Partially Quenched Chiral Perturbation Theory and a Massless Up Quark: A Lattice Calculation of the Light-Quark-Mass Ratio
Abstract
The nontrivial topological structure of the QCD gauge vacuum generates a CP breaking term in the QCD Lagrangian. However, measurements of the neutron electric dipole moment have demonstrated that the term's coefficient is unnaturally small, a dilemma known as the strong CP problem. A massless up quark is one potential solution, as the term could then be absorbed through chiral rotations. Through the light-quark-mass ratio mu / md, leading order Chiral Perturbation Theory appears to rule this scenario out. However, the Kaplan-Manohar ambiguity demonstrates that certain strong next-to-leading order corrections are indistinguishable from an up quark mass. Only a direct calculation of the Gasser-Leutwyler coefficient combination 2 L8 - L5 can resolve the issue. We carry out such a calculation, using partially quenched Nf = 3 staggered fermions and hypercubic blocking, and make a quantitative assessment of our systematic error. We find 2 L8 - L5 = (0.22 +/- 0.14) x 10-3, which corresponds to a light-quark-mass ratio of mu / md = 0.408 +/- 0.035. Thus, the massless-up-quark solution to the strong CP problem is ruled out. This is the first calculation of its type to use a physical number of light quarks, Nf = 3, and the first determination of 2 L8 - L5 to include a comprehensive study of statistical error.
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