The decay $\eta \to 3 \pi$: study of the Dalitz plot and extraction of the quark mass ratio $Q$

TL;DR

This paper uses dispersive calculations and experimental data to analyze the decay $ ext{eta} o 3 ext{pi}$, providing a precise determination of the quark mass ratio $Q$ with implications for understanding quark mass differences.

Contribution

It presents a dispersive approach to the $ ext{eta} o 3 ext{pi}$ decay amplitude and extracts the quark mass ratio $Q$ from experimental data, improving the precision of quark mass ratio estimates.

Findings

Predicted neutral Dalitz plot in agreement with experiment

Determined $Q = 22.0 \, extpm 0.7$ from decay analysis

Validated dispersive method with experimental data

Abstract

The $\eta \to 3 \pi$ amplitude is sensitive to the quark mass difference $m_u-m_d$ and offers a unique way to determine the quark mass ratio $Q^2 \equiv (m_s^2-m_{ud}^2)/(m_d^2-m_u^2)$ from experiment. We calculate the amplitude dispersively and fit the KLOE data on the charged mode, varying the subtraction constants in the range allowed by chiral perturbation theory. The parameter-free predictions obtained for the neutral Dalitz plot and the neutral-to-charged branching ratio are in excellent agreement with experiment. Our representation of the transition amplitude implies $Q = 22.0 \pm 0.7$.