Lattice QCD Calculation of π0 → e+ e- Decay

We extend the application of lattice QCD to the two-photon-mediated, order alpha(2) rare decay pi(0) -> e(+)e(-). By combining Minkowski-and Euclidean-space methods we are able to calculate the complex amplitude describing this decay directly from the underlying theories (QCD and QED) which predict this decay. The leading connected and disconnected diagrams are considered; a continuum limit is evaluated and the systematic errors are estimated. We find ReA = 18.60(1.19)(1.05) eV, ImA = 32.59(1.50)(1.65) eV, a more accurate value for the ratio (ReA/ImA) = 0.571(10)(4), and a result for the partial width Gamma(pi(0) -> gamma gamma) = 6.60(0.61)(0.67) eV. Here the first errors are statistical and the second systematic. This calculation is the first step in determining the more challenging, two-photon-mediated decay amplitude that contributes to the rare decay K -> mu(+)mu(-).

Automated summary

We extend the application of lattice QCD to calculate the rare decay pi(0) -> e(+)e(-) mediated by two photons. By combining Minkowski-and Euclidean-space methods, we are able to directly calculate the complex amplitude describing this decay from the underlying theories. The results provide more accurate values for various parameters and lay the foundation for further calculations on the two-photon-mediated decay amplitude contributing to the rare decay K -> mu(+)mu(-).