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

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.