On the proton radius problem

TL;DR

This paper investigates the proton radius discrepancy between muonic-hydrogen spectroscopy and electron scattering, proposing a Lorentz transformation approach to reconcile measurements taken in different reference frames.

Contribution

It provides a general derivation of how Lorentz transformations of charge density can explain the proton radius measurement differences.

Findings

Lorentz transformation of charge density explains measurement discrepancies

The proton radius discrepancy can be resolved without new physics

A general framework for comparing charge radii in different frames

Abstract

The recent values of the proton charge radius obtained by means of muonic-hydrogen laser spectroscopy are about $4\%$ different from the electron scattering data. It has been suggested that the proton radius is actually measured in different frames and that, starting from a non relativistic quark model calculation, the Lorentz transformation of the form factors accounts properly for the discepancy. We shall show that the relation between the charge radii measured in different frames can be determined on very general grounds by taking into account the Lorentz transformation of the charge density. In this way, the discrepancy between muonic-hydrogen laser spectroscopy and electron scattering data can be removed.