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

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.