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.

Figure 1

The branching ratio of ${\gamma }^{\prime }\to a{e}^{+}{e}^{-}$ and ${\gamma }^{\prime }\to a{\mu }^{+}{\mu }^{-}$ through the dark axion portal in the $m_a\ll m_{{\gamma }^{\prime }}$ limit. The leptonic decay processes are forbidden for $m_{{\gamma }^{\prime }}<2m_{\ell }$ ($\ell =e$, $\mu$). The slight dip near 0.8 GeV is due to the presence of hadronic decay channels.

Figure 2

Limits on $G_{a\gamma {\gamma }^{\prime }}$ from high intensity experiments and the projected sensitivity of the SHiP, FASER and MATHUSLA experiments for $m_a\ll m_{{\gamma }^{\prime }}$ with $ϵ=0$. The limits from LSND and MiniBooNE come from excess neutral current-like elastic scattering events above the expected background from neutrino and non-neutrino SM sources. The LSND limit reflects an excess of $2\sigma$ over expected backgrounds, while MiniBooNE assumes zero background and excludes the scenario at a 90% confidence level. The CHARM constraint reflects sensitivity to a $2\sigma$ excess in monophoton production through ${\gamma }^{\prime }\to a\gamma$ 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 $2\sigma$. The BABAR and Belle-II lines all represent exclusions from $2\sigma$ monophoton excesses through the annihilation process $e^{+}{e}^{-}\to a({\gamma }^{\prime }\to a\gamma )$. Further details on these limits can be found in Ref. [13]. The SHiP projection denotes a 95% confidence level excess of greater than three $e^{+}{e}^{-}$ events reaching the SHiP electromagnetic calorimeter produced through the decay ${\gamma }^{\prime }\to a{e}^{+}{e}^{-}$, while the FASER and FASER 2 projections reflect the same for three events. Finally, the green MATHUSLA limit denotes an excess of greater than four observed events.

Figure 3

The expected shape of a SHiP monophoton exclusion contour, with a required event rate of 100 chosen for comparison with the electron-positron signal. The monophoton search does not suffer any suppression in its sensitivity for $m_{{\gamma }^{\prime }}\approx 2m_e$, 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.

Figure 4

Leading constraints on visibly decaying dark photon ${\gamma }^{\prime }$ coupling to the Standard Model through the vector portal. Limits are at a 90% confidence level and given in terms of the kinetic mixing parameter $ϵ$. The blue shaded region shows where a dark photon can correct $(g-2{)}_{\mu }$ to within $2\sigma$ of its measured value [1, 39, 40, 41, 42]. Shown are the limits from BABAR [44, 45], KLOE-2 [46, 47], PHENIX [48], A1 [49], $\mathrm{NA}48/2$ [50], E774 [51] and E141 [52] from Ref. [53], NA64 [54] and electron $g-2$ [55]. Relevant limits suppressed for readability include two additional limits from KLOE-2 [56, 57], WASA-at-COSY [58] and HADES [59]. Appearing at larger masses than are visible on this plot are those produced by LHCb [60]. Several of the curves used in the making of this plot were taken from data files [61, 62].

Figure 5

The branching ratio of the vector portal process $\gamma \to e^{+}{e}^{-}$ for five different ratios of $G_{a\gamma {\gamma }^{\prime }}$ to $ϵ$. The kink at approximately 210 MeV is due to the ${\gamma }^{\prime }\to {\mu }^{+}{\mu }^{-}$ channel. For small $m_{{\gamma }^{\prime }}\ge 2m_e$, the kinetic mixing decay dominates due to the weaker dependence of (9) on the mass of the dark photon. At $m_{{\gamma }^{\prime }}\le 2m_e$, ${\gamma }^{\prime }\to e^{+}{e}^{-}$ 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.

Figure 6

The minimum value of $G_{a\gamma {\gamma }^{\prime }}$ required to suppress the vector portal limits shown in Fig. 4 such that the $a_{\mu }$ favored region is not completely excluded superimposed upon a cutout of the limits of Fig. 2. The line does not extend below 25 MeV as $a_e$ limits exclude this region. While the plot could be extended above 0.5 GeV, its calculation is complicated by KLOE-2 searches [46, 57], as they do not rely solely on the ${\gamma }^{\prime }\to e^{+}{e}^{-}$ signal.

Figure 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 $a\gamma$ 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 $a\to \gamma \gamma$.

Figure 8

The mean travel distance before decay of a ${\gamma }^{\prime }$ with energy equal to 10 and 20 GeV for two interesting values of $G_{a\gamma {\gamma }^{\prime }}$. 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 photon 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.