Fixing the vector coupling constant $g_\rho = 5.0$ in the NJL model and final-state interactions in processes $\rho \to e^+e^-[\mu^+\mu^-]$, $\rho \to \pi^+\pi^-$, $\tau \to \pi^-\pi^0\nu_\tau$, and $e^+e^-\to\pi^+\pi^-$

TL;DR

This paper demonstrates that fixing the vector coupling constant $g_\rho=5.0$ using the decay width of $\rho \to e^+e^-$ allows for a consistent theoretical description of multiple related meson and lepton processes within the NJL model, aligning well with experimental data.

Contribution

The study introduces a method to fix $g_\rho$ at 5.0 in the NJL model and shows that including final-state interactions yields a unified description of several meson decay and scattering processes.

Findings

Consistent description of $\rho$ decay and scattering processes achieved.

Final-state interactions are crucial for accurate modeling.

Theoretical results agree with experimental data.

Abstract

The possibility to use the width of the decay $\rho \to e^{+}e^{-}$ to fix the input parameter $g_\rho=5.0$ of the $SU(2) \times SU(2)$ chiral-symmetric Nambu--Jona-Lasinio model is discussed. It is shown that for a consistent simultaneous description of the processes $\rho \to e^{+}e^{-}$, $\rho \to \pi^{+}\pi^{-}$, $\tau^{-} \to \pi^{-}\pi^{0} \nu_{\tau}$, and $e^{+}e^{-} \to \pi^{+}\pi^{-}$ can be constructed. Taking into account the interaction of pions in the final state appears to be important. The obtained theoretical results for the considered processes are in a satisfactory agreement with experimental data.