Abstract
It is found that in the presence of electroweak interactions the gauge covariant diagonalization of the axial-vector--pseudoscalar mixing in the effective meson Lagrangian leads to a deviation from the vector meson and the axial-vector meson dominance of the entire hadronic electroweak current. The essential features of such a modification of the theory are investigated in the framework of the extended Nambu-Jona-Lasinio model with explicit breaking of chiral $U(2)\ifmmode\times\else\texttimes\fi{}U(2)$ symmetry. The Schwinger-DeWitt method is used as a major tool in our study of the real part of the relevant effective action. Some straightforward applications are considered.
Highlights
At low energies, the strong and electroweak interactions of mesons can be described by effective chiral Lagrangians [1,2,3,4,5,6,7,8,9,10,11,12,13]
In the present paper we extend the idea of covariant diagonalization to the case of electroweak interactions governed by the non-Abelian group of local SUð2ÞL × Uð1ÞR symmetry
Starting from an extended Uð2ÞL × Uð2ÞR chiral symmetric NJL model with explicit flavor symmetry breaking we have derived an effective meson Lagrangian which describes both the strong and electroweak low-energy interactions of hadrons. This theory describes the phenomenon of dynamical chiral symmetry breaking
Summary
The strong and electroweak interactions of mesons can be described by effective chiral Lagrangians [1,2,3,4,5,6,7,8,9,10,11,12,13]. It has been noticed that a covariant diagonalization aμ → aμ þ κmDμp; ð3Þ where Dμp 1⁄4 ∂μp − ieAμ1⁄2Q; p, and Aμ is the electromagnetic field, leads to a gauge invariant result, but the price is a deviation from the VMD picture (the covariant derivative induces a coupling of the quark-antiquark pair with the charged pseudoscalar and the photon fields, which is the source of the new non-VMD-type electromagnetic interactions) This result has physical consequences, and should be very carefully scrutinized. The purpose of this paper is to exhibit a Lagrangian theory in which the effective electroweak interactions of mesons may deviate from the phenomenologically successful ideas of VMD and axial-vector dominance due to the p − aμ mixing and gauge symmetry requirements. XI we summarize our results and discuss the possible role of the non-VMD (and axial-vector dominance) electroweak contributions for the theory
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