Sub-GeV $U(1)_{R}$ gauge boson to address the proton radius discrepancy

We propose a Standard Model extension by a $U(1)_{R}$ gauge symmetry where only right-handed chiral fermions can carry a non-trivial charge. Here we show that the simplest anomaly-free solution to accommodate the proton charge radius discrepancy takes right-handed muons $mu_R$ and first generation quarks, $u_R$ and $d_R$. Consistency with the latest muons $(g-2)$ measurements is achieved through an extra light scalar, which itself must lie in the tens of MeV mass range to be viable.