基于QCD理论与Bethe-Salpeter方程研究含重夸克的奇特介子共振态

In the last decade many new meson resonances containing heavy quarks were discovered in experiments, which do not fit in the conventional quark-antiquark picture. According to the experimental results, it is suggested that these exotic mesons are hadronic molecule states consisting of two heavy mesons induced by the strong interaction. However, in previous works, two heavy mesons in the molecular state are considered as point-like objects, and the effective interaction potential between these two heavy mesons is dubious. In this research, using the nonperturbative methods (Bethe-Salpeter (BS) equation, chiral perturbation theory and QCD sum rules), we investigate these observed exotic states which are considered as molecular states. When constructing the interaction kernel between two heavy mesons derived from one light meson exchange, we consider that the heavy meson is composed of a heavy quark and a light quark and then investigate the light meson interaction with the quarks in the heavy meson based on chiral perturbation theory. Through the heavy meson form factors we can obtain the kernel between two heavy mesons. Obviously, this kernel in our approach contains more inspiration of QCD, which is the main difference between our approach and the previous works. Finally, numerically solving the BS equation with this kernel, we can obtain the mass and BS wave function of the molecular state. Then using the obtained BS wave function, we can calculate the width of exotic meson.

近十几年来，粒子物理学家发现了许多包含重夸克却无法用传统的正反夸克模型解释的介子共振态。虽然理论物理学家结合实验提出了强子分子态模型来解释这些奇特介子共振态，即认为它们是两个重介子由于强相互作用而组成的分子态，但是目前关于分子态的理论还很不完善。本项目将用量子场论中的非微扰方法（Bethe-Salpeter(BS)方程、手征微扰理论和QCD求和法则）研究这些奇特态的分子态结构，从而建立一套系统、准确地描述强子分子态的理论。与以往的研究方法不同，本课题首先考虑重介子内部的重-轻夸克结构，然后基于手征微扰理论考虑重介子中的夸克和交换轻介子的相互作用，通过计算重介子的形状因子得到两个重介子之间的相互作用核后，解BS方程得到奇特介子共振态的质量和描述分子态结构的BS波函数。接着利用得到的BS波函数计算该奇特介子共振态的衰变宽度。

目前，粒子物理学中关于分子态的理论还很不完善。本项目建立了一套系统地、准确地描述强子分子态的理论。与以往的研究方法不同，项目组成员从QCD出发，在量子场论的框架中得到了能够描述分子态结构的四夸克态的generalized Bethe–Salpeter(GBS)波函数；根据衰变过程找到了最低阶不可约格林函数，接着得到了两个矢量介子组成的分子态衰变成一重一轻介子的矩阵元的一般形式；补充了两个矢量场组成的束缚态所满足的Bethe–Salpeter (BS)波函数的一般形式，从而修正了描述分子态结构的四夸克态的GBS波函数；根据Weinberg-Salam模型和衰变过程找到了不可约格林函数，接着得到了两个矢量介子组成的分子态衰变成两个光子的矩阵元的一般形式。我们的方法适用于各种的介子-介子分子态结构以及各种衰变方式。该方法还可将真空凝聚的非微扰贡献引入到GBS波函数中，这样理论计算结果可以包含更多的非微扰QCD效应。本项目的成果为分子态结构的进一步研究和Bethe-Salpeter方程的应用奠定了基础。