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

Abstract: We present the first calculation of the electromagnetic form factor of the $\pi$ 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 space-like $q<sup>2$ from 0.0 to -0.1 $\mathrm{GeV}<sup>2$ and from their shape we extract mean square radii. Our vector form factor agrees well with experiment and we find $$\langle r² \rangle_V = 0.403(18)(6) \,\mathrm{fm}<sup>2$$. 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) flavour-singlet and octet scalar mean square radii, obtaining: $$\langle r² \rangle_S^{{\mathrm{singlet}}} = 0.506(38)(53) \mathrm{fm}<sup>2$$ and $$\langle r² \rangle_S^{{\mathrm{octet}}} = 0.431(38)(46) \mathrm{fm}<sup>2$$. We discuss the comparison with expectations from chiral perturbation theory.