Partially Quenched Chiral Perturbation Theory and a Massless Up Quark: A Lattice Calculation of the Light-Quark-Mass Ratio

TL;DR

This study uses lattice QCD calculations to determine the light-quark-mass ratio and conclusively rules out the massless-up-quark solution to the strong CP problem, providing the first such comprehensive analysis.

Contribution

The paper presents the first lattice QCD calculation of the Gasser-Leutwyler coefficient combination 2 L_8 - L_5 with N_f=3 light quarks, clarifying the up quark mass scenario.

Findings

Calculated 2 L_8 - L_5 = (0.22 +/- 0.14) x 10^-3

Derived a light-quark-mass ratio m_u / m_d = 0.408 +/- 0.035

Ruled out the massless-up-quark solution to the strong CP problem

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 m_u / m_d, 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 L_8 - L_5 can resolve the issue. We carry out such a calculation, using partially quenched N_f = 3 staggered fermions and hypercubic blocking, and make a quantitative assessment of our systematic error. We find 2 L_8 - L_5 = (0.22 +/- 0.14) x 10^-3, which corresponds to a light-quark-mass ratio of m_u / m_d = 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, N_f = 3, and the first determination of 2 L_8 - L_5 to include a comprehensive study of statistical error.