First-principles determination of anomaly-induced pion decay beyond the chiral limit

Abstract

The two-photon decay of the neutral pion is fixed in the chiral limit by the Adler-Bell-Jackiw anomaly, while nonzero quark masses induce few-percent corrections that must be determined for precision tests of QCD beyond the chiral limit. Using the anomalous PCAC relation, we compute them in lattice QCD as deviations from the exact anomaly condition at $q^2=0$, thereby avoiding both four-point functions and the cancellation of chiral logarithms that limits conventional approaches. Because the correction is proportional to the light-quark masses, both statistical and systematic uncertainties are correspondingly suppressed, making a precision calculation feasible. On two nearly-physical domain-wall ensembles we achieve $\sim1\%$ statistical precision each for the decay width, obtaining $Γ(π^0\toγγ)=8.09(22) eV$ after continuum extrapolation. The $2.3(1.4)\%$ mass correction to the decay amplitude, positive and isospin-breaking dominated, provides the first ab initio confirmation of the $π^0$-$η$-$η'$ mixing enhancement.