A closer look at the $U(1)_{B-L}$ explanation of the ATOMKI nuclear anomalies

Abstract

We revisit the gauged $U(1)_{B-L}$ explanation of the ATOMKI nuclear anomalies, in which the new gauge boson is the hypothetical $X(17)$ particle. It is known that the vanilla $B-L$ scenario is unable to account for appropriate couplings, namely the suppression of the couplings of $X(17)$ to neutrinos, which motivates adding vector-like leptons. The simplest case, in which the new fields have $B-L$ charges equal to $1$, is highly disfavoured since it requires large mixing with the Standard Model fields. One solution recently put forward is to consider large $B-L$ charges to counterbalance small mixing. We show that, in this scenario, and after taking into account several phenomenological constraints, the dominant contribution to the muon anomalous magnetic moment $(g-2)_\mu$ is expected to be extremely large and with a negative sign, being thus excluded by experiment.