The proton radius (puzzle?) and its relatives

TL;DR

This paper reviews various methods of determining the proton charge radius, unifies their theoretical descriptions using effective field theories, and discusses the implications for current and future experiments.

Contribution

It provides a unified effective field theory framework for low-energy constants related to the proton radius and clarifies their relation to QCD operators.

Findings

Proton radius from spectroscopy and scattering are related at ${\cal O}(\alpha)$ accuracy.

Unified framework for low-energy constants of the proton's electromagnetic interactions.

Discussion on model dependence and prospects for effective field theories in experiments.

Abstract

We review determinations of the electric proton charge radius from a diverse set of low-energy observables. We explore under which conditions it can be related to Wilson coefficients of appropriate effective field theories. This discussion is generalized to other low-energy constants. This provides us with a unified framework to deal with a set of low-energy constants of the proton associated with its electromagnetic interactions. Unambiguous definitions of these objects are given, as well as their relation with expectation values of QCD operators. We show that the proton radius obtained from spectroscopy and lepton-proton scattering (when both the lepton and proton move with nonrelativistic velocities) is related to the same object of the underlying field theory with ${\cal O}(\alpha)$ precision. The model dependence of these analyses is discussed. The prospects of constructing effective field theories valid for the kinematic configuration of present, or near-future, lepton-proton scattering experiments are discussed.