Theoretical study of a $d^{\ast }$ resonance in ${}^3{G}_3$ partial wave of nucleon-nucleon scattering

Abstract

Inspired by the recent results of the WASA-at-COSY Collaboration, in which they found a resonance pole in the coupled ${}^3{D}_3$ - ${}^3{G}_3$ partial waves as expected from the $d^{\ast }$ resonance hypothesis, we calculated the resonance structure in the coupled ${}^3{D}_3$ - ${}^3{G}_3$ partial wave phase shifts of nucleon-nucleon scattering in the framework of two constituent quark models: the quark delocalization color screening model and the chiral quark model. Our results show that there is a resonance ${}^7{S}_3^{\Delta \Delta }$ in the coupled ${}^3{D}_3^{NN}$ and ${}^3{G}_3^{NN}$ partial waves in both of these two models, which is in accordance with the expectation from the $d^{\ast }$ resonance structure. The resonance shape in the ${}^3{D}_3^{NN}$ partial wave is remarkable, whereas in the ${}^3{G}_3^{NN}$ phase shifts there is a small rise around the resonance energy. This result is in agreement with the recent experimental observations of WASA-at-COSY Collaboration.

Comments: 5 pages, 3 figures