Accommodating three low-scale anomalies (g-2, Lamb shift, and Atomki) in the framed standard model

Abstract

The framed standard model (FSM) predicts a $0^+$ boson with mass around 20 MeV in the "hidden sector", which mixes at tree level with the standard Higgs $h_W$ and hence acquires small couplings to quarks and leptons which can be calculated in the FSM apart from the mixing parameter $\rho_{Uh}$. The exchange of this mixed state $U$ will contribute to $g - 2$ and to the Lamb shift. By adjusting $\rho_{Uh}$ alone, it is found that the FSM can satisfy all present experimental bounds on the $g - 2$ and Lamb shift anomalies for $\mu$ and $e$, and for the latter for both hydrogen and deuterium. The FSM predicts also a $1^-$ boson in the "hidden sector" with a mass of 17 MeV, that is, right on top of the Atomki anomaly $X$. This mixes with the photon at 1-loop level and couples thereby like a dark photon to quarks and leptons. It is however a compound state and is thought likely to possess additional compound couplings to hadrons. By adjusting the mixing parameter and the $X$'s compound coupling to nucleons, the FSM can reproduce the production rate of the $X$ in beryllium decay as well as satisfy all the bounds on $X$ listed so far in the literature. The above two results are consistent in that the $U$, being $0^+$, does not contribute to the Atomki anomaly if parity and angular momentum are conserved, while $X$, though contributing to $g - 2$ and Lamb shift, has smaller couplings than $U$ and can, at first instance, be neglected there. Despite the tentative nature of the 3 anomalies in experiment and of the FSM as theory, the accommodation of the former in the latter has strengthened the credibility of both. If this FSM interpretation were correct, it would change the whole aspect of the anomalies from just curiosities to windows into a vast hitherto hidden sector comprising at least in part the dark matter which makes up the bulk of our universe.