Study of ${\eta }^{\prime }\to \eta \pi \pi$ Decays in Large-$N_C$ Chiral Perturbation Theory

Abstract

We investigate the ${\eta }^{\prime }\to \eta \pi \pi$ decays within the framework of large-$N_C$ chiral perturbation theory, by calculating the decay amplitudes up to next-to-next-to-leading order in a simultaneous expansion in powers of external momenta, quark masses, and $1/N_C$. Projecting the amplitudes onto partial waves allows us to implement a unitarization procedure to account for the $S$- and $D$-wave $\pi \pi$ final-state interactions. The relevant low-energy constants are determined by fitting our theoretical results to the precise experimental data from the A2 collaboration. A comparison of fits with and without $\pi \pi$ final-state interactions demonstrates that including these effects significantly improves the agreement of our theoretical predictions with the experimental measurements. Consequently, the Dalitz-plot parameters are extracted as $a=-0.085(18{)}_{\mathrm{stat}}(4{)}_{\mathrm{syst}}$, $b=-0.081(10{)}_{\mathrm{stat}}(6{)}_{\mathrm{syst}}$, and $d=-0.045(6{)}_{\mathrm{stat}}(8{)}_{\mathrm{syst}}$. Our results provide therefore a refined theoretical description of the ${\eta }^{\prime }\to \eta \pi \pi$ decay dynamics.

Comments: 34 pages, 8 figures, 1 table