Hadron and light nucleus radii from electron scattering

TL;DR

This paper discusses the importance of accurately measuring hadron and light nucleus radii using electron scattering, highlighting the need to eliminate bias in data analysis, and introduces the statistical Schlessinger point method (SPM) as a robust, unbiased technique applicable across various systems.

Contribution

It introduces the Schlessinger point method (SPM) for unbiased, analytic extraction of radii from electron scattering data, applicable to multiple hadronic systems.

Findings

SPM provides unbiased radius estimates.

SPM is versatile across different particles.

SPM is grounded in analytic function theory.

Abstract

Conceptually, radii are amongst the simplest Poincar\'e-invariant properties that can be associated with hadrons and light nuclei. Accurate values of these quantities are necessary so that one may judge the character of putative solutions to the strong interaction problem within the Standard Model. However, limiting their ability to serve in this role, recent measurements and new analyses of older data have revealed uncertainties and imprecisions in the radii of the proton, pion, kaon, and deuteron. In the context of radius measurement using electron + hadron elastic scattering, the past decade has shown that reliable extraction requires complete elimination of bias associated with practitioner-dependent choices of data fitting functions. Different answers to that challenge have been offered; and this perspective describes the statistical Schlessinger point method (SPM), in unifying applications to proton, pion, kaon, and deuteron radii. Grounded in analytic function theory, independent of assumptions about underlying dynamics, free from practitioner-induced bias, and applicable in the same form to diverse systems and observables, the SPM returns an objective expression of the information contained in any data under consideration. Its robust nature and versatility make it suitable for use in many branches of experiment and theory.