Is the up-quark massless?

TL;DR

This study uses lattice QCD simulations with two dynamical quark flavors to estimate low-energy constants, providing evidence against the hypothesis that the up-quark is massless.

Contribution

It offers the first precise determination of alpha5 and alpha8 in two-flavor lattice QCD, testing the massless up-quark hypothesis with improved accuracy.

Findings

Results disfavor a massless up-quark hypothesis.

Weak dependence of constants on the number of dynamical flavors.

Small qualitative differences compared to quenched approximation.

Abstract

We report on determinations of the low-energy constants alpha5 and alpha8 in the effective chiral Lagrangian at O(p^4), using lattice simulations with N_f=2 flavours of dynamical quarks. Precise knowledge of these constants is required to test the hypothesis whether or not the up-quark is massless. Our results are obtained by studying the quark mass dependence of suitably defined ratios of pseudoscalar meson masses and matrix elements. Although comparisons with an earlier study in the quenched approximation reveal small qualitative differences in the quark mass behaviour, numerical estimates for alpha5 and alpha8 show only a weak dependence on the number of dynamical quark flavours. Our results disfavour the possibility of a massless up-quark, provided that the quark mass dependence in the physical three-flavour case is not fundamentally different from the two-flavour case studied here.