On the pi pi continuum in the nucleon form factors and the proton radius puzzle

TL;DR

This paper refines the calculation of the pion-pion continuum's impact on nucleon form factors, providing insights relevant to the proton radius puzzle by integrating recent data and addressing isospin effects.

Contribution

It offers an improved, comprehensive analysis of the pion-pion continuum contribution to nucleon form factors, incorporating latest Roy-Steiner results and isospin-violation considerations.

Findings

Slight preference for a smaller proton charge radius

Enhanced understanding of the pion-pion contribution to nucleon form factors

Refined estimates of nucleon electric and magnetic radii

Abstract

We present an improved determination of the $\pi\pi$ continuum contribution to the isovector spectral functions of the nucleon electromagnetic form factors. Our analysis includes the most up-to-date results for the $\pi\pi\to\bar N N$ partial waves extracted from Roy-Steiner equations, consistent input for the pion vector form factor, and a thorough discussion of isospin-violating effects and uncertainty estimates. As an application, we consider the $\pi\pi$ contribution to the isovector electric and magnetic radii by means of sum rules, which, in combination with the accurately known neutron electric radius, are found to slightly prefer a small proton charge radius.