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We present the first calculation of the electromagnetic form factor of the$\pi$ meson at physical light quark masses. We use configurations generated bythe MILC collaboration including the effect of $u$, $d$, $s$ and $c$ sea quarkswith the Highly Improved Staggered Quark formalism. We work at three values ofthe lattice spacing on large volumes and with $u$/$d$ quark masses going downto the physical value. We study scalar and vector form factors for a range inspace-like $q^2$ from 0.0 to -0.1 $\mathrm{GeV}^2$ and from their shape weextract mean square radii. Our vector form factor agrees well with experimentand we find $\langle r^2 \rangle_V = 0.403(18)(6) \,\mathrm{fm}^2$. For thescalar form factor we include quark-line disconnected contributions which havea 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 thecomparison with expectations from chiral perturbation theory.

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