Pion charge radius from pion+electron elastic scattering data

TL;DR

This paper introduces a model-independent interpolation method to extract the pion charge radius from elastic scattering data, finding a value slightly below the current average and highlighting the need for more precise low-$Q^2$ data.

Contribution

The paper presents a novel, assumption-free interpolation technique using continued fractions for analyzing elastic scattering data to determine charge radii.

Findings

Pion charge radius estimated as 0.640(7) fm, below the average.

Current kaon data insufficient for radius extraction.

Emphasizes need for new low-$Q^2$ precise measurements.

Abstract

With the aim of extracting the pion charge radius, we analyse extant precise pion+electron elastic scattering data on $Q^2 \in [0.015,0.144]\,$GeV$^2$ using a method based on interpolation via continued fractions augmented by statistical sampling. The scheme avoids any assumptions on the form of function used for the representation of data and subsequent extrapolation onto $Q^2\simeq 0$. Combining results obtained from the two available data sets, we obtain $r_\pi = 0.640(7)\,$fm, a value $2.4\,\sigma$ below today's commonly quoted average. The tension may be relieved by collection and similar analysis of new precise data that densely cover a domain which reaches well below $Q^2 = 0.015\,$GeV$^2$. Considering available kaon+electron elastic scattering data sets, our analysis reveals that they contain insufficient information to extract an objective result for the charged-kaon radius, $r_K$. New data with much improved precision, low-$Q^2$ reach and coverage are necessary before a sound result for $r_K$ can be recorded.