Comment on "Ambiguities in the Up-Quark Mass"
  Creutz [hep-ph/0312225] has argued that nonperturbative effects in QCD lead to an additive ambiguity in the up quark mass, and that "this calls into question the acceptability of attempts to solve the strong CP problem via a vanishing mass for the lightest quark." We show that if the determinant of the light quark mass matrix vanishes at any scale, then it is real at all scales. 
Mark Srednicki