Photoproduction of axion-like particles

TL;DR

This paper investigates the potential of photon-beam experiments to detect axion-like particles (ALPs) with QCD-scale masses, introducing a new data-driven method to improve sensitivity and setting leading limits on ALP couplings.

Contribution

It presents a novel data-driven approach to enhance ALP detection sensitivity and explores the potential of existing and future experiments like PrimEx and GlueX for ALP searches.

Findings

PrimEx data could significantly improve ALP sensitivity in certain mass ranges.

First study of photoproduction sensitivity for ALPs coupled to gluons.

Set world-leading limits on ALP-gluon and ALP-photon couplings.

Abstract

We explore the sensitivity of photon-beam experiments to axion-like particles (ALPs) with QCD-scale masses whose dominant coupling to the Standard Model is either to photons or gluons. We introduce a novel data-driven method that eliminates the need for knowledge of nuclear form factors or the photon-beam flux when considering coherent Primakoff production off a nuclear target, and show that data collected by the PrimEx experiment could substantially improve the sensitivity to ALPs with $0.03 \lesssim m_a \lesssim 0.3$ GeV. Furthermore, we explore the potential sensitivity of running the GlueX experiment with a nuclear target and its planned PrimEx-like calorimeter. For the case where the dominant coupling is to gluons, we study photoproduction for the first time, and predict the future sensitivity of the GlueX experiment using its nominal proton target. Finally, we set world-leading limits for both the ALP-gluon coupling and the ALP-photon coupling based on public mass plots.

Tables

Table 1. Table S1: PrimEx \xspace data-taking conditions in both experimental runs.

PrimEx\xspacerun	target	thickness [$X_0$]	integrated luminosity [1/pb]	beam energy [GeV]
I	12C	5%	0.3	4.9–5.5
I	208Pb	5%	0.002	4.9–5.5
II	12C	8%	0.4	4.4–5.3
II	28Si	10%	0.3	4.4–5.3

Equations

$${\mathcal{L}}_{\mathrm{eff}}\supset \frac{c_{\gamma }}{4\Lambda }a{F}^{\mu \nu }{\tilde{F}}_{\mu \nu }-\frac{4\pi {\alpha }_s{c}_g}{\Lambda }a{G}^{\mu \nu }{\tilde{G}}_{\mu \nu },$$

$$\frac{d{\sigma }_{\gamma N\to aN}^{\mathrm{elastic}}}{dt}=\alpha Z_N^2{F}_N^2(t){\Gamma }_{a\to \gamma \gamma }\mathcal{H}(m_N,m_a,s,t),$$

$$\mathcal{H}(m_N,m_a,s,t)\equiv 128\pi \frac{m_N^4}{m_a^3}$$

$$\times \frac{m_a^{2}t(m_N^2+s)-m_a^4{m}_N^2-t((s-m_N^2{)}^2+st)}{t^2(s-m_N^2{)}^2(t-4m_N^2{)}^2}.$$

$$\frac{d{\sigma }_{\gamma N\to aN}^{\mathrm{elastic}}}{dt}=\frac{{\Gamma }_{a\to \gamma \gamma }}{{\Gamma }_{P\to \gamma \gamma }}\frac{\mathcal{H}(m_N,m_a,s,t)}{\mathcal{H}(m_N,m_P,s,t)}\frac{d{\sigma }_{\gamma N\to PN}^{\mathrm{elastic}}}{dt}.$$

$$\frac{d{\sigma }_{\gamma p\to ap}}{dt}\approx$$

$$\times \left[|⟨\mathbf{a}{\mathbf{\pi }}^0⟩{|}^2\frac{d{\sigma }_{\gamma p\to {\pi }^{0}p}}{dt}+|⟨\mathbf{a\eta }⟩{|}^2\frac{d{\sigma }_{\gamma p\to \eta p}}{dt}\right],$$

$$n_a(s,t)\approx$$

$$\displaystyle+|\langle\bm{a\eta}\rangle|^{2}\frac{n_{\eta}(s,t)\epsilon(m_{a},s,t)}{\mathcal{B}(\eta\to\gamma\gamma)\epsilon(m_{\eta},s,t)}\Bigg{]}\mathcal{B}(a\to\gamma\gamma)\,,$$

$$\gamma (k_{\gamma })+N(k_N)\to a(p_a)+X(p_X),$$

$$k_{\gamma }=(k,0,0,k),$$

$$k_N=(m_N,0,0,0),$$

$$p_a=\left(p,\sin \theta \sqrt{p^2-m_a^2},0,\cos \theta \sqrt{p^2-m_a^2}\right),$$

$$p_X=k_N+k_{\gamma }-p_a,$$

$$q=k_{\gamma }-p_a=(\omega ,\vec{q}).$$

$$s=(k_{\gamma }+k_N{)}^2=(p_a+p_X{)}^2=m_N^2+2m_{N}k,$$

$$t=(k_{\gamma }-p_a{)}^2=(k_N-p_X{)}^2,$$

$$u=(k_{\gamma }-p_X{)}^2=(p_a-k_N{)}^2,$$

$$m_X^2$$

$$i\mathcal{M}=e\frac{c_{\gamma }}{\Lambda }\frac{1}{t}{J}_{\mathrm{had}}^{\mu }{J}_{\gamma -a,\mu },$$

$${\left|\overline{\mathcal{M}}\right|}^2=e^2\frac{c_{\gamma }^2}{{\Lambda }^2}\frac{1}{t^2}{L}_{\mu \nu }{W}^{\mu \nu }.$$

$$W^{\mu \nu }=\sum _{\mathrm{had},\mathrm{avg}}{J}_{\mathrm{had}}^{\mu \ast }{J}_{\mathrm{had}}^{\nu }=-{\tilde{W}}_1\left(g^{\mu \nu }-\frac{q^{\mu }{q}^{\nu }}{t}\right)+{\tilde{W}}_2{V}_i^{\mu }{V}_i^{\nu },$$

$$V_i^{\mu }=\frac{1}{m_N}\left[k_N^{\mu }-\frac{q\cdot k_N}{t}{q}^{\mu }\right]=\frac{1}{m_N}\left[k_N^{\mu }+\frac{q^{\mu }}{2x}\right].$$

$$L^{\mu \nu }=-\frac{1}{8}{\left(t-m_a^2\right)}^2{g}^{\mu \nu }-\left(\frac{t-m_a^2}{4}\right)(k_{\gamma }^{\mu }{p}_a^{\nu }+k_{\gamma }^{\nu }{p}_a^{\mu })-\frac{m_a^2}{2}{k}_{\gamma }^{\nu }{k}_{\gamma }^{\mu }.$$

$$\frac{d^2\sigma }{d{m}_X^{2}dt}=\frac{-t}{2(t+m_N^2-m_X^2{)}^2}\frac{d^2\sigma }{dxdt}=\frac{1}{(s-m_N^2{)}^2}\frac{{\left|\overline{\mathcal{M}}\right|}^2}{16\pi }.$$

$$m_X^2\in \left[m_N^2,(\sqrt{s}-m_a{)}^2\right],t_0(t_1)={\left[\frac{m_X^2-m_a^2-m_N^2}{2\sqrt{s}}\right]}^2-{\left(k_{\mathrm{cm}}\mp p_{\mathrm{cm}}\right)}^2,$$

$$k_{\mathrm{cm}}=\frac{k{m}_N}{\sqrt{s}},p_{\mathrm{cm}}=\sqrt{{\left(\frac{s+m_a^2-m_X^2}{2\sqrt{s}}\right)}^2-m_a^2}.$$

$$W_T=m_N{R}_T=-\left(g_{ij}+\frac{q_i{q}_j}{|\vec{q}{|}^2}\right)W^{ij},W_L=m_N{R}_L=W^{00}.$$

$$W_T=2{\tilde{W}}_1,W_L=-{\tilde{W}}_1\left(1-\frac{t}{4x^2{m}_N^2}\right)+{\tilde{W}}_2{\left(1-\frac{t}{4x^2{m}_N^2}\right)}^2.$$

$${\tilde{W}}_1=\frac{1}{2}{W}_T,{\tilde{W}}_2={\rho }^2{W}_L+\frac{\rho }{2}{W}_T.$$

$$W_{T,L}=W_{T,L}^{(n)}+W_{T,L}^{(p)}.$$

$$W_{L,T}^{(a)}=$$

$$\kappa$$

$$\lambda$$

$$\tau$$

Full text

††preprint: CERN-TH-2019-023

Axion-like particles (ALPs) are hypothetical pseudoscalars found in many proposed extensions to the Standard Model (SM), since they naturally address the Strong $CP$ Peccei:1977hh ; Peccei:1977ur ; Weinberg:1977ma ; Wilczek:1977pj and Hierarchy problems Graham:2015cka . Furthermore, ALPs may explain the muon magnetic moment anomaly Chang:2000ii ; Marciano:2016yhf , and could connect SM particles to dark matter by providing a portal Nomura:2008ru ; Freytsis:2010ne ; Dolan:2014ska ; Hochberg:2018rjs . The couplings of ALPs to the SM are highly suppressed at low energies by a large cut-off scale $\Lambda$; however, since ALPs, $a$, are pseudo-Nambu-Goldstone bosons, their mass $(m_{a})$ can be much smaller than the scale that controls their dynamics, i.e. $m_{a}\ll\Lambda\,$. Recently, ALPs with MeV-to-GeV scale masses, henceforth QCD scale, have received considerable interest Marciano:2016yhf ; Jaeckel:2015jla ; Dobrich:2015jyk ; Izaguirre:2016dfi ; Knapen:2016moh ; Mariotti:2017vtv ; Bauer:2017ris ; CidVidal:2018blh ; Bauer:2018uxu ; Harland-Lang:2019zur ; Ebadi:2019gij ; Mimasu:2014nea ; Brivio:2017ije (see, in addition, Refs.Essig:2013lka ; Marsh:2015xka ; Graham:2015ouw ; Irastorza:2018dyq ; Beacham:2019nyx for recent ALP reviews).

In this Letter, we explore the discovery potential of photon-beam experiments for ALPs with QCD-scale masses. Specifically, we consider two cases: ALPs whose dominant coupling to SM particles is to photons or to gluons. For the former, the best sensitivity involves coherent Primakoff production off a nuclear target (see Fig. 1 top). While ALP production using the Primakoff process has been studied before GasparianTalk ; Marciano:2016yhf , our work is novel in three aspects: (i) we introduce a fully data-driven ALP normalization method, which eliminates the need for knowledge of nuclear form factors or the photon-beam flux; (ii) we show that data collected by the PrimEx\xspaceexperiment at Jefferson Lab could substantially improve the sensitivity to ALPs with $0.03\lesssim m_{a}\lesssim 0.3$ GeV, in fact, we are able to set world-leading limits from a diphoton mass plot published in Ref. Larin:2010kq from a single angular bin; and (iii) we explore for the first time the potential sensitivity of running the GlueX\xspaceexperiment at Jefferson Lab with a nuclear target and its planned PrimEx\xspace-like calorimeter. For the case where the dominant SM coupling of ALPs is to gluons, we extend our work in Ref. Aloni:2018vki and study photoproduction for the first time. The dominant photoproduction mechanism is photon–vector-meson mixing and $t$-channel vector-meson exchange (see Fig. 1 bottom). We obtain the future sensitivity of the GlueX\xspaceexperiment using its nominal proton target, and set world-leading limits based on a public mass plot.

The effective Lagrangian describing the interactions of ALPs with photons and gluons is

[TABLE]

where $F_{\mu\nu}\,(G_{\mu\nu})$ is the photon (gluon) field strength tensor with $\tilde{F}_{\mu\nu}=\frac{1}{2}\epsilon_{\mu\nu\alpha\beta}F^{\alpha\beta}$ ($\tilde{G}_{\mu\nu}$ satisfies a similar expression). Our approach to studying ALP-hadron interactions follows Refs. Georgi:1986df ; Bardeen:1986yb ; Krauss:1986bq , and we take the ALP-pseudoscalar mixing, along with the ALP lifetime and branching fractions, directly from Ref. Aloni:2018vki . The two scenarios considered in this Letter correspond to $c_{g}\!=\!0$, $c_{\gamma}\!=\!1$ and $c_{g}\!=\!1$, $c_{\gamma}\!=\!0$; however, we stress that our results can be generalized to any other set of ALP couplings to the SM particles (see Ref. Aloni:2018vki ).

First, we consider the case where the dominant ALP-SM coupling is to photons. When a photon beam is incident on a nuclear target, the production of pseudoscalars—either the mesons $P=\pi^{0},\eta$ or ALPs—at forward angles is dominantly via the coherent Primakoff process for $m_{a,P}\lesssim 1$ GeV. The differential cross section for elastic coherent Primakoff production from a nucleus, $N$, is given by

[TABLE]

where $t$ and $s$ are the Mandelstam variables, $F_{N}$ is the nuclear form factor (see the Supplemental Material SuppMat to this Letter and Refs. RevModPhys.29.144 ; PhysRevLett.8.110 ; PDG ), $\Gamma_{a\to\gamma\gamma}=c^{2}_{\gamma}m^{3}_{a}/(64\pi\Lambda^{2})$ is the partial decay width of the decay $a\to\gamma\gamma$, and

[TABLE]

For pseudoscalar mesons, the corresponding differential cross section is obtained by the replacement $a\to P$.

For small values of $t$ (forward angles), where elastic coherent Primakoff production is dominant, the nuclear form factor dependence can be canceled by forming the ratio of the ALP and $P$ differential cross sections as follows:

[TABLE]

Therefore, the ALP yield—up to a factor of the model parameters $(c_{\gamma}/\Lambda)^{2}$—can be determined from the observed $\pi^{0}$ and/or $\eta$ Primakoff yields, making this a completely data-driven search. The nuclear form factor does not need to be known, and the photon flux also cancels using our approach. A correction must be applied to account for any mass dependence in the detector efficiency at fixed $t$ and $s$, though this should be easy to obtain from simulation given that the $a\to\gamma\gamma$ decay distribution is known (it must be uniform in the $a$ rest frame). Finally, we note that quasi-elastic ALP Primakoff production can be estimated using a similar approach; however, this production mechanism is negligible in the $m_{a}$ range considered here (see the Supplemental Material SuppMat ).

The first run of the PrimEx\xspaceexperiment was in Hall B at Jefferson Lab in 2004 Larin:2010kq . Data were collected on both C and Pb targets using a 4.9–5.5 GeV photon beam and a high-resolution multichannel calorimeter, which allowed PrimEx\xspaceto make the most precise measurement to date of the $\pi^{0}\to\gamma\gamma$ decay width. The integrated luminosities were 0.3/pb for C and 0.002/pb for Pb. A follow-up run of PrimEx\xspacewas performed in 2010, which collected 0.4/pb on C and 0.3/pb on Si, though only preliminary results have been produced thus far from this data set.

Reference Larin:2010kq published the diphoton mass spectrum near the $\pi^{0}$ peak for one forward angular bin from the C data obtained in the first PrimEx\xspacerun (see Fig. 2 of Ref. Larin:2010kq ). The diphoton efficiency is roughly constant within such a small angular and mass window; therefore, using the observed $\pi^{0}$ yield in the published peak (${\approx 5100}$) and the background yield at each $m_{\gamma\gamma}$, we can use Eq. (4) to place constraints on $\Lambda$ for $c_{\gamma}=1$ and $c_{g}=0$. For example, at $m_{a}=0.11$ GeV the background in a $\pm 2\sigma$ window is $\approx 300$ giving a rough estimate of the sensitivity to the ALP yield of $\approx 2\sqrt{300}$. Using Eq. (4) we estimate this corresponds to $\Lambda\approx 0.6$ TeV, which is comparable to the world-leading constraint from LEP at this mass Abbiendi:2002je ; Knapen:2016moh . In the Supplemental Material SuppMat , we perform a more rigorous study of this spectrum, the results of which are shown in Fig. 2 and confirm that this small fraction of the PrimEx\xspacedata sample provides competitive sensitivity to LEP—and even gives world-leading constraints at a few masses.

To estimate the sensitivity of each PrimEx\xspacedata sample, i.e. not just the one bin shown in Fig. 2 of Ref. Larin:2010kq , we need to determine the mass dependence of the efficiency and to estimate the background versus $m_{\gamma\gamma}$ in each sample. A detailed description of this part of the analysis is provided in the Supplemental Material SuppMat , and briefly summarized here. We assume that the same selection criteria applied in Ref. Larin:2010kq are used for the ALP search and take the PrimEx\xspacecalorimeter acceptance and resolution from Refs. kubantsev2006performance ; larin2011new . Furthermore, we assume that the ALP bump hunt will only use candidates with $\theta_{\gamma\gamma}<0.5^{\circ}$, where $\pi^{0}$ production is dominated by the Primakoff process for all targets.

Using the known nuclear form factors and Primakoff differential cross section Donnelly:2017aaa ; Alberico:1988bv ; DeJager:1974liz , we generate Primakoff $\pi^{0}$ Monte Carlo events for the PrimEx\xspacephoton-beam energy. We require that both photons from the $\pi^{0}\to\gamma\gamma$ decay are in the PrimEx\xspacecalorimeter fiducial acceptance region Larin:2010kq and apply the required smearing to account for resolution. The width of our Monte Carlo $\pi^{0}$ peak is consistent with the data in Ref. Larin:2010kq . We then apply the full selection of Ref. Larin:2010kq and find that our predicted $\pi^{0}$ Primakoff yields are consistent with those observed in Refs. PrimExPAC33 ; YangThesis . We assume that the reconstruction efficiency is independent of the ALP mass in the search region (excluding geometrical acceptance effects). In addition, we discard the low-$m_{a}$ region where the photon clusters begin to overlap and the acceptance has strong mass dependence. Lower masses can likely be explored in an analysis of the actual PrimEx\xspacedata with access to a full detector simulation.

As in any bump hunt, obtaining a data-driven background estimate is straightforward using the $m_{\gamma\gamma}$ sidebands at each $m_{a}$ (see, e.g., Refs. Williams:2015xfa ; Williams:2017gwf ). However, estimating the background without the data is considerably more difficult, so we adopt a conservative approach. We considered many possible backgrounds, e.g. $\gamma N\to N\omega(\pi^{0}[\gamma\gamma]\gamma)$ where one photon is not reconstructed or the $\pi^{0}$ photons are merged into a single cluster, though we found that no hadronic reactions are capable of contributing background at a rate comparable to that observed in Fig. 2 of Ref. Larin:2010kq in the mass range probed by PrimEx\xspace. Thus, we conclude that the PrimEx\xspacebackground is dominantly due to electromagnetic interactions of the photon beam with the target that produce either additional photons or $e^{+}e^{-}$ pairs. Figure 2 of Ref. Larin:2010kq shows the forward-most angular region. Given that the beam backgrounds should decrease moving away from the beam line, using this angular bin—and assuming a uniformly distributed background—provides a conservative background estimate. We also conservatively assume that the background density above (below) the $m_{\gamma\gamma}$ region shown in Fig. 2 of Ref. Larin:2010kq takes on the value at the upper-most (lower-most) bin of the published $m_{\gamma\gamma}$ spectrum. Finally, we scale the beam-induced background, which is shown for the first C run, by the product of the target radiation length and the number of photons on target for other PrimEx\xspaceruns.

Our projected sensitivity for the entire PrimEx\xspacedata sample is shown in Fig. 2, i.e. our estimate combines all of the PrimEx\xspaceruns. The PrimEx\xspacesensitivity would be substantially better than LEP for $0.03\lesssim m_{a}\lesssim 0.3$ GeV and provide world-leading sensitivity up to about 0.4 GeV. We stress again that the PrimEx\xspacedata are already on tape, and are well calibrated and understood. All that is needed is to perform a bump hunt on the forward-angle data in the region dominated by Primakoff production. Following the approach we proposed above, the normalization can be done in a purely data-driven way using the observed $\pi^{0}$ Primakoff yield differentially versus $t$.

An updated version of the PrimEx\xspaceexperiment recently ran in Hall D at Jefferson Lab using the GlueX\xspacedetector with an additional small-angle calorimeter Primakoff2010 . This new experiment has the potential to explore higher masses than PrimEx\xspacedue to the higher photon-beam energy of 11 GeV and the larger acceptance of the GlueX\xspaceforward calorimeter; however, the use of a helium target in this new run makes it less sensitive than PrimEx\xspacefor ALPs. There are several proposals for future GlueX\xspacerunning with heavy nuclear targets PAC , so it is interesting to explore the potential sensitivity to ALPs of such runs. Specifically, we consider a Pb target here. We take the GlueX\xspaceacceptance, efficiency, and resolution from Refs. beattie2018construction ; hardin2018upgrading , and the corresponding values for the small-angle calorimeter from Ref. Primakoff2010 . For $m_{a}<m_{\eta}$, we rescale the expected beam background from the PrimEx\xspacePb run. There are three additional backgrounds that contribute to the GlueX\xspacerun at higher masses: Primakoff production of $\eta$ and $\eta^{\prime}$ mesons, and coherent nuclear production of $\gamma N\to N\omega(\pi^{0}[\gamma\gamma]\gamma)$ (as described above). The cross sections for these processes are well known, making it straightforward to estimate their yields using Monte Carlo.

An additional complication arises when projecting the sensitivity of GlueX\xspace. The GlueX\xspaceexperiment could explore regions of ALP parameter space where the ALP flight distance becomes nonnegligible. Using Monte Carlo, we estimate that the impact on the ALP mass resolution and acceptance is small provided that its lab-frame flight distance is $\lesssim 30$ cm (the length of the nominal liquid hydrogen target cell). For simplicity, we apply a fiducial cut on the flight distance at 30 cm, which is conservative since ALPs that decay after this distance could still be detected and a detailed study could determine the appropriate signal shape for each value of $\Lambda$. Our estimate of the projected reach for GlueX\xspaceincluding the PrimEx\xspace-like calorimeter is shown in Fig. 2. The larger data set assumes that as much data is collected as is expected in the full GlueX\xspaceproton-target run. The smaller data set corresponds to collecting 1/pb of Pb-target data.

Figure 2 shows that Primakoff production using photon beams can provide unique sensitivity to ALPs. The data from PrimEx\xspace, which has been on tape for a decade, could provide substantially better sensitivity than LEP for $0.03\lesssim m_{a}\lesssim 0.3$ GeV. Running the GlueX\xspaceexperiment for a few years with a Pb target and its PrimEx\xspace-like small-angle calorimeter could explore the remaining parameter space down to where future beam-dump experiments will have sensitivity. Much of this parameter space is not accessible at any other current or proposed future experiment.

We now move on to considering the case where the dominant ALP-SM coupling is to gluons. In this scenario, nuclear targets do not provide a large advantage since both the signal and background scale similarly with the number of nucleons, so we consider the nominal liquid-hydrogen target and default experimental GlueX\xspacesetup, which has been running for the past few years. When a photon beam is incident on a proton target, exclusive pseudoscalar production is dominantly via photon–vector-meson mixing as shown in Fig. 1 bottom. In the Supplemental Material SuppMat , we show that—once both $\pi^{0}$ and $\eta$ photoproduction are well understood—it is possible to derive a fully data-driven normalization strategy similar to the one we proposed above for Primakoff production. As discussed in Ref. AlGhoul:2017nbp , $\eta$ production at GlueX\xspaceenergies, while clearly dominantly $t$-channel, is not yet fully understood. Therefore, we will adopt a simplified approach below, though we do provide a complete description of how to implement the fully data-driven strategy for future searches in the Supplemental Material SuppMat .

In principle, ALP searches at GlueX\xspacecould look for hadronic final states like $a\to 3\pi$ and $a\to\eta\pi\pi$; however, we studied these and found that the mass resolution at GlueX\xspacemakes ALP peaks comparable in width to $\omega,\eta^{\prime},\phi\to 3\pi$ and $\eta^{\prime},f_{2}\to\eta\pi\pi$ making it likely that large mass regions need to be vetoed in such searches. Furthermore, the sensitivity at higher masses would not be competitive with $b$ -hadron decays Aloni:2018vki . Therefore, we choose to focus on the $a\to\gamma\gamma$ decay in the region between the $\pi^{0}$ and $\eta$ mesons, where its branching fraction is close to unity and diphoton backgrounds are small. Since $a\to\pi\pi$ and $a\to\pi^{0}\gamma$ are forbidden by $CP$ and $C$, respectively, the $a\to\gamma\gamma$ decay is dominant in all ALP models in most of this mass region.

For $m_{\pi^{0}}<m_{a}<m_{\eta}$, the ALP-gluon coupling can be replaced by ALP–pseudoscalar-meson mixing by performing a chiral transformation of the light-quark fields Georgi:1986df ; Bardeen:1986yb ; Krauss:1986bq . Following Ref. Aloni:2018vki , we denote the mixing of the ALP with the $\pi^{0}$ and $\eta$ as $\langle\bm{a\pi^{0}}\rangle$ and $\langle\bm{a\eta}\rangle$, respectively, and we take these $m_{a}$-dependent mixings directly from Ref. Aloni:2018vki . For $|t|\lesssim 1$ GeV2 in this $m_{a}$ region, at fixed $s$ and $t$ the following approximation is valid to $\mathcal{O}(1)$, which is roughly the same fidelity with which the ALP-pseudoscalar mixing terms are known:

[TABLE]

where $f_{\pi}$ and $f_{a}=\Lambda/(32\pi^{2}c_{g})$ are the pion and ALP decay constants. This approximation works well in this mass range due to the dominance of the contributions from $\pi^{0}$ or $\eta$ mixing to the ALP $U(3)$ representation. We adopt the relevant numerical values from Refs. Fujiwara:1984mp ; Machleidt:1987hj ; Mathieu:2015eia , see Supplemental Material for details.

Ref. AlGhoul:2017nbp published the $m_{\gamma\gamma}$ spectrum, along with the yields and efficiencies versus $t$ of both the $\pi^{0}$ and $\eta$ mesons. In the Supplemental Material, we perform a bump hunt of the $m_{\gamma\gamma}$ spectrum to obtain upper limits on the ALP yield at each $m_{a}$. The expected ALP yield in a small bin of $[s,t]$ is related to $\Lambda$ (or $f_{a}$) using Eq. (5) according to

[TABLE]

where $\epsilon$ denotes the product of the detector acceptance and efficiency. We linearly interpolate the efficiencies given in Ref. AlGhoul:2017nbp at $m_{\pi^{0}}$ and $m_{\eta}$ for $m_{a}$, and confirm this approach is valid to $\mathcal{O}(10\%)$ using toy Monte Carlo as described in the Supplemental Material SuppMat (additionally, the same ALP lifetime correction is applied here, though this is a small correction). The total expected ALP yield is simply the sum of $n_{a}(s,t)$ over all bins. By comparing the expected ALP yields to the upper limits obtained from the bump hunt of the $m_{\gamma\gamma}$ spectrum, we place constraints on $c_{g}/\Lambda$ (see Fig. 3). These limits are the best over some of the $0.15<m_{a}<0.46$ GeV region. Finally, we also provide the expected sensitivity from a 1/fb GlueX\xspacedata set, which is substantially better than any existing limits over most of this mass region.

In summary, we explored the sensitivity of photon-beam experiments to ALPs with QCD-scale masses whose dominant coupling is to either photons or gluons. For the photon-dominant coupling scenario, we introduced a novel data-driven method that eliminates the need for knowledge of nuclear form factors or the photon-beam flux when considering coherent Primakoff production off of a nuclear target, and showed that data collected by PrimEx\xspacecould substantially improve the sensitivity to ALPs with $0.03\lesssim m_{a}\lesssim 0.3$ GeV. We also explored the potential sensitivity of running the GlueX\xspaceexperiment with a nuclear target. For the case where the dominant coupling is to gluons, we studied photoproduction for the first time, and predicted the future sensitivity of the GlueX\xspaceexperiment using its nominal proton target. For both scenarios, we set world-leading limits based on public mass plots.