Partially Quenched Chiral Perturbation Theory and a Massless Up Quark: A Lattice Calculation of the Light-Quark-Mass Ratio
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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 has long been seen as a potential solution, as the term could then be absorbed through the resulting freedom to perform arbitrary chiral rotations on the up quark field.
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 the effects of an up quark mass. Only a direct calculation of the Gasser-Leutwyler coefficient combination 2L8 - L5 can resolve the issue.
New theoretical insights into partial quenched Chiral Perturbation Theory have revealed that a calculation of the low-energy constants of the partially quenched chiral Lagrangian is equivalent to a determination of the physical Gasser-Leutwyler coefficients. The coefficient combination in question is directly accessible through the pion mass’s dependence on the valence quark mass, a dependence ripe for determination via Lattice Quantum Chromodynamics.
We carry out such a partially quenched lattice calculation using Nf = 3 staggered fermions and the recently developed smearing technique known as hypercubic blocking. Through the use of several ensembles, we make a quantitative assessment of our systematic error. We find 2L8 - L5 = (0.22 ± 0.14 ) × 10-3, which corresponds to a light-quark-mass ratio of mu/md = 0.408 ± 0.035. Thus, our study rules out the massless-up-quark solution to the strong CP problem. This is the first calculation of its type to use a physical number of light quarks, Nf = 3, and the first determination of L8 - L5 to include a comprehensive study of statistical error.
Document number: osu1038343149
Permalink: http://rave.ohiolink.edu/etdc/view?acc_num=osu1038343149
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