I discuss the properties of pions in “partially quenched” theories, i.e., those in which the valence and sea quark masses $m_V$ and $m_S$ are different. I point out that for lattice fermions which retain some chiral symmetry on the lattice, e.g., staggered fermions, the leading order prediction of the chiral expansion is that the mass of the pion depends only on $m_V,$ and is independent of $m_S.$ This surprising result is shown to receive corrections from loop effects which are of relative size $m_S\ln m_V,$ and which thus diverge when the valence quark mass vanishes. Using partially quenched chiral perturbation theory, I calculate the full one-loop correction to the mass and decay constant of pions composed of two nondegenerate quarks, and suggest various combinations for which the prediction is independent of the unknown coefficients of the analytic terms in the chiral Lagrangian. These results can also be tested with Wilson fermions if one uses a nonperturbative definition of the quark mass.

• Received 17 July 1997

DOI:https://doi.org/10.1103/PhysRevD.56.7052