Pion charge radius from pion+electron elastic scattering data

Zhu-Fang Cui,Daniele Binosi,Craig D Roberts,Sebastian M Schmidt

doi:10.1016/j.physletb.2021.136631

Abstract

With the aim of extracting the pion charge radius, we analyse extant precise pion+electron elastic scattering data on Q2∈[0.015,0.144] GeV2 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 Q2≃0. Combining results obtained from the two available data sets, we obtain rπ=0.640(7) fm, a value 2.4σ 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 Q2=0.015 GeV2. 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, rK. New data with much improved precision, low-Q2 reach and coverage are necessary before a sound result for rK can be recorded.

Highlights

The pion is Nature’s lightest hadron [1], with its mass, mπ, known to a precision of 0.0001%
Contemporary theory explains the pion as simultaneously both a pseudoscalar bound-state of a light-quark and -antiquark and, in the absence of Higgs-boson couplings into quantum chromodynamics (QCD), the strong interaction sector of the Standard Model of particle physics (SM), the massless Nambu-Goldstone boson that emerges as a consequence of dynamical chiral symmetry breaking (DCSB)
It has become clear that pion observables provide the cleanest window onto the phenomenon of emergent hadron mass (EHM), viz. the origin of more than 98% of visible mass in the Universe [8,9,10,11,12]

Summary

Introduction

The pion is Nature’s lightest hadron [1], with its mass, mπ, known to a precision of 0.0001%. [37,38,39,40,41,42,43], and typically described as the statistical Schlessinger point method (SPM) [44, 45], the approach produces a form-unbiased interpolation of data as the basis for a well-constrained extrapolation and, radius determination [46] It is worth reconsidering available low-Q2 pion form factor data with a view to employing the SPM in a fresh determination of rπ. In order to estimate the error associated with a given SPMdetermined pion radius, one must first account for the experimental error in the data set We achieve this by using a statistical bootstrap procedure [48], generating 1 000 replicas of the set by replacing each datum by a new point, randomly distributed around a mean defined by the datum itself with variance equal to its associated error. ΣδM σrMj for all j values in the range specified above, i.e., the result is independent of our chosen value of M

Dipole Gaussian

Findings

SPM yields