Dynamical Up-quark Mass Generation in QCD-like theories

We calculate the dynamically generated up quark mass in some QCD-like theories with $F=3$ light flavors, obtained from supersymmetric QCD perturbed via anomaly mediated supersymmetry breaking. We match the low-energy effective theory to the traditional chiral Lagrangian of QCD and determine the coefficients to next-to-leading order in chiral perturbation theory, while also varying the number of colors $N$. We find that the dynamically generated up quark mass vanishes in the large $N$ limit, and is small for $F<N$, however for $F=N$ there is a sizeable $O(1)$ contribution. While our results are reliable only for small supersymmetry breaking, we observe that extrapolating the $F=N$ result to large supersymmetry breaking would lead to a dynamical up quark mass that is large enough to account for its entire physical mass.