Lattice calculation of the pion transition form factor ${\pi }^0\to {\gamma }^{\ast }{\gamma }^{\ast }$

Abstract

We calculate the pion transition form factor ${\mathcal{F}}_{{\pi }^0{\gamma }^{\ast }{\gamma }^{\ast }}(q_1^2,q_2^2)$, which describe the interaction of an on-shell pion with two off-shell photons, using lattice QCD simulations with two degenerate flavors of dynamical quarks. This form factor is the main ingredient in the calculation of the pion-pole contribution to hadronic light-by-light scattering in the muon $g-2$, $a_{\mu }^{\mathrm{HLbL};{\pi }^0}$. We focus our study on the spacelike region with photon virtualities up to $1.5{\mathrm{GeV}}^2$, not yet measured experimentally. Several lattice spacings and pion masses are used to extrapolate the results to the physical point and a comparison with different phenomenological models is performed. Finally, we use our extrapolated form factor to provide a lattice determinaiton of $a_{\mu }^{\mathrm{HLbL};{\pi }^0}$.

Comments: 7 pages, 10 figures. Proceedings of the 34th International Symposium on Lattice Field Theory (Lattice 2016), 24-30 July 2016, University of Southampton, UK