An improvement of model-independent method for meson charge radius calculation

TL;DR

This paper introduces an improved, more robust model-independent lattice method for calculating meson charge radii, reducing finite-volume effects and systematic uncertainties.

Contribution

It reformulates the existing method using an auxiliary function to further suppress higher-order contributions, enhancing accuracy in small-volume, large-radius scenarios.

Findings

Method reduces residual finite-volume effects.

Application to lattice data yields consistent charge radius estimates.

Reformulation improves robustness over previous approaches.

Abstract

We propose a variant of the model-independent method for determining meson charge radii from spatial moments of correlation functions on the lattice. Traditional determinations based on fits to the momentum transfer squared dependence of form factors are subject to systematic uncertainties arising from the choice of fit ansatz. By contrast, model-independent methods based on spatial moments provide a useful framework for determining the slope of the form factor without assuming its functional form. Recently, Feng et al. proposed a model-independent method, which drastically suppresses the finite-volume effect in the charge radius coming from higher-order contributions of the expansion of the form factor with respect to the momentum transfer squared. In this work, we introduce an auxiliary function of the momentum transfer squared and reformulate the method in terms of its product with the form factor, rather than the form factor itself, thereby further suppressing higher-order contributions, notably in cases of small volume and large radius. In particular, we investigate quadratic and logarithmic forms as practical choices for this auxiliary function. Applying this method to mock data based on a monopole form factor, as well as to actual lattice QCD data using $N_f=2+1$ gauge ensembles at $m_\pi \simeq 0.5$ and $0.3$ GeV, we find that it reduces residual finite-volume effects and provides an effective framework for meson charge radius determinations.