The 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 $\pi$ 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 ${\mathrm{G}\mathrm{e}\mathrm{V}}^2$ and from their shape we extract mean square radii. Our vector form factor agrees well with experiment and we find $⟨r^2{⟩}_V=0.403(18)(6){\mathrm{f}\mathrm{m}}^2$. 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{s}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e}\mathrm{t}$} = 0.506(38)(53) $\mathrm{f}\mathrm{m}$^2$and$\langle r^2 \rangle_S^{$\mathrm{o}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{t}$} = 0.431(38)(46) $\mathrm{f}\mathrm{m}$^2$. We discuss the comparison with expectations from chiral perturbation theory.