The decay ${\eta }^{\mathrm{\prime }}\to \pi \rho$ in the chiral NJL model

The branching fraction of the decay ${\eta }^{\mathrm{\prime }}\to \pi \rho$ is calculated in the chiral quark NJL model. The decay exists due to the mass difference between $u$- and $d$-quarks leading to ${\pi }^0-{\eta }^{{}^{\mathrm{\prime }}}$ mixing. Two different approaches are applied: the approximate calculation of this process taking into account the transition ${\pi }^0-{\eta }^{{}^{\mathrm{\prime }}}$ 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 ${\eta }^{{}^{\mathrm{\prime }}}$. The obtained results are in satisfactory agreement with current experimental data.