A general framework to diagonalize vector--scalar and axial-vector--pseudoscalar transitions in the effective meson Lagrangian

Abstract

A new mathematical framework for the diagonalization of the nondiagonal vector--scalar and axial-vector--pseudoscalar mixing in the effective meson Lagrangian is described. This procedure has unexpected connections with the Hadamard product of $n\times n$ matrices describing the couplings, masses, and fields involved. The approach is shown to be much more efficient as compared with the standard methods employed previously. The difference is especially noticeable if the chiral symmetry is broken explicitly. The paper ends with an illustrative application to the chiral model with broken $SU(3{)}_L\times SU(3{)}_R$ symmetry.

16 pages

References in corpus (3)

• Quark magnetar in three-flavor Nambu--Jona-Lasinio model with vector interaction and magnetized gluon potential
• Strange quark matter in the presence of explicit symmetry breaking interactions
• Masses of the lowest spin-0 and spin-1 meson nonets: explicit symmetry breaking effects

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• $U_A(1)$ symmetry breaking quark interactions from vacuum polarization
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• Account for axial vector mesons in the $\eta \to {\pi }^{+}{\pi }^{-}\gamma$ and ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\gamma$ decays
• Proper-time evaluation of the effective action: unequal masses in the loop