Several lattice calculations of a combination of the low energy constants of the chiral Lagrangian, 2\alpha_8-\alpha_5, are presented. This combination is critical for the preclusion of a massless up quark. The result found is 2\alpha_8-\alpha_5 = 0.115 \pm 0.051^{stat} \pm 0.25^{syst}, which is well outside of the range allowed by a massless up quark.
@article{arxiv.hep-lat/0110112,
title = {Is the Up Quark Massless?},
author = {Daniel R. Nelson and George T. Fleming and Greg W. Kilcup},
journal= {arXiv preprint arXiv:hep-lat/0110112},
year = {2011}
}