A step towards estimation of the neutral-hadron size: the gravitational mass radius of pi0 meson in a relativistic theory of composite particles

TL;DR

This paper estimates the neutral pion's size using a relativistic nonperturbative approach, calculating a mass mean square radius around 0.5 fm, and discusses the ambiguities in defining the pion's size.

Contribution

It introduces a novel relativistic method to estimate the neutral pion's size and clarifies the choice of mass mean square radius for this purpose.

Findings

Estimated pi0 meson size: (0.5-0.53) fm

Electromagnetic form factor of pi0 is zero

Discussion of ambiguities in size definitions

Abstract

We extend our nonperturbative essentially relativistic approach, elaborated previously, to perform an approximate estimation of the size of pi0 meson. We present detailed argumentation for choosing the mass mean square radius (MSR) for this purpose. Its value calculated in our approach, using three model quark-antiquark wave functions in pion, is (0.5-0.53) fm. The neutral-pion electromagnetic form factor is zero in accordance with the charge-conjugation symmetry. We demonstrate ambiguities encountered when using standard definitions of mechanical MSR for the size. We discuss MSRs obtained in various approaches and their comparison with each other and with our results.