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We give an accurate determination of the vector (electromagnetic) formfactor, $F(Q^2)$, for a light pseudoscalar meson up to squared momentumtransfer $Q^2$ values of 6 $\mathrm{GeV}^2$ for the first time from fulllattice QCD, including $u$, $d$, $s$ and $c$ quarks in the sea at multiplevalues of the lattice spacing. Our results show good control of latticediscretisation and sea quark mass effects. We study a pseudoscalar meson madeof valence $s$ quarks but the qualitative picture obtained applies also to the$\pi$ meson, relevant to upcoming experiments at Jefferson Lab. We find that$Q^2F(Q^2)$ becomes flat in the region between $Q^2$ of 2 $\mathrm{GeV}^2$ and6 $\mathrm{GeV}^2$, with a value well above that of the asymptotic perturbativeQCD expectation, but well below that of the vector-meson dominance pole formappropriate to low $Q^2$ values. Our calculations show that we can reach higher$Q^2$ values in future to shed further light on where the perturbative QCDresult emerges.

The pseudoscalar meson electromagnetic form factor at high $Q^2$ from full lattice QCD