energies (E 10 MeV) where fluxes are too low to be detected in a realistic experiment of the type we discuss.
Pulsars. For a typical magnetosphere of a neutron star we assume the magnetic field B ∼ 10 13 G at lengths L ∼ 10 km. Due to such extreme magnetic fields, the conditions for maximal mixing would be fulfilled at energies as low as E 10 −4 eV. To estimate the fluxes of axion like particles at E 100 MeV, we use EGRET data [15]; there are five pulsars detected which emit such hard gamma rays (see Table 1). The spectral index α is determined as where dN/dE is the flux and 100 MeV≤ E ≤ 10 GeV is the photon energy. The fluxes of these five objects at lower energies were extrapolated from 100 MeV down using the spectrum of the Crab pulsar (see e.g. Fig. 5 of Ref. [16] from which we find α ≈ 2.35 for 100 keV≤ E ≤ 100 MeV). The contribution of other pulsars, important at soft gamma-ray energies only, was estimated with the help of the INTEGRAL reference catalog [17]. In that reference, the sources' spectra are classified in different ways. The three relevant spectral models are the following: WP ("wabs powerlaw"): WHP ("wabs highcut powerlaw"): for Γ = 1, E cut = 10 keV, E fold = 15 keV. WC ("wabs cutoff"): For all models, w(E) is the Galactic absorption factor which is negligible at the level of approximations made in this paper and hence we set it equal to unity within our precision, S(E) is the spectral energy distribution and A is given in Table 2, where these pulsars are listed, for E 0 = 1 keV.
Gamma-ray bursts. The magnetic field in a gammaray burst (GRB) is B ∼ 10 9 G in a region of L ∼ 10 7 m, so the resonant mixing happens for E 1 eV. As an approximation we suppose that all GRBs have the same spectra which differ only by the peak fluxes. A useful compilation of models for the GRB fluxes may be found in Ref. [18]. For the spectral energy distribution of a GRB, we use the Band function [19]: We use the mean values of parameters seen by BATSE as given in Ref. [20]: A ≈ 0.01 keV −1 normalizes the Band function to one, To determine the dimensionfull coefficient in front of the Band function, we need to sum up the intensities of all GRBs for a given period of time. We use the distribution of the peak count rates of BATSE bursts from Ref. [21]. The data used is for the energy band between 50 keV and 300 keV, that is why we took this band in the normalisation. We performed the integration of the histogram in Fig. 23 of Ref. [21] and obtained approximately 10 5 photons/cm 2 /s/year for the sum of peak count rates of all BATSE-detected bursts. The peak count rate is 0.75 times the peak flux [21]. We have to correct also for the BATSE exposure (GRBs which happened when BATSE did not look at that part of the sky). According to Ref. [22], the exposure correction for 50÷300 keV is 0.480.
Finally, we have to relate the peak count rate and the total energy of a GRB. To this end, we use the temporal development of the spectrum. A universal parametrisation for it reads [23,24]: To relate A to the coefficient in the integral spectrum, we integrate the flux over time (the dimensionality of the following equation is photons/cm 2 /keV): We finally obtain the spectrum of our typical GRB with peak count rate P as 0.66 P photons/cm 2 /s B(E) photons cm 2 · keV .
In our assumption that all GRBs have the same spectra up to P , the total flux is obtained by taking P = 10 5 photons/cm 2 /s/year and dividing by the exposure factor, which results in the contribution of all GRBs of The total expected flux of astrophysical axions from pulsars and GRBs is plotted, as a function of energy, in Fig. 1.
Let us now consider possible ways in which these axionlike particles (a) could be detected in a laboratory experiment. One of the ideas of detection proposed a long time ago [25] for searching of solar axions is the following. If a is a long-lived particle, the flux of energetic a's would penetrate the Earth atmosphere without significant attenuation and would be observed in a detector via the inverse Primakoff effect, namely in the process of interaction of (pseudo)scalars with virtual photons from the static magnetic field of a superconducting magnet. An example of this kind of experiment on high-energy axion-photon conversion may be found in Refs. [26].
The sketch of the experiment we propose is shown in Fig. 2. The main design feature of the detector is the presence of a volume V of a high (≃ 1 T) magnetic field B with its internal surface covered with an electromagnetic calorimeter (ECAL) and surrounded by a VETO detector. The ECAL detects photons with energy E γ 10 keV. The VETO serves for efficient supression of environmental and cosmic backgrounds. The experimental signature of a → γ conversion is a single energetic photon detected in the ECAL (either through the photo electric effect or through Compton scattering) which will not be accompanied by any energy deposition in the VETO detector. Since the conversion happens due to the presence of the magnetic field, one could also search for it in the detector by comparing event rates in the ECAL taken with and without the magnetic field.
The statistical limit on the sensitivity of the experiment searching for cosmic a → γ conversion scales roughly as B 2 · V [25]. Thus, to improve the sensitivity, large volume and strong magnetic field are required. Since the gamma-ray (and potential axion) spectra from the astrophysical objects are steep, see Fig. 1, the detection of low- energy recoil electrons in the ECAL is also crucial for the improvement of the sensitivity of the search. As an example, Fig. 3 presents the number of events per year as a function of the detection energy threshold in a detector of 1m length and 1m radius filled with 1 Tesla magnetic field. The signal in such a detector will be optimised not for maximal mixing, as the mixing length in that situation will be much larger than the size of the detector. The presence of a non-zero electron density allow one to tune the mixing length so that the probability is increased, despite the fact that the mixing angle will be reduced. It is seen that at lower energies one expects thousands of events. Note that the majority of axions at these energies arrives from pulsars; as is seen from Tables 1, 2, there are only a few strong sources among them, hence the background might be reduced if the gamma direction can be determined. In any case, such matters would have to be considered in detail if one had to choose the actual orientation of the detector. A possible approach which could satisfy the requirements discussed above is to use a massive liquid argon time projection chamber (TPC) as the ECAL. The external region of the chamber could also be used as the VETO. An example of such a detector is the one being developed in the framework of the ArDM project for the search of the Dark Matter [27]. This experiment is designed to run with an effective target mass of almost 1 ton and is capable of measuring energy depositions as low as 10 keV.
The first results from a liquid argon TPC in a magnetic field look quite promising [28]. A small liquid argon Time Projection Chamber (LAr TPC) was operated for the first time in a magnetic field of 0.55 Tesla. The imaging properties of the detector were not affected by the magnetic field. In a test run with cosmic rays, a sample of through going and stopping muons was collected. The chamber with the readout electronics and the experimental setup are de-scribed in Ref. [28], where examples of reconstructed and analyzed events are presented.
The significance of the a-particles discovery with the proposed detector scales as [29]: where n s and n b are the number of detected signal and background events, respectively. Thus, assuming the PVLAS value for the axion-photon coupling, requiring that S 3 and assuming n s ≃ 10 2 at the ECAL energy threshold ≃ 0.1 MeV (see Figure 3) a background level of n b 3 event/day has to be achieved, which seems to be quite realistic [27].
One of the main sources of the background to a → γ events in the proposed experiment is expected from the neutrino processes with a significant electromagnetic component in the final state and with no significant energy deposition in the VETO. The expected amount of neutrino background events can be evaluated using Monte Carlo simulations. Assuming a total mass of the active part of the detector to be ≃ 1 ton, the neutrino background is estimated to be n b 1 event/day. Note that the above considerations give the correct order of magnitude for the sensitivity of the proposed experiment and may be strengthened and extended to the low recoil energy E 10 keV by more accurate and detailed Monte Carlo simulations.
Let us turn now to the lower energies. As it has been pointed out above, pulsars provide necessary conditions for maximal axion-photon mixing at E 1 eV. We note that, assuming the PVLAS-favoured couplings, keV-energy axions should be detected by CAST if it is pointed to the Crab pulsar. Such pointing was indeed performed [30] but the study has not yet been published. Given the Crab pulsar flux of about 2 photons/cm 2 /s in the energy interval 1 keV E 14 keV [16], one expects (for the PVLASfavoured parameters) ∼ 0.05 events per 24 hours of observation by CAST (to be compared with ∼ 7 events expected -and not observed -from the Sun for the minimal axion model with M ∼ 10 10 GeV). This flux can be tested by the experiment on the time scale of a year, given 3 hours of pointing per day. Other pulsars have much lower fluxes and give negligible contributions.
To summarize, the presence of an axion-like particle with PVLAS-favoured parameters, no matter what kind of interactions it has in the extreme conditions (e.g. inside the Sun), can be tested with dedicated experiments using particle-physics detectors of meter-scale size and Teslascale magnetic fields. At E 100 keV, several dosen events per year are expected in a ∼ 1 m 3 , ∼ 1 T detector. At the energies of a few keV, CAST (properly pointed) may detect about one event from the Crab pulsar per ∼ 480 hours observational time. Non-observation of the predicted number of events would disfavour the axion explanation of the PVLAS anomaly.