Electromagnetic mass differences from an effective Lagrangian

Abstract

An effective-Lagrangian model that gave finite lowest-order dynamical electromagnetic corrections to the masses of vector mesons is generalized to a chiral O(4) model, which includes A$sub 1$ mesons and pions. Aside from a PCAC (partial-conservation-of-axial-vector-current) ''tadpole'' term, the Lagrangian is chiral-O(4)-symmetric, but a term responsible for supplying a part of the A$sub 1$ mass is not gauge-symmetric. Both pion and A$sub 1$ mass differences contain logarithmically divergent terms, as in chiral current-algebra calculations. The soft-pion part of the pion mass difference is, however, 3.2 MeV, instead of 5.0 MeV as given by current-algebra and other effective- Lagrangian calculations. (AIP)