Construction of the eta->3pi (and K->3pi) amplitudes using dispersive approach

TL;DR

This paper develops a model-independent dispersive method to accurately describe eta and K three-pion decays, incorporating two-loop corrections and matching with chiral perturbation theory to improve decay amplitude predictions.

Contribution

It introduces a dispersive framework based on fundamental principles for eta and K three-pion decays, including two-loop corrections and matching with ChPT results.

Findings

Dispersive approach successfully models eta->3pi decay amplitudes.

Matching with two-loop ChPT enhances prediction accuracy.

Predictions for Dalitz plot slope parameter alpha are discussed.

Abstract

The dispersive approach based only on very general principles, unitarity, analyticity and crossing symmetry, combined with chiral counting enables to construct fully relativistic model-independent representations of the eta and K three-pion decays valid up to and including two-loop corrections. Here we demonstrate the procedure on the eta->3pi^0 decay. We perform possible matchings of our dispersive approach with the two-loop ChPT result and briefly discuss corresponding predictions of the Dalitz plot slope parameter alpha.