Quark mass dependence of the pion vector form factor

TL;DR

This paper investigates how the quark mass influences the pion vector form factor, using lattice data and the Omnes representation to estimate curvature and test chiral extrapolation systematics.

Contribution

It introduces a method to estimate the quark mass dependence of the pion form factor using lattice data and the Omnes representation, providing new insights into rho-pi-pi coupling.

Findings

Estimated the curvature of the pion form factor at physical quark masses.

Provided a new value for the curvature, <r^4> = 0.73 ± 0.09 fm^4.

Validated the assumption of rho coupling independence from quark mass.

Abstract

We examine the quark mass dependence of the pion vector form factor, particularly the curvature (mean quartic radius). We focus our study on the consequences of assuming that the coupling constant of the rho to pions is largely independent of the quark mass while the quark mass dependence of the rho--mass is given by recent lattice data. By employing the Omnes representation we can provide a very clean estimate for a certain combination of the curvature and the square radius, whose quark mass dependence could be determined from lattice computations. This study provides an independent access to the quark mass dependence of the rho-pi-pi coupling and in this way a non-trivial check of the systematics of chiral extrapolations. We also provide an improved value for the curvature for physical values for the quark masses, namely <r^4> = 0.73 +- 0.09 fm^4 or equivalently c_V=4.00\pm 0.50 GeV^{-4}.