The pion's electromagnetic form factor at small momentum transfer in full lattice QCD

TL;DR

This study calculates the pion's electromagnetic form factor at low Q^2 using lattice QCD with twisted boundary conditions, achieving results consistent with experimental data and demonstrating computational efficiency improvements.

Contribution

It introduces a method to compute low Q^2 pion form factors in lattice QCD with reduced computational cost using stochastic sources.

Findings

Charge radius at m_pi=330MeV: 0.354(31) fm^2

Extrapolated physical pion charge radius: 0.418(31) fm^2

Computational cost reduced by a factor of 12 using stochastic sources

Abstract

We compute the electromagnetic form factor of a "pion" with mass m_pi=330MeV at low values of Q^2\equiv -q^2, where q is the momentum transfer. The computations are performed in a lattice simulation using an ensemble of the RBC/UKQCD collaboration's gauge configurations with Domain Wall Fermions and the Iwasaki gauge action with an inverse lattice spacing of 1.73(3)GeV. In order to be able to reach low momentum transfers we use partially twisted boundary conditions using the techniques we have developed and tested earlier. For the pion of mass 330MeV we find a charge radius given by <r_pi^2>_{330MeV}=0.354(31)fm^2 which, using NLO SU(2) chiral perturbation theory, extrapolates to a value of <r_pi^2>=0.418(31)fm^2 for a physical pion, in agreement with the experimentally determined result. We confirm that there is a significant reduction in computational cost when using propagators computed from a single time-slice stochastic source compared to using those with a point source; for m_pi=330MeV and volume (2.74fm)^3 we find the reduction is approximately a factor of 12.