The ?? ? ?? anomaly from lattice QCD and dispersion relations

A bstract We propose a formalism to extract the ?? ? ?? chiral anomaly F 3 ? from calculations in lattice QCD performed at larger-than-physical pion masses. To this end, we start dispersive representation of ? (*) amplitude, whose main quark-mass dependence arises scattering phase shift and can be derived perturbation theory via inverse-amplitude method. With parameters constrained by P -wave shift, use combination dispersion relations effective field extrapolate two recent physical point. Our allows us radiative coupling ? (770) meson and, for first time, = 38(16)(11) GeV ? . The result is consistent with prediction albeit within large uncertainties, which will improve accordance progress future lattice-QCD computations.