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

Abstract

We give an accurate determination of the vector (electromagnetic) form factor, $F(Q^2)$, for a light pseudoscalar meson up to squared momentum transfer $Q^2$ values of 6 ${\mathrm{GeV}}^2$ for the first time from full lattice QCD, including $u$, $d$, $s$ and $c$ quarks in the sea at multiple values of the lattice spacing. Our results show good control of lattice discretisation and sea quark mass effects. We study a pseudoscalar meson made of valence $s$ quarks but the qualitative picture obtained applies also to the $\ddot{I}€$ meson, relevant to upcoming experiments at Jefferson Lab. We find that $Q^{2}F(Q^2)$ becomes flat in the region between $Q^2$ of 2 ${\mathrm{GeV}}^2$ and 6 ${\mathrm{GeV}}^2$, with a value well above that of the asymptotic perturbative QCD expectation, but well below that of the vector-meson dominance pole form appropriate 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 QCD result emerges.

8 pages, 6 figures. Version accepted by Physical Review D. Includes results from a third value of the lattice spacing, change to the title and two additional figures in the appendix discussing analysis of systematic and statistical errors