标题： 电弱三体衰变在存在两体和三体束缚态的情况下 显示英文标题

标题： Electroweak three-body decays in the presence of two- and three-body bound states

摘要： 最近，已经推导出一种形式主义，用于研究无限体积和有限体积下三体系统的电弱转变振幅。 该形式主义提供了无限体积振幅必须满足的精确关系，以及物理振幅与有限体积矩阵元之间的关系，这些可以由格点QCD计算来约束。 与类似且已广泛研究的两体情况相比，这种形式主义带来了额外的挑战，包括求解奇异函数积分方程的必要步骤。 在本工作中，我们对该上述形式主义进行了若干非平凡的分析和数值测试。 特别是，我们考虑了一种三粒子系统可以具有三体束缚态以及两体子系统中的束缚态的情况。 对于低于三体阈值的动力学情况，我们证明了散射振幅满足单位性。 我们还验证了对于这些动力学情况，有限体积矩阵元在指数抑制修正范围内由两体系统的形式主义准确描述。 最后，我们验证了在三体束缚态的情况下，有限体积矩阵元等于束缚态的无限体积耦合，指数抑制误差除外。 显示英文摘要

摘要： Recently, formalism has been derived for studying electroweak transition amplitudes for three-body systems both in infinite and finite volumes. The formalism provides exact relations that the infinite-volume amplitudes must satisfy, as well as a relationship between physical amplitudes and finite-volume matrix elements, which can be constrained from lattice QCD calculations. This formalism poses additional challenges when compared with the analogous well-studied two-body equivalent one, including the necessary step of solving integral equations of singular functions. In this work, we provide some non-trivial analytical and numerical tests on the aforementioned formalism. In particular, we consider a case where the three-particle system can have three-body bound states as well as bound states in the two-body subsystem. For kinematics below the three-body threshold, we demonstrate that the scattering amplitudes satisfy unitarity. We also check that for these kinematics the finite-volume matrix elements are accurately described by the formalism for two-body systems up to exponentially suppressed corrections. Finally, we verify that in the case of the three-body bound state, the finite-volume matrix element is equal to the infinite-volume coupling of the bound state, up to exponentially suppressed errors.