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

TL;DR

This paper proposes a new U(1)_R gauge symmetry extension of the Standard Model, introducing a light gauge boson to address the proton radius discrepancy while remaining consistent with muon g-2 measurements.

Contribution

It introduces a minimal anomaly-free U(1)_R model with right-handed fermions to explain the proton radius puzzle and muon g-2 anomaly.

Findings

Identifies a viable U(1)_R gauge boson in the sub-GeV range.

Achieves consistency with muon g-2 measurements.

Proposes a light scalar in the tens of MeV range.

Abstract

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 muon's $(g-2)$ measurements is achieved through an extra light scalar, which itself must lie in the tens of MeV mass range to be viable.