  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.
