Chiral expansions of the pi0 lifetime

TL;DR

This paper reexamines the light quark mass corrections to the neutral pion lifetime using NNLO chiral perturbation theory, including loop calculations and matching with lattice QCD, providing refined theoretical predictions.

Contribution

It performs a comprehensive NNLO analysis of the $ au_{pi^0}$ decay amplitude within two-flavour chiral expansion, including loop diagrams and matching with lattice QCD results.

Findings

Chiral logarithms appear at NNLO, unlike at NLO.

The decay amplitude result is renormalizable and consistent with Weinberg conditions.

Updated inputs lead to a refined phenomenological prediction.

Abstract

The corrections induced by light quark masses to the current algebra result for the $\pi^0$ lifetime are reexamined. We consider NNLO corrections and we compute all the one-loop and the two-loop diagrams which contribute to the decay amplitude at NNLO in the two-flavour 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 NLO. 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-flavour and the three-flavour 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.