The Extended Nambu-Jona-Lasinio Model and Hidden Local Symmetry of Low Energy QCD

Abstract

Using the standard auxiliary field method, we derive from the extended Nambu-Jona-Lasinio model an effective meson action containing vector and axial-vector mesons in addition to Goldstone bosons. The vector and axial-vector mesons in this effective action transform as gauge fields of hidden local symmetry $G_{local} = {[U(n)_L \times U(n)_R]}_{local}$. Here, the realization of enlarged hidden local symmetry is accomplished via the introduction of two kinds of ``compensating'' fields. For obtaining the intrinsic-parity violating part of the action, we generalize the standard gauged Wess-Zumino-Witten action such that it also contains two kinds of ``compensators'' in addition to the usual Goldstone bosons as well as the vector and axial-vector mesons. This generalized gauged Wess-Zumino-Witten action turns out to have $G_{globa} \times G_{local}$ symmetry, where $G_{global}$ being the usual $U(n)_L \times U(n)_R$ global chiral symmetry while $G_{local}$ being the $U(n)_L \times U(n)_R$ hidden local symmetry. This means that $G_{local}$ has no gauge anomaly and its associated vector and axial-vector mesons can be regarded as gauge bosons of $G_{local}$. The introduction of the coupling with the external electroweak fields requires us to gauge some appropriate subgroup of $G_{global}$. To perform it in consistent with the anomaly structure of QCD is a nontrivial problem. We explain how this can be done, following the recent suggestion by several authors.