The pion vector form factor from Lattice QCD at the physical point

TL;DR

This study computes the electromagnetic pion form factor at physical quark masses using lattice QCD, providing a precise determination of the pion charge radius and related low-energy constants.

Contribution

First lattice QCD calculation of $F_(Q^2)$ at physical pion mass with controlled finite volume effects and chiral perturbation theory analysis.

Findings

Pion charge radius $raket{r^2}_ = 0.443(29) \,\mathrm{fm}^2$

Determination of SU(2) low-energy constant $ar{\\ell}_6 = 16.2(1.0)$

Consistent results across different lattice volumes and pion masses.

Abstract

We present an investigation of the electromagnetic pion form factor, $F_\pi(Q^2)$, at small values of the four-momentum transfer $Q^2$ ($\lesssim 0.25$ GeV$^2$), based on the gauge configurations generated by European Twisted Mass Collaboration with $N_f = 2$ twisted-mass quarks at maximal twist including a clover term. Momentum is injected using non-periodic boundary conditions and the calculations are carried out at a fixed lattice spacing ($a \simeq 0.09$ fm) and with pion masses equal to its physical value, 240 MeV and 340 MeV. Our data are successfully analyzed using Chiral Perturbation Theory at next-to-leading order in the light-quark mass. For each pion mass two different lattice volumes are used to take care of finite size effects. Our final result for the squared charge radius is $\langle r^2 \rangle_\pi = 0.443~(29)$ fm$^2$, where the error includes several sources of systematic errors except the uncertainty related to discretization effects. The corresponding value of the SU(2) chiral low-energy constant $\overline{\ell}_6$ is equal to $\overline{\ell}_6 = 16.2 ~ (1.0)$.