Identification of the $G(3900)$ as the P-wave $D{\bar{D}}^{\ast }/\bar{D}{D}^{\ast }$ resonance

Abstract

The BESIII Collaboration recently performed a precise measurement of the $e^{+}{e}^{-}\to D\bar{D}$ Born cross sections, and confirmed the $G(3900)$ structure reported by BaBar and Belle with high significance. We identify the $G(3900)$ as the first P-wave $\text{DDbar}$ molecular resonance. The experimental and theoretical identification of the P-wave dimeson state holds paramount importance in enhancing our comprehension of the non-perturbative QCD and few-body physics. Its existence is firmly established in a unified meson-exchange model which simultaneously depicts the features of the ${\chi }_{c1}(3872)$, $Z_c(3900)$ and $T_{cc}(3875)$. This scenario can be directly examined in the $e^{+}{e}^{-}\to D{\bar{D}}^{\ast }/\bar{D}{D}^{\ast }$ cross section by seeing whether a resonance exists at the threshold. The credibility of the investigations is also ensured by the fact that the P-wave interaction dominantly arises from the well-known long-range pion exchange. Additionally, thanks to the centrifugal barrier, it is easier to form resonances in P-wave than in S-wave. We extensively calculate all systems up to P-wave with various quantum numbers and predict a dense population of the $\text{DDbar}$ and $\text{DD}$ states, where the S-wave $\text{DDbar}$ state with $I^G(J^{PC})=0^{-}(1^{+-})$, P-wave $\text{DDbar}$ state with $I^G(J^{PC})=0^{+}(0^{-+})$, and P-wave $\text{DD}$ state with $I(J^P)=0(0^{-})$ are more likely to be observed in experiments.

Comments: 8 pages, 4 figures. PRL(in press)