Vertex functions for d-wave mesons and applications in the light-front approach 天津大学 柯红卫 khw020056@tju.edu.cn What do the radiative decays of X(3872) tell us arXiv:1107.0443 Accepted by PRD Vertex functions for d-wave mesons in the light-front approach arXiv:1104.3996 Eur. Phys. J. C 71:1776 (2011) Hong-Wei Ke and Xue-Qian Li
一、Motivation 1.关于 light-front quark model的文献只涉及了S波和P波介子的计算 2.ψ(3770) 和ψ(4153) 被认为主量子数n=1和 n=2 的d-wave charmonia，CLEO观察到了Υ（13D2 ），新的分析认为 X(3872) 可能是 1D2。
二、 Vertex functions for d-wave mesons in the light-front quark model 1. Vertex functions in the conventional light-front approach
总动量为P，总自旋为J的介子
对于D波介子 于是
利用 进一步化简
2. Vertex functions in the covariant light-front approach
以3D1为例
One first needs to integrate over as discussed in Ref One first needs to integrate over as discussed in Ref. . Integrating over is completed by a contour integration where the antiquark is set on shell. Then the integration turns into
三、Applications 1. 研究1– 的D波介子
2.研究X(3872)的辐射衰变
得到振幅
最后振幅可以表达成
确定模型参数
计算结果
对的 依赖