论文标题
带有梯度流的Kaon Bag参数的四个夸克操作员
Four quark operators for kaon bag parameter with gradient flow
论文作者
论文摘要
为了使用$ K_0- \ bar {K} _0 $振荡研究CP-violation，我们需要在领先的Feynman图中代表QCD校正的Kaon Bag参数。晶格QCD为我们提供了直接从QCD的第一原理评估Kaon Bag参数的唯一方法。但是，通过理论上声音的四个夸克操作员的计算威尔逊型格子夸克必须承担数字上额外的重新夸大负担，并且由于明显的侵犯了手性侵犯，并分辨出了额外的混合。最近，提出了基于梯度流量的一般方法，提出了较小的流动时间扩展（SFTX）方法，以正确计算晶格上的任何重新归一化的可观察物，而与晶格上相关对称性的显式违规无关。要应用SFTX方法，我们需要匹配的系数，这将梯度流程中的小流量时有限运算符与常规重新归一化方案中的重新归一化可观测值相关联。在本文中，我们计算了与Kaon Bag参数相关的四个夸克操作员和Quark Bi-Linear运算符的匹配系数。
To study the CP-violation using the $K_0-\bar{K}_0$ oscillation, we need the kaon bag parameter which represents QCD corrections in the leading Feynman diagrams. The lattice QCD provides us with the only way to evaluate the kaon bag parameter directly from the first principles of QCD. However, a calculation of relevant four quark operators with theoretically sound Wilson-type lattice quarks had to carry a numerically big burden of extra renormalizations and resolution of extra mixings due to the explicit chiral violation. Recently, the Small Flow-time eXpansion (SFtX) method was proposed as a general method based on the gradient flow to correctly calculate any renormalized observables on the lattice, irrespective of the explicit violations of related symmetries on the lattice. To apply the SFtX method, we need matching coefficients, which relate finite operators at small flow-times in the gradient flow scheme to renormalized observables in conventional renormalization schemes. In this paper, we calculate the matching coefficients for four quark operators and quark bi-linear operators, relevant to the kaon bag parameter.
