Size of the pion from full lattice QCD with physical u, d, s and c quarks

We present the first calculation of the electromagnetic form factor of the π meson at physical light quark masses. We use configurations generated by the MILC Collaboration including the effect of u, d, s and c sea quarks with the highly improved staggered quark formalism. We work at three values of the lattice spacing on large volumes and with u=d quark masses going down to the physical value. We study scalar and vector form factors for a range in spacelike q from 0.0 to −0.13 GeV and from their shape we extract mean square radii. Our vector form factor agrees well with experiment and we find hriV 1⁄4 0.403ð18Þð6Þ fm. For the scalar form factor we include quark-line disconnected contributions which have a significant impact on the radius. We give the first results for SU(3) flavor-singlet and flavor-octet scalar mean square radii, obtaining hr2i S 1⁄4 0.506ð38Þð53Þ fm and hr2ioctet S 1⁄4 0.431ð38Þð46Þ fm. We discuss the comparison with expectations from chiral perturbation theory.