A standing mystery in the Standard Model is the unnatural smallness of the strong CP violating phase, θ ≤ 10-9. The possibility of a massless up quark has long been proposed as a potential solution. Several lattice calculations of a combination of the low energy constants of the chiral Lagrangian essential for the determination of the up quark mass, 2α8 − α5, are presented. We find 2α8 − α5 = 0.115 ± 0.051stat ± 0.25syst, which is well outside the range allowing a massless up quark.
D. R. Nelson, G. T. Fleming and G. W. Kilcup, Is strong CP due to a massless up quark? hep-lat/0112029, submitted to Phys. Rev. Lett.