论文标题
稀有衰减$σ^+\ to p \ ell^+\ ell^ - $的晶格计算的前景计算
Prospects for a lattice calculation of the rare decay $Σ^+\to p\ell^+\ell^-$
论文作者
论文摘要
我们提出了一种使用lattice QCD来计算$σ^+（UUS）$ baryon $σ^+（UUS）$ baryon的罕见衰减的策略。为了确定这一可观察到的需要数字评估与目标过程相关的双，三和四点相关函数。特别是，四点功能源于插入和外向的重子的插入，以及较弱的汉密尔顿式介导$ s \ to $ s \ $ to $ transition和电磁电流产生了传出的卵子。正如其他情况下先前的工作所描述的那样，由于核子和核子 - 肽中间状态，这种四点函数与可观察的物理观察员具有高度不平凡的关系。这些导致欧几里得时间的依赖性增长，并且在核子态状态下会导致功率样效应。我们讨论了如何在$σ^+\ rightarrow p \ ell^+\ ell^ - $衰减的背景下处理这些问题，尤其是详细介绍了有限体积估计器与物理，复杂值振幅之间的关系。这样一来，我们还建立了文献中各种方法之间的联系。
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.
