Implications of the dark axion portal for the muon $g-2$, $B$ factories, fixed target neutrino experiments, and beam dumps

The dark axion portal is a recently introduced portal between the standard model and the dark sector. It connects both the dark photon and the axion (or axionlike particle) to the photon simultaneously through an anomaly triangle. While the vector portal and the axion portal have been popular venues to search for the dark photon and axion, respectively, the new portal provides new detection channels if they coexist. The dark axion portal is not a result of the simple combination of the two portals, and its value is not determined by the other portal values; it should be tested independently. In this paper, we discuss implications of the new portal for the leptonic $g-2$, $B$ factories, fixed target neutrino experiments and beam dumps. We provide the model-independent constraints on the axion-photon-dark photon coupling and discuss the sensitivities of the recently activated Belle-II experiment, which will play an important role in testing the new portal.

Figure 1

Electron-positron annihilation to on shell $a$ and ${\gamma }^{\prime }$. Observable at $B$ factories as a monophoton produced through subsequent decay ${\gamma }^{\prime }\to \gamma a$.

Figure 2

As an illustration, we provide a histogram of the cosine of the center-of-mass emission angle $\cos {\theta }_{\gamma }^{*}$ for a sample of $4\times 10^5$ secondary photons produced through $e^{+}{e}^{-}\to a({\gamma }^{\prime }\to a\gamma )$ for High-Cut energies. The boxed window reflects the imposed High-Cut $\cos {\theta }_{\gamma }^{*}$ range detailed in Table 1. Of the $10^6$ events initially generated, $1.36\times 10^5$ survive both the energy and angle cuts. The bin size for this histogram was chosen to provide a good representation of the angular distribution, but is not relevant to the analysis.

Figure 3

Cross sections for the processes $e^{+}{e}^{-}\to a{\gamma }^{\prime }$ and $e^{+}{e}^{-}\to a\gamma {\gamma }^{\prime }$ with $m_a\ll m_{{\gamma }^{\prime }}$ $E_{\gamma }\in [2.2,5.5]\mathrm{GeV}$. The cross section of $e^{+}{e}^{-}\to a\gamma {\gamma }^{\prime }$ is heavily suppressed relative to $e^{+}{e}^{-}\to a{\gamma }^{\prime }$ due in part to the three body final state.

Figure 4

Limits placed on $G_{a\gamma {\gamma }^{\prime }}$ for the hierarchical mass scenario with $m_a\ll m_{{\gamma }^{\prime }}$. The BABAR line refers to searches for monophotons produced through $e^{+}{e}^{-}\to a{\gamma }^{\prime }$ followed by the decay ${\gamma }^{\prime }\to a\gamma$. Also shown are projected sensitivities for a similar search in Phase-II and III of the Belle-II experiment. The LSND and MiniBooNE lines reflect a search for excess neutral current elastic scattering events in the LSND and MiniBooNE detectors. The CHARM constraint is the result of a search for ${\gamma }^{\prime }\to a\gamma$ decays in the CHARM fine-grain detector. The electron and muon g-2 constraints represent parameter space for which the scenario is excluded due to changes in the lepton anomalous magnetic moment that are incompatible with current experimental measurements.

Figure 5

Two-loop diagram providing the leading contribution to lepton anomalous magnetic moment including $a$-$\gamma$-${\gamma }^{\prime }$ vertices.

Figure 6

Decay of the pseudoscalar mesons ${\pi }^0$ and $\eta$ to $\gamma a{\gamma }^{\prime }$ used in the analysis of LSND, MiniBooNE and CHARM. The off shell internal photon and three body final state suppress the branching ratio.

Figure 7

Inelastic scattering channels observable by MiniBooNE and LSND. The diagram (b) is always kinematically accessible, while the diagram (a) requires an energetic $a$ to enable scattering into the higher mass ${\gamma }^{\prime }$ state.

Figure 8

Mean travel distance before decay for characteristic energies of ${\gamma }^{\prime }$ at (a) LSND and (b) MiniBooNE. Also marked are relevant distance scales: the distance to the LSND and the MiniBooNE detectors as well as the 1 m fiducial volume cut. The secondary ${\gamma }^{\prime }$ produced in the LSND and MiniBooNE detectors through $ae\to {\gamma }^{\prime }e$ scattering have lower energies than those produced in the target.

Figure 9

Invariant mass spectrum of the photon and recoil electron produced through $ae\to {\gamma }^{\prime }e\to \gamma ae$, where $s=(p_{\gamma }+p_e{)}^2$. The histogram shown is for the MiniBooNE off-target run, in which the proton beam was impacted on the 50 m steel beam dump, with $m_{{\gamma }^{\prime }}=3\mathrm{MeV}$ and $G_{a\gamma {\gamma }^{\prime }}=0.01$. This invariant mass range is too small to survive the cuts placed by the MiniBooNE ${\pi }^0$ reconstruction, as it requires $\sqrt{s}=[80,200]\mathrm{MeV}$. A search of the $m_{\gamma \gamma }$ spectrum for smaller invariant masses would be sensitive to this scenario.

Figure 10

The branching ratio of ${\gamma }^{\prime }\to a{e}^{+}{e}^{-}$, only considering decays through the $a\gamma {\gamma }^{\prime }$ vertex.

Figure 11

New photon vacuum polarization diagram that contributes to ${\mathrm{\Pi }}^{\mu \nu }(q^2)$ with the introduction of the $a$-$\gamma$-${\gamma }^{\prime }$ vertex.