Determination of the m_u and m_d quark masses from η → 3π decay

Martin Zdráhal (Prague)

A natural method for the precise determination of the m_d-m_u mass difference, which is still beyond the reach of direct lattice simulations, is a comparison of a measured value of some quark-mass dependent observable with its chiral perturbation theory (ChPT) prediction.  The most promising processes for such a study seem to be η → 3π decays.  Unfortunately, achieving this goal is complicated by large chiral corrections to the amplitudes of these processes and by the observed discrepancies between the experimentally measured values of Dalitz parameters describing their energy dependencies and the values predicted from ChPT.

We present a method based on our analytic dispersive representation, which uses the information we have from the two-loop ChPT result together with the one obtained from the KLOE measurement on the charged η → 3π decay in a consistent way, thereby determining the value of the quark mass ratio 1/R~(m_d-m_u).  Our result is R=37.7±2.2.  Using the recent lattice values for m_s and for the isospin averaged value of (m_u+m_d)/2, our determination leads to m_u(2GeV)=(2.2±0.6) MeV and m_d(2GeV)=(4.6±0.6) MeV.  Provided a better access to the measured energy dependence of the (charged) η → 3π amplitude is available, this result can be still substantially improved.

(Seminarraum II)