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 \(q^2\) from 0.0 to -0.1 \(\mathrm{GeV}^2\) and from their shape we extract mean square radii. Our vector form factor agrees well with experiment and we find \(\langle r^2 \rangle_V = 0.403(18)(6) \,\mathrm{fm}^2\). 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: \(\langle r^2 \rangle_S^{\mathrm{singlet}} = 0.506(38)(53) \mathrm{fm}^2\) and \(\langle r^2 \rangle_S^{\mathrm{octet}} = 0.431(38)(46) \mathrm{fm}^2\). We discuss the comparison with expectations from chiral perturbation theory.