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

We compute the electromagnetic form factor of a ``pion" with massm_π = 330 MeV at low values of Q²≡−q², 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 330 MeV we find a charge radius given by ⟨r_π²⟩_330 MeV = 0.354(31) fm² which, using NLO SU(2) chiral perturbation theory, translates to a value of ⟨r_π²⟩ = 0.418(31) fm² 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; form_π = 330 MeV and volume (2.74 fm)³ we find the reduction is approximately a factor of 12.