Revisiting the assignment of $1^{3}D_{1}$ meson nonet

Based on the mass relations from the Regge phenomenology, we revisit the mass spectrum of $1^{3}D_{1}$ meson nonet. The masses of kaon and $s\bar{s}$ member of $1^{3}D_{1}$ ($1^{3}D_{1}(s\bar{s})$) meson nonet are obtained and the results are compared with the values from different theoretical models. Moreover, the strong decay properties of the kaon and $1^{3}D_{1}(s\bar{s})$ are presented in the $^{3}P_{0}$ model. On the basis of results, we suggest the assignment of $1^{3}D_{1}$ meson nonet need further tested in the new experiment in the future. Our results also provide mass constraints for the study of these states.