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.
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