A 17 MeV pseudoscalar and the LSND, MiniBooNE and ATOMKI anomalies

In the absence of any new physics signals at the Large Hadron Collider (LHC), anomalous results at low energy experiments have become the subject of increased attention. We focus on three such results from the LSND, MiniBooNE (MB), and ATOMKI experiments. A 17 MeV pseudoscalar mediator ($a'$) can account for two ($^8$Be and $^4$He) out of the three cases in which excess events have been seen in pair creation transitions in ATOMKI. We incorporate this mediator in a gauge invariant extension of the Standard Model (SM) with a second Higgs doublet and three singlet (seesaw) neutrinos ($N_i, i=1,2,3$). $N_{1,2}$ participate in an interaction in MB and LSND which, with $a'$ as mediator, leads to the production of $e^+ e^-$ pairs. The $N_i$ also lead to mass-squared differences for SM neutrinos in agreement with global oscillation data. We first show that such a model offers a natural joint solution to the MB and LSND excesses, providing excellent fits to their data. Next, using the values of the couplings to the quarks and electrons which are required to explain pair creation nuclear transition data for $^8$Be and $^4$He in ATOMKI, we show that these values still lead to fits for MB and LSND data. However, once ATOMKI is incorporated, we find that strong constraints from the decays $K^+ \rightarrow \pi^+ a' \, (a'\rightarrow e^+e^-)$ and $\pi^+ \rightarrow $ $ e^+ ~\nu_e ~e^+ e^- $ come into play. While our solution is in conformity with the bounds on the former decay, it remains in tension with $90\%$ CL bounds on the latter. We also discuss other constraints from both collider and non-collider experiments and from electroweak precision data, stability and unitarity. We compute the contributions to the electron and muon $g-2$ up to two loops for our model. We discuss tests of the model in upcoming experiments.