Theoretical study of a $d^{*}$ resonance in the coupled ${}^3{D}_3\text{−}{}^3{G}_3$ partial waves of nucleon-nucleon scattering

We calculated the phase shifts of the coupled ${}^3{D}_3\text{−}{}^3{G}_3$ partial waves of nucleon-nucleon scattering taking into account the ${}^7{S}_3$ $\Delta \text{−}\Delta$ channel coupling 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 from ${}^7{S}_3^{\Delta \Delta }$ coupling to the ${}^3{D}_3^{NN}$ and ${}^3{G}_3^{NN}$ partial waves in both of these two models, which is consistent with the $d$* resonance observed by WASA-at-COSY collaboration. The resonance structure in the ${}^3{D}_3^{NN}$ partial wave is remarkable, whereas in the ${}^3{G}_3^{NN}$ phase shifts there is only a small bump around the resonance energy. This result is in agreement with the recent experimental results of WASA-at-COSY Collaboration.

Figure 1

${}^3{D}_3^{NN}$ and ${}^3{G}_3^{NN}$ phase shifts including their mixing angles ${\varepsilon }_3$ in QDCSM.

Figure 2

${}^3{D}_3^{NN}$ and ${}^3{G}_3^{NN}$ phase shifts including their mixing angles ${\varepsilon }_3$ in ChQM.

Figure 3

${}^3{D}_3^{NN}$ and ${}^3{G}_3^{NN}$ amplitudes including their mixing amplitude ${\varepsilon }_3$ in two quark models. Solid (dotted) curves give the real (imaginary) part of partial-wave amplitudes in QDCSM, whereas the dashed (dash-dotted) curves represent the real (imaginary) part of partial-wave amplitudes in ChQM. Results from Ref. [6] are shown as solid circles (real part) and solid triangles (imaginary part).