Implications of the dark axion portal for SHiP and FASER and the advantages of monophoton signals

We investigate the implications of the dark axion portal interaction, the axion-photon-dark photon vertex, for the future experiments SHiP and FASER. We also study the phenomenology of the combined vector portal (kinetic mixing of the photon and dark photon) and dark axion portal. The muon $g-2$ discrepancy is unfortunately not solved even with the two portals, but the low-energy beam dump experiments with monophoton detection capability can open new opportunities in light dark sector searches using the combined portals.


I. INTRODUCTION
The existence of dark matter is one of the most important motivators for new physics scenarios. The Standard Model (SM) can only explain about 5% of the total energy budget of the Universe, while dark matter is expected to make up a much larger 27% [1]. Although the weakly interacting massive particle (WIMP) picture has been a driving force in dark matter studies, the atmosphere has changed somewhat in the past decade due in part to the absence of signals after extensive searches by both underground and collider experiments [2]. Among the various alternative pictures that have been put forward are that the dark sector could contain multiple different dark sector particles such as dark fermions, dark Higgs, the dark photon, and axions.
Communication between the dark sector and the SM can be established through the concept of a 'portal.' For instance, the vector portal connects the SM photon to the dark photon through kinetic mixing [3] and the axion portals such as the axion-photon-photon vertex connects the axion to two SM particles [4]. These portals have been widely used by experiments to search for dark sector particles [5]. Recently, a new portal called 'dark axion portal' was suggested that connects both the axion and dark photon to the SM through axion-photon-dark photon as well as axion-dark photon-dark photon vertices, which can be exploited to study the axion and dark photon without relying on the two existing portals [6].
There have been several previous studies using this portal (for examples, see Refs. [7][8][9][10][11][12][13][14]). Of particular relevance to this work, Ref. [13] studied how measurements of lepton g−2 and experiments such as B-factories, fixed target neutrino experiments and beam dump experiments could be used to constrain the dark axion portal coupling G aγγ . The primary purposes of this paper are (i) to study the implications of the dark axion portal for the future experiments SHiP and FASER, and (ii) to explore new channels that become available when we consider both the vector portal and the dark axion portal. For the latter, we discuss whether the 3.5σ level muon g − 2 anomaly [1] can be explained in the presence of the two portals, and also point out substantial advan-tages in exploring the combined dark sector if monophoton searches can be implemented in beam dump experiments.
The rest of the paper is organized as follows. In Sec. II, we provide a short overview of the dark axion portal and define our parameterization. In Sec. III, we calculate the projected sensitivity of the SHiP experiment using CERN's SPS proton beamline. In Sec. IV, we calculate the projected sensitivity of the FASER and FASER 2 experiments at the LHC. In Sec. V, we show that a combination of the vector and dark axion portals is incapable of explaining the muon g − 2 discrepancy due to constraints on the coupling strengths of the two portals. In Sec. VI, we discuss how a beam dump experiment exploiting the monophoton signal may be used to probe a combination of the dark axion and vector portals. In Sec. VII, we summarize the results.

II. DARK AXION PORTAL
The axion and dark axion portals introduce the following new interaction terms, where a stands for the axion (or axion-like particle), and G µν , F µν , Z µν stand for the gluon (g), photon (γ), and dark photon (γ ) field strengths, respectively. The axion and dark axion portals are produced through anomaly triangles although the exact couplings are dependent on the underlying model. An example implementation through the dark KSVZ model can be found in Ref. [6]. The vector portal is compatible with the dark axion portal, and introduces a kinetic mixing (parameterized by ε) between the photon and the dark photon, We will assume the same setup as Ref. [13], that is that m a m γ , and that the model-dependent parameters The branching ratio of γ → ae + e − and γ → aµ + µ − through the dark axion portal in the ma m γ limit. The leptonic decay processes are forbidden for m γ < 2m ( = e, µ). The slight dip near 0.8 GeV is due to the presence of hadronic decay channels.
are arranged such that G aγγ is sufficiently small that its effects can be neglected in the processes considered in this paper. The small mass m a ensures that the a is long-lived on the time scales considered by beam dump and fixed target experiments. We will focus on the effects of the new G aγγ coupling introduced by the dark axion portal in the regime where kinetic mixing ε = 0 in sections III and IV and consider the case where both portals are open afterward.
It is worthwhile to mention that the G aγγ coupling could potentially be constrained directly or indirectly by channels we do not consider in this paper. Directly by considering the astroparticle phenomena such as the stellar cooling or horizontal branch stars; indirectly by the relation between the G aγγ and G aγγ depending on the model. In this paper, however, we limit ourselves only to controlled laboratory experiments and study what they tell us about the direct constraints and implications of the new portal.
The dark photon γ may decay through a number of different channels in the dark axion model. The twobody decay γ → aγ through the dark axion portal is the dominant channel with a decay width The three-body decay processes γ → e + e − a and γ → µ + µ − a are also possible, with a branching fraction of a few percent that increases with m γ , as shown in Fig.  1. While not dominant, these channels provide a signature very similar to the lepton anti-lepton signal used to search for kinetically mixed visibly decaying dark photons, and those searches can be repurposed as probes of the dark axion portal. Limits on G aγγ from high intensity experiments and the projected sensitivity of the SHiP experiment for ma m γ with ε = 0. The limits from LSND and Mini-BooNE come from excess neutral current-like elastic scattering events above expected the background from neutrino and non-neutrino SM sources. The CHARM constraint reflects sensitivity to monophoton production through γ → aγ decays in the CHARM fine-grain detector. The electron and muon g-2 lines indicate where the scenario would degrade the agreement between theory and experiment by more than 2σ. The BaBar and Belle-II lines all represent exclusions from monophoton excesses through the annihilation process e + e − → a(γ → aγ). Further details on these limits can be found in Ref. [13]. The SHiP projection denotes an excess of greater than 3 e + e − events reaching the SHiP electromagnetic calorimeter produced through the decay γ → ae + e − , while the FASER and FASER 2 projections reflect the same for 2.3 events.

III. SHIP
The Search for Hidden Particles (SHiP) [15,16] is a proposed proton beam dump experiment using the CERN SPS. They plan to impact 2 × 10 20 protons with 400 GeV of energy onto a molybdenum target over five years of running. The current plans call for both a neutrino detector capable of searching for ν τ interactions and a decay pipe followed by electron and hadron calorimeters to search for the decays of rare, long-lived particles. This analysis will focus on dark axion portal signals visible in the SHiP decay volume: electron-positron pair production and a monophoton signal.
We will follow the γ search of Ref. [17] with some input from Refs. [18,19] for a possible decay volume and detector geometry. We assume a 50-meter long cylindrical decay pipe with a diameter of 5 meters. The upstream face of the cylinder is located 50 meters from the production target and is parallel to the beamline with no horizontal or vertical offset.
Following previous work in modeling dark axion portal production at the CHARM experiment in Ref. [13], we consider production through the decays of the pseudoscalar mesons π 0 and η. The neutral pseudoscalar mesons are produced in large quantities at fixed target and beam dump experiments, though rarely studied as they do not supply significant background or signal without the introduction of New Physics. The rare decays through the dark axion portal π 0 , η → aγγ provide an important source of dark photons whose visible decay products could be detected in beam dump experiments like SHiP. We could also consider production through bremsstrahlung, though the required 2 → 4 production process is expected to suppress the overall production rate significantly.
The simulation of the production, propagation, and decay of dark axion portal particles was performed with a modified version of the BdNMC software package [20]. The simulation of pseudoscalar meson decays requires knowledge of the angular-momentum production distributions for both the π 0 and η, as well as an estimate of the overall production rate. As neither meson's production distribution has been studied in detail by fixed target experiments, a reasonable alternative is to use the mean of a pair of appropriate π + and π − distributions, as this closely matches the expected π 0 momentum distribution at energies far above the pion mass [21,22]. The η distribution is quite similar to the π 0 distribution when it is above threshold production energies, and we will use the same distribution for both particles. For SHiP energies, we adopt the charged pion distributions of Ref. [23], collectively denoted the BMPT distribution, as they are suitable for a variety of target materials and beam energies.
The overall π 0 production rate N π 0 was estimated to be approximately 2.7 per Proton on Target (POT) in Ref. [19]. Note that the number of γ per POT normalized by ε −2 was calculated to be 5.41. The branching ratio of [24], and neglecting the mass dependent phase space factors, we can divide by two to obtain the estimated number of π 0 s per POT. This estimate is slightly larger than but not inconsistent with those used previously in Refs. [15,20]. The η production rate is scaled to that of the π 0 . For the SHiP energy, we take N η = 0.1 × N π 0 [19].
Sample meson 4-momenta are generated from the BMPT distribution using a simple acceptance-rejection algorithm. As the lifetime of the π 0 and η are extremely short at O(10 −17 s) or less [1], they do not propagate a significant distance before decaying. We simulate the three-body decay π 0 , η → aγγ as described in Ref. [13], discarding the γ and a 4-momenta as they do not contribute to the SHiP decay signal. The resulting list of γ 4-momenta is used to calculate the expected dark axion portal signal.
The probability that a γ with label i decays inside the SHiP decay pipe through an observable channel is given by where • E i is the energy of the γ , • τ is the lifetime of a γ with mass m γ and coupling strength G aγγ , • L 1,i is the distance the γ propagates before entering the decay volume, and • L 2,i is the total distance travelled before exiting the decay volume.
Each γ is decayed into an ae + e − final state. In order for this state to be accepted, both leptons must intersect with the end cap of the decay volume in order to enter the SHiP calorimeters, and the momenta must satisfy p e + , p e − > 1 GeV [17]. The total event rate expected from the decays of meson j can be calculated as • P decay,i = 0 if the γ does not intersect the detector, • θ(p e + ,i , p e − ,i ) = 1 if the end-state leptons satisfy the cuts mentioned above and 0 otherwise, • eff = 1 is the detection efficiency, and • N trials is the total number of γ trajectories generated.
The total event rate is found by summing over j. The projected sensitivity curve in Fig. 2 was generated by scanning the dark axion parameter space in G aγγ and m γ . We assume zero background, and therefore exclude the scenario when the predicted number of events generated N event > 3. Note that the signal weakens considerably as m γ → 2m e , as the decay width of γ → ae + e − becomes heavily suppressed by the available phase space, as shown in Fig. 1. The branching ratio suppression is not reflected in the otherwise similar CHARM limit, as it instead considered a monophoton signal produced through γ → aγ. Despite sizeable backgrounds, the monophoton search at CHARM was considerably more sensitive than a search for e + e − final states. SHiP may benefit from a similar monophoton search, but this would require an estimate of the expected monophoton backgrounds, the analysis of which is currently in progress (private communication with Walter Bonivento, January 2019). To illustrate the potential of a SHiP monophoton search, we have simulated the potential signal, requiring that the emitted photon intersects with the end of the SHiP decay pipe and possess energy larger than 2 GeV to match the combined energy of the The monophoton search does not suffer any suppression in its sensitivity for m γ ≈ 2me, and is therefore capable of greatly improving upon the electron-positron signal at low masses. The 100-event contour matches or surpasses the zero-background electron-positron contour over the entire parameter space of interest. Note that this is not a projection of sensitivity, as the actual backgrounds could be substantially worse and will require study by the collaboration to estimate.
electron and positron. In Fig. 3, we show the contour where SHiP would observe 100 events, as was used in the CHARM monophoton analysis. Note that the SHiP monophoton contour does not suffer from the suppression in signal strength at m γ ≈ 2m e exhibited by the SHiP electron-positron signal.
There are a few interesting comments to be made about this search: • We have assumed that the a possesses a lifetime sufficiently long to not decay on the timescale required to travel from the SHiP target to the SHiP decay volume, but this is not essential to the analysis. There is no requirement that the a produced through meson decay survive to reach the detector, and the secondary a produced through the γ → ae + e − would result in a diphoton coincident with the e + e − signal. The additional particles could either be ignored or an additional analysis could search for this more complicated endstate. A search for γ → aγ would also need to consider a three-photon final state produced through the axion portal decay a → γγ. The advantage of these more complex final states is that all of the 4-momentum would be accounted for, rendering it possible to reconstruct the mass of the γ if the uncertainties in the measured energies are sufficiently small while simultaneously providing a window into the interactions of the a.
• We did not consider the aµ + µ − final state, nor the possibility of bremsstrahlung γ production through the dark axion portal, but their inclusion may extend SHiP's sensitivity to slightly larger values of m γ .

IV. FASER
The ForwArd Search ExpeRiment (FASER) [25][26][27] is a proposed experiment with sensitivity to weakly coupled, long-lived particles at the LHC. Searches for longlived particles with high transverse momenta are difficult at the LHC due to the small Standard Model production cross sections for such particles. By placing a detector in the far-forward region of an existing LHC interaction point, FASER can search for low transverse momentum, long-lived particles for which the production cross section is much larger. The planned location of FASER is 480 m downstream from an LHC interaction point, by which point the beam has curved away, and the intervening rock and dirt have removed most SM particles. FASER would then search for the visible decays of weakly-coupled longlived particles, taking advantage of the extremely high boost from the high energy of the LHC to extend their lifespans.
The FASER collaboration has performed a preliminary analysis of its sensitivity to visible dark photon decays in Refs. [26,28], and we will be adopting these searches to the dark axion portal. The inelastic proton-proton cross section was measured to be σ inelastic ∼ 75 mb during the 13 TeV LHC run, and is not expected to differ greatly for the 14 TeV collisions of LHC Run 3. The total number of inelastic collisions is therefore expected to be N inelastic ≈ 1.1 × 10 16 for 150 fb −1 in LHC Run 3.
As with the beam dump experiments studied previously, we expect π 0 and η decays to provide the primary source of dark axion portal particles. The π 0 and η production rates and distributions were generated with EPOS-LHC [29] through the CRMC v1.7 framework [30]. Note that these rates were also compared with SIBYLL v2.3 and found to be consistent at the small angles required by FASER [31,32]. The total number of π 0 s (ηs) per interaction in one hemisphere of the interaction point was calculated to be 19 (2.1). The production estimate is conservative, as we would also expect secondary meson production to result from other collision products impacting on material between the interaction point and the FASER detector.
For this analysis, FASER is assumed to be a 1.5 m long cylindrical decay region with 10 cm radius located 480 m from the interaction point operating during LHC Run 3. We will also consider the sensitivity of a hypothetical FASER 2 detector, a 5 m cylinder with 1 m radius located 480 m downstream from the interaction point. FASER 2 would take data during the high luminosity LHC runs with an expected luminosity 20 times larger than that of LHC Run 3.
that of the kinetically mixed dark photon. We will follow the cuts imposed by the FASER dark photon analysis: The dark photon must decay in the decay volume, both the electron and positron must cross through the downstream face of the decay volume, and the total visible energy must satisfy E e + + E e − > 100 GeV. If we only consider mesons with energies greater than 100 GeV, the number of π 0 s (ηs) per POT drops to 2.43 (0.43) in the hemisphere facing FASER.
We assume negligible background and therefore impose a cut on the parameter space predicted to generate more than 2.3 events. We show the resulting contours in Fig.  2, where the small inner contour represents the sensitivity of FASER and the larger outer contour that of FASER 2. The comparatively low luminosity hampers the ability of FASER to probe the scenario compared to beam dump experiments, and only FASER 2 is capable of excluding new parameter space. Improving on this search with a monophoton analysis would be challenging, as photon backgrounds are expected to be significant, and CHARM already excludes the region where the most improvement is expected (as shown in a hypothetical SHiP monophoton search in Fig. 3).

V. MUON g − 2 RECONSIDERED
The addition of the dark axion portal introduces corrections to the coupling between leptons and the photon For small m γ ≥ 2me, the kinetic mixing decay dominates due to the weaker dependence of 9 on the mass of the dark photon. At m γ ≤ 2me, γ → e + e − is forbidden by energy conservation, and this appears in the plot as a nearly vertical line next to the y-axis where the branching ratio drops to zero.
in the form of a new two-loop diagram, which changes the predicted value of the lepton anomalous magnetic moment (g − 2) . New contributions to a µ ≡ (g−2)µ 2 are of particular interest, as the experimental measurements of the anomalous magnetic moment of the muon from Brookhaven National Laboratory [33][34][35][36] exceed the best theoretical calculations by over three standard deviations [1]: ∆a µ = a µ (exp) − a µ (SM) = (26.8 ± 7.6) × 10 −10 . (7) As was discussed in Ref. [13], the dark axion portal contribution is negative, and therefore aggravates the disagreement between theory and experiment.
The vector portal has the potential to explain the discrepancy between theory and experiment by introducing a new one-loop correction with a contribution equal to [55]: Values of ε sufficiently large to correct the discrepancy have already been excluded by experimental searches, as shown in Fig. 4. An intriguing possibility is that the combination of the two portals could correct the discrepancy in (g − 2) µ while weakening the constraints placed by electron-positron decays through the vector portal. In order to accomplish this, we must satisfy three conditions: 1. The kinetic mixing parameter ε must be sufficiently large to make a meaningful correction to a µ , reflected in Fig. 4 as the blue (g − 2) µ favoured band.  Fig. 4 such that the aµ favoured region is not completely excluded superimposed upon a cutout of the limits of Fig. 2. The line does not extend below 25 MeV as ae limits exclude this region. While the plot could be extended above 0.5 GeV, its calculation is complicated by KLOE-2 searches [39,50], as they do not rely solely on the γ → e + e − signal.
This begins at ε > 10 −3 for small m γ , and grows larger with the mass.
2. G aγγ must be sufficiently small as to not be ruled out by constraints from BaBar or make large changes to a µ . The limits found previously in [13] and summarized in Fig. 2 require that G aγγ 3 × 10 −3 .
Most of the vector portal limits are weakened when G aγγ /ε is sufficiently large that the γ decays preferentially through the dark axion portal process γ → aγ, as this decreases Br(γ → e + e − ). The limit on a e is not affected by the introduction of the dark axion portal decay channel γ → aγ, but may change due to corrections resulting from new dark axion portal diagrams. Finally, beam dump searches may also have their sensitivity suppressed somewhat by the reduction in the branching ratio of γ → + − , and may be altered further by the increase in Γ γ due to the introduction of new decay channels. Experiments for which the mean distance before decay is shorter than the distance between the target and decay volume will experience an exponential suppression of their sensitivity, as shown in Eq. 6.
The width of γ → + − through the vector portal is  FIG. 7. A schematic of an electron beam dump experiment searching for monophoton signals. A scenario of particular interest is one for which dark photon production proceeds through vector portal bremsstrahlung, while the decay to aγ proceeds through the dark axion portal. The photon is observed in the detector as a monophoton, while the invisible a escapes. A possible variant involves searching for the decay of a sufficiently short-lived a, resulting in a three-photon signal produced through the axion portal decay a → γγ.
given by where e = √ 4πα em . A plot of Br(γ → e + e − ) for different ratios of G aγγ to ε is shown in Fig. 5. An important feature to note is that the γ → e + e − decay channel dominates the dark photon width when m γ is small.
We can now calculate the branching ratio Br(γ → e + e − + X) required for limits on the vector portal to no longer exclude the 2σ a µ favored region, and therefore the minimum value of G aγγ required to satisfy our previous conditions. In Fig. 6 we plot the value of this G aγγ favored line which satisfies this condition for m γ ∈ [0.025, 0.5] GeV and find that these values of G aγγ are easily excluded by the BaBar monophoton search. Worse, the coupling is sufficiently large that the dark axion portal contribution to (g − 2) µ , which we recall worsens the (g−2) µ discrepancy, is of a comparable magnitude to the vector portal contribution. For m γ < 0.025 GeV, limits from measurements of a e completely exclude the (g 2 ) µ favored region. For m γ > 0.5 GeV, the vector portal limits no longer rely solely on the γ → e + e − + X signature, and our simple treatment is no longer sufficient to calculate the G aγγ favored line. The combination of the vector and dark axion portals is incapable of resolving the (g − 2) µ anomaly while satisfying existing constraints.

VI. MONOPHOTON SEARCH
The previous section considered the effects of combining the vector and dark axion portals but ignored the possibility that there may be strong new experimental constraints on a scenario combining both portals. Frequently, one portal will dominate over the other in interactions with the SM, but this need not always be the case, and for some combinations, production may occur FIG. 8. The mean travel distance before decay of a γ with energy equal to 10 and 20 GeV for two interesting values of G aγγ . Dark photons produced through electron bremsstrahlung are highly collimated with the beam direction and possess an energy nearly equal to that of the electron beam itself. Parameters for which the decay length is much shorter than a meter are likely to decay before escaping the target and any shielding present, while extremely large decay lengths many times larger than the detector size result in very few of the dark photons decays inside of the detector. The target-detector distance for E137, a comparable electron beam dump experiment with a beam energy of 20 GeV, is shown in (b) for reference.
through one portal, while detection proceeds through another.
The production rate of γ and a is suppressed in the dark axion portal by the need to produce the particles in pairs, resulting in three-body final states or worse. If vector portal processes instead produced the dark photons, the production rate could be greatly enhanced at the cost of satisfying the robust existing constraints on the kinetic mixing parameter ε. We can suppress the limits on a kinetically mixed dark photon if the dark axion portal decay γ → aγ dominates over leptonic decay modes. As was shown in section V, this requires G aγγ ε/GeV, which is possible due to the comparatively weak constraints on the dark axion portal, and that m γ be greater than few tens of MeV. The latter requirement is due to the strong m γ dependence of the branching ratio shown in Fig. 5. There is still the potential for an improvement over the proton beam dump limits we have considered previously on a timescale shorter than that required by SHiP, particularly from electron beam dump experiments with dark photon bremsstrahlung as a production channel as suggested in Fig. 7.
Electron beam dumps could supplement the exclusion regions already provided by BaBar and CHARM, though their exact reach is dependent on the magnitude of the kinetic mixing parameter ε. A beam dump experiment's sensitivity is at its greatest when the mean decay length is equal to the distance between the decay volume and the production target. This distance is dependent on both the coupling through which the decay proceeds and the energy of the decaying particle. For electron bremsstrahlung, we can use the Improved Weizsäcker-Williams approximation [56][57][58] to find that the emitted dark photon will possess an energy nearly equal to that of the electron beam itself so long as the electron beam energy is far greater than the electron mass [46,59,60]. We consider the mean travel distance for both 10 and 20 GeV electron beams for G aγγ = 10 −3 , 10 −4 GeV −1 in Fig. 8 to illustrate the regions of greatest potential reach for such an experiment. Of particular interest is the m γ < 100 MeV region below the existing CHARM limit. As an example, the E137 experiment may be capable of placing new limits, but with a target-to-detector distance of 383 meters, it is likely only to be sensitive to the m γ < 30 MeV region already covered by CHARM. An electron beam dump could make a significant improvement on these experiments with a shorter target-detector distance on the order of tens of meters and the ability to record monophoton events. Note that the limits on the dark photon from vector portal couplings are particularly strong for m γ of a few MeV, as the electron-positron decay channel dominates for these masses, as shown in Fig.  5.

VII. SUMMARY AND DISCUSSION
We calculated the sensitivity of the proposed SHiP, FASER and FASER 2 experiments to the dark axion portal in the m a m γ limit, and summarized them in Fig.  2. We examined the effects of combining the vector portal and dark axion portal on the anomalous magnetic moment of the muon, and building on this we suggested that the two portals could be combined to search for kinetically mixed dark photons with monophoton decay signatures produced through γ → aγ.
SHiP is capable of great improvements over the existing beam dump limits from CHARM by searching for the dark photon decay signature γ → e + e − a using the same selection cuts as the planned vector portal dark photon search under the assumption of zero backgrounds. The large boost and short baseline provide SHiP with sensi-tivity to values of m γ as large as 250 MeV. A monophoton search could further improve SHiP's sensitivity, with particularly large gains for m γ ∼ 2m e , though the exact enhancement is heavily dependent on the severity of γ related background. Fig. 3 shows a possible 100-event contour.
FASER and FASER 2 were also studied, and provide an interesting contrast with SHiP. The much lower collision rate between protons and smaller length of decay volume relative to the interaction point-detector distance severely weakens FASER's sensitivity to the dark axion portal. FASER 2's possesses greatly improved sensitivity due to its much larger size and available luminosity significantly improve its sensitivity, allowing it to probe regions of the parameter space unavailable to CHARM. We briefly considered the benefits of a monophoton search at FASER 2, but it may be challenging to overcome SM backgrounds.
We calculated the effect on (g − 2) µ of the combined dark axion and vector portals in an attempt to resolve the discrepancy between theory and experiment. We found that by introducing the γ → aγ decay channel the constraints on the kinetic mixing ε could be suppressed, freeing the (g − 2) µ favored region of the parameter space shown in Fig. 4 from existing limits. However, the values of G aγγ required to sufficiently suppress the constraints on ε were excluded by limits from BaBar.
Novel searches are possible for the combined vector and dark axion portal scenario. One possibility is the production of dark photons through bremsstrahlung and decay to a monophoton through γ → aγ. The combination of portals can take advantage of the numerous electron beam dump experiments that would otherwise lack sensitivity to the dark axion portal, but the absence of monophoton analyses may hamper their potential searches. A short-baseline electron beam dump experiment with sensitivity to monophoton signals would provide an ideal environment for this kind of search.

ACKNOWLEDGMENTS
This work was supported in part by IBS (Project Code IBS-R018-D1) and NRF Strategic Research Program (NRF-2017R1E1A1A01072736). We would like to thank Walter Bonivento for helpful discussions regarding the SHiP experiment. We also would like to thank the participants of the Light Dark World International Forum 2018 (KAIST, December 2018) for engaging discussions.