Generalized proper-time approach for the case of broken isospin symmetry -art. no. 094009

We present a derivation of the low-energy effective meson Lagrangian of the Nambu-Jona-Lasinio (NJL) model on the basis of Schwinger's proper-time reg ularization of the one-loop fermion determinant. We consider the case in wh ich the SU(2)xSU(2) chiral symmetry of the NJL Lagrangian is broken by the current quark mass matrix with (m) over cap (u)not equal(m) over cap (d). T he non-degeneracy of d and u masses destroys one of the most crucial featur es of the proper-time expansion-the chiral-invariant structure of Seeley-De Witt coefficients. We show however that systematic resummations inside the proper-time expansion are still possible and derive a result which is in fu ll agreement with the chiral Ward-Takahashi identities.