$\eta \to 3 \pi$ at Two Loops In Chiral Perturbation Theory

TL;DR

This paper computes the decay rate and Dalitz plot parameters for the $ ext{eta} o 3 ext{pi}$ process at two-loop order in Chiral Perturbation Theory, revealing larger corrections than previous estimates.

Contribution

It provides a detailed two-loop calculation of $ ext{eta} o 3 ext{pi}$ decay, including numerical results and inequalities between slope parameters, advancing theoretical understanding in chiral dynamics.

Findings

Corrections are larger than dispersive estimates suggested.

Numerical values for Dalitz plot parameters and decay ratios are provided.

An inequality between slope parameters of charged and neutral decays is derived.

Abstract

We calculate the decay $\eta\to3\pi$ at next-to-next-to-leading order or order $p^6$ in Chiral Perturbation Theory. The corrections are somewhat larger than was indicated by dispersive estimates. We present numerical results for the Dalitz plot parameters, the ratio $r$ of the neutral to charged decay and the total decay rate. In addition we derive an inequality between the slope parameters of the charged and neutral decay. The experimental charged decay rate leads to central values for the isospin breaking quantities $R=42.2$ and $Q=23.2$.