天津大学 柯红卫 What do the radiative decays of X(3872) tell us

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1 Vertex functions for d-wave mesons and applications in the light-front approach
天津大学 柯红卫 What do the radiative decays of X(3872) tell us arXiv: Accepted by PRD Vertex functions for d-wave mesons in the light-front approach arXiv: Eur. Phys. J. C 71:1776 (2011) Hong-Wei Ke and Xue-Qian Li

2 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。

3 二、 Vertex functions for d-wave mesons in the light-front quark model
1. Vertex functions in the conventional light-front approach

4 总动量为P，总自旋为J的介子

5 对于D波介子 于是

6 利用 进一步化简

7 2. Vertex functions in the covariant light-front approach

8 以3D1为例

9 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

10 三、Applications 1. 研究1– 的D波介子

11 2.研究X(3872)的辐射衰变

12

13 得到振幅

14 最后振幅可以表达成

15 确定模型参数

16 计算结果

17

18 对的 依赖