Determination of the $m_u$ and $m_d$ quark masses from $\eta \to 3\pi$ decay

TL;DR

This paper proposes a dispersive analytic method to determine the up and down quark masses from the decay process $ ext{eta} o 3 ext{pi}$, addressing discrepancies in chiral perturbation theory predictions.

Contribution

It introduces a dispersive analysis approach that accounts for chiral correction discrepancies, improving quark mass determination from $ ext{eta} o 3 ext{pi}$ decay.

Findings

Quark mass values consistent with multiple constraints.

Dispersive method reduces uncertainties from chiral corrections.

Provides refined estimates of $m_u$ and $m_d$.

Abstract

For a precise determination of the m_u and m_d quark masses, it is useful to combine isospin symmetric results of lattice or sum rules QCD techniques with some isospin breaking study performed in chiral perturbation theory (ChPT). The most promising process for the later is $\eta \to 3\pi$ decay. However, this process is affected by large chiral corrections and there are observed discrepancies between the values of Dalitz plot parameters stemming from the standard ChPT computation of its amplitude and those experimentally measured. We describe here the method based on analytic dispersive representation which attempts to obtain the information on the masses by taking this discrepancy into account independently of its exact origin. Together with the results of this analysis we present a review of some other constraints on the light quark masses and conclude with values of the masses compatible with them.