Current algebra derivation of temperature dependence of hadron couplings with currents

The vector and the axial-vector meson couplings with the vector and the axial-vector currents respectively at finite temperature were obtained by calculating all the relevant one-loop Feynman graphs with vertices obtained from the effective chiral Lagrangian. On the other hand, the same couplings were also derived by applying the method of current algebras and the hypothesis of partial conservation of axial-vector currents. The latter method appears to miss certain terms; in the case of the vector meson coupling with the vector current, for example, a term containing the ρωπ coupling is missed. A similar situation would also appear for the nucleon coupling with the nucleon current. In this note we resolve these differences.