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

Abstract

We present an investigation of the electromagnetic pion form factor, $F_{\ddot{I}}€(Q^2)$, 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 $⟨r^2{⟩}_{\ddot{I}}€=0.443(29)$ 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 ${\overline{\ell }}_6=16.2(1.0)$.

23 pages, 9 figures, 7 tables