Two-Photon Decay of the Neutral Pion in Lattice QCD

We perform a nonperturbative calculation of the ${\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ transition form factor and the associated decay width using lattice QCD. The amplitude for a two-photon final state, which is not an eigenstate of QCD, is extracted through a Euclidean time integral of the relevant three-point function. We utilize the all-to-all quark propagator technique to carry out this integration as well as to include the disconnected quark diagram contributions. The overlap fermion formulation is employed on the lattice to ensure exact chiral symmetry on the lattice. After examining various sources of systematic effects, except for a possible discretization effect, we obtain ${\ensuremath{\Gamma}}_{{\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}}=7.83(31)(49)\text{ }\text{ }\mathrm{eV}$ for the pion decay width, where the first error is statistical and the second is our estimate of the systematic error.