Mending $\rho\pi\pi$ vertex through the $\pi a_1$ diagonalization

TL;DR

This paper addresses the momentum dependence issue of the $ ho ext{-}\pi ext{-}\pi$ vertex in the extended Nambu--Jona-Lasinio model by redefining spin-1 fields, deriving a new Lagrangian, and calculating relevant decay widths.

Contribution

It introduces a novel field choice for spin-1 particles to fix the momentum dependence problem and derives a corresponding phenomenological Lagrangian.

Findings

Calculated decay widths of $ ho o\pi ext{-}\pi$ and $a_1 o ho ext{-}\pi$ match empirical data.

Resolved the strong momentum dependence issue in the $ ho ext{-}\pi ext{-}\pi$ vertex.

Provided a new theoretical framework for meson interactions in the extended NJL model.

Abstract

The problem of the strong momentum dependence of the $\rho\pi\pi$-vertex in the extended Nambu -- Jona-Lasinio model is solved by an appropriate choice of fields for spin-1 particles. A corresponding phenomenological Lagrangian is derived. As straightforward applications, the decay widths of $\rho\to\pi\pi$, and $a_1\to\rho\pi$ transitions are calculated and compared with known empirical data and previous theoretical estimates.