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 $⟨r^2{⟩}_V=0.403(18)(6){\mathrm{fm}}^2$. 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: $⟨r^2{⟩}_S^{\mathrm{singlet}}=0.506(38)(53){\mathrm{fm}}^2$ and $⟨r^2{⟩}_S^{\mathrm{octet}}=0.431(38)(46){\mathrm{fm}}^2$. We discuss the comparison with expectations from chiral perturbation theory.

13 pages, 11 figures

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