标题： 从$S$-和$P$-波$D\bar{D}^*$相互作用的极点轨迹 显示英文标题

标题： Pole trajectories from $S$- and $P$-wave $D\bar{D}^*$ interactions

摘要： 在本工作中，我们研究了$S$和$P$波相互作用的$D\bar{D}^*$系统，在准势 Bethe-Salpeter 方程的框架内，旨在探索可能的分子态及其相应的极点轨迹。 相互作用势能是通过单玻色子交换模型构建的，结合了$\pi$、$\eta$、$\rho$、$\omega$、$\sigma$和$J/\psi$介子的交换，基于重夸克有效拉格朗日量。 散射振幅的极点被分析，并随着截断参数增加到 5 GeV，系统地追踪了其在两个黎曼面上的演化。 我们识别出由$S$-波$D\bar{D}^*$相互作用产生的四个分子态。 其中，具有量子数$I^G(J^{PC}) = 0^+(1^{++})$的束缚态与实验上观察到的$X(3872)$非常吻合，而其同位旋矢量伙伴具有$I^G(J^{PC})= 1^-(1^{++})$仅被发现作为虚态存在。 此外，一个$0^-(1^{+-})$态表现为束缚态。 该等矢量$1^{+-}$状态，可能与$Z_c(3900)$相关，被观察到随着相互作用强度的减小，从束缚态演化为虚态。 对于$P$波$D\bar{D}^*$相互作用，最近在BESIII上观察到的结构$G(3900)$很可能与$0^-(1^{--})$状态有关。 此通道中也预测了$0^+(0^{-+})$状态。 根据相互作用强度的不同，两者都可以表现为共振态或束缚态/虚态。 显示英文摘要

摘要： In this work, we investigate the $S$- and $P$-wave interactions of the $D\bar{D}^*$ system within the framework of the quasipotential Bethe-Salpeter equation, with the aim of exploring possible molecular states and their corresponding pole trajectories. The interaction potentials are constructed using the one-boson-exchange model, incorporating the exchanges of $\pi$, $\eta$, $\rho$, $\omega$, $\sigma$, and $J/\psi$ mesons, based on heavy quark effective Lagrangians. The poles of the scattering amplitude are analyzed and their evolution on two Riemann sheets is systematically traced as the cutoff parameter increases up to 5 GeV. We identify four molecular states arising from the $S$-wave $D\bar{D}^*$ interaction. Among them, the bound state with quantum numbers $I^G(J^{PC}) = 0^+(1^{++})$ corresponds well to the experimentally observed $X(3872)$, while its isovector partner with $I^G(J^{PC})= 1^-(1^{++})$ is found to exist only as a virtual state. Additionally, a $0^-(1^{+-})$ state appears as a bound state. The isovector $1^{+-}$ state, which may be associated with the $Z_c(3900)$, is observed to evolve from a bound state to a virtual state as the interaction strength decreases. For the $P$-wave $D\bar{D}^*$ interaction, the structure $G(3900)$ recently observed at BESIII is likely connected to a $0^-(1^{--})$ state. A $0^+(0^{-+})$ state is also predicted in this channel. Both can appear as either resonance or bound/virtual state depending on the interaction strength.