The decay $\eta' \to \pi\rho$ in the chiral NJL model

TL;DR

This paper calculates the decay rate of $ ext{η'} o ext{π} ext{ρ}$ using the chiral NJL model, considering quark mass differences and mixing effects, and compares two approaches for accuracy.

Contribution

It introduces two methods for calculating the decay, including a precise diagonalisation approach, and shows results align with experimental data.

Findings

Decay rate consistent with experimental measurements

Two approaches yield comparable results

Mass difference induces the decay via mixing effects

Abstract

The branching fraction of the decay $\eta' \to \pi\rho$ is calculated in the chiral quark NJL model. The decay exists due to the mass difference between $u$- and $d$-quarks leading to $\pi^{0}-\eta^{'}$ mixing. Two different approaches are applied: the approximate calculation of this process taking into account the transition $\pi^{0}-\eta^{'}$ explicitly without dioganalisation and a more precise approach consisting in the diagonalisation of the singlet and octet states leading to the physical fields $\pi^{0}$, $\eta$ and $\eta^{'}$. The obtained results are in satisfactory agreement with current experimental data.