Relativistic, model-independent determination of electromagnetic finite-size effects beyond the point-like approximation

TL;DR

This paper introduces a relativistic, model-independent method to calculate electromagnetic finite-size effects in particles, applicable at high orders and using experimental or lattice data for form factors.

Contribution

It develops a systematic, automatable approach to determine structure-dependent electromagnetic effects beyond the point-like approximation, applicable at arbitrarily high orders.

Findings

Derived finite-size effects on pseudoscalar meson mass and decay amplitude.

Effects depend on meson charge radius and radiative amplitude, known experimentally.

Method applicable to high-order calculations in large-volume expansions.

Abstract

We present a relativistic and model-independent method to derive structure-dependent electromagnetic finite-size effects. This is a systematic procedure, particularly well-suited for automatization, which works at arbitrarily high orders in the large-volume expansion. Structure-dependent coefficients appear as zero-momentum derivatives of physical form factors which can be obtained through experimental measurements or auxiliary lattice calculations. As an application we derive the electromagnetic finite-size effects on the pseudoscalar meson mass and leptonic decay amplitude, through orders $\mathcal{O}(1/L^3)$ and $\mathcal{O}(1/L^2)$, respectively. The structure dependence appears at this order through the meson charge radius and the real radiative leptonic amplitude, which are known experimentally.