Description of the processes $e^+ e^- \to \pi^+ \pi^-$ and $\tau^- \to \pi^- \pi^0 \nu_\tau$ in the NJL model with value of the vector coupling constant $ g_{\rho} = 6$

TL;DR

This paper demonstrates that the processes $e^+ e^- o \pi^+ \pi^-$ and $ au^- o \pi^- \\pi^0 u_ au$ can be effectively described within the NJL model using a vector coupling constant of 6, incorporating meson and quark loops for accurate results.

Contribution

It introduces a unified NJL model approach with meson and quark loops to describe specific meson processes, emphasizing the importance of meson loops at next order in $1/N_c$.

Findings

Processes are well described with $g_{\rho} = 6$

Meson loops are essential for accurate transition descriptions

Unified approach aligns with experimental data

Abstract

It is shown that the processes $e^+ e^- \to \pi^+ \pi^-$ and $\tau^- \to \pi^- \pi^0 \nu_\tau$ can be described in a unified approach in satisfactory agreement with experiment using the vector coupling constant $g_{\rho} = 6$. In this case, in addition to quark loops, it is also necessary to take into account meson loops corresponding to the next order in $1/N_c$. These loops must be taken into account when describing the $\gamma (W) \to \rho$ transition, as well as in interaction of mesons in the final state.