Light Quarks at Large $N$

TL;DR

This paper uses large-N approximation and effective field theory to analyze light quark masses, providing new constraints on the $m_u=0$ hypothesis and predictions for lattice and phenomenological results.

Contribution

It extends previous work by determining non-linear sigma model parameters to second order in quark mass and tests the validity of the large-N approach for light quarks.

Findings

Rules out the $m_u=0$ hypothesis for light quark masses.

Provides predictions for lattice calculations and phenomenological fits.

Shows consistency with existing lattice results and phenomenological data.

Abstract

Lattice gauge theory simulations are our principal probe of the masses of the light quarks. Results from such computations are the primary evidence against the $m_u=0$ solution to the strong CP problem. The large-$N$ approximation offers an independent approach to light quarks. We extend existing literature, noting that one can determine the parameters of the non-linear sigma model through second order in quark mass, rule out the $m_u=0$ hypothesis, and make predictions for outputs of lattice calculations and phenomenological fits. A crucial feature of this analysis is a Wilsonian effective action at scales above the $\eta^\prime$ mass. One can self-consistently test the validity of aspects of this framework, and it may well be good to the part-in-three level. We also note consistency with some phenomenological fits and existing lattice results.