Chiral expansions of theπ0lifetime

The corrections induced by light quark masses to the current algebra result for the ${\pi }^0$ lifetime are reexamined. We consider next-to-next-to-leading order corrections and we compute all the one-loop and the two-loop diagrams which contribute to the decay amplitude at this order in the two-flavor chiral expansion. We show that the result is renormalizable, as Weinberg consistency conditions are satisfied. We find that chiral logarithms are present at this order unlike the case at next-to-leading order. The result could be used in conjunction with lattice QCD simulations, the feasibility of which was recently demonstrated. We discuss the matching between the two-flavor and the three-flavor chiral expansions in the anomalous sector at order one-loop and derive the relations between the coupling constants. A modified chiral counting is proposed, in which $m_s$ counts as $O(p)$. We have updated the various inputs needed and used this to make a phenomenological prediction.