格点计算稀有衰变$Σ^+\to p\ell^+\ell^-$的前景
Prospects for a lattice calculation of the rare decay $Σ^+\to p\ell^+\ell^-$
AI总结：
本研究提出利用格点QCD计算$Σ^+\to p\ell^+\ell^-$稀有衰变的策略，分析关联函数计算中的中间态效应等问题，明确有限体积估计量与物理振幅的关系并梳理相关研究方法。
摘要：
我们提出了一种利用格点QCD（量子色动力学）计算$Σ^+ (uus)$重子稀有衰变为质子$(uud)$和双轻子对的策略。要确定这一可观测量，需要数值计算与目标过程相关的重子两点、三点和四点关联函数。具体而言，四点关联函数来自入射和出射重子的插入，以及介导$s\to d$跃迁的弱哈密顿量和产生出射轻子的电磁流。正如此前其他方向的工作所述，由于核子和核子-π中间态的存在，该四点关联函数与物理可观测量之间存在极为复杂的关系。这些中间态会导致欧几里得时间依赖关系增强，而对于核子-π态，还会引发幂律体积效应。我们讨论了在$Σ^+\rightarrow p\ell^+\ell^-$衰变研究中如何处理这些问题，尤其详细阐述了有限体积估计量与物理复值振幅之间的关系，同时也梳理了文献中多种方法之间的关联。
英文摘要：
We present a strategy for calculating the rare decay of a $Σ^+ (uus)$ baryon to a proton $(uud)$ and di-lepton pair using lattice QCD. To determine this observable one needs to numerically evaluate baryonic two-, three-, and four-point correlation functions related to the target process. In particular, the four-point function arises from the insertion of incoming and outgoing baryons, together with a weak Hamiltonian mediating the $s \to d$ transition and an electromagnetic current creating the outgoing leptons. As is described in previous work in other contexts, this four-point function has a highly non-trivial relation to the physical observable, due to nucleon and nucleon-pion intermediate states. These lead to growing Euclidean time dependence and, in the case of the nucleon-pion states, to power-like volume effects. We discuss how to treat these issues in the context of the $Σ^+\rightarrow p\ell^+\ell^-$ decay and, in particular, detail the relation between the finite-volume estimator and the physical, complex-valued amplitude. In doing so, we also make connections between various approaches in the literature.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
