CP破坏算子的短流时系数
Short flow-time coefficients of CP-violating operators
摘要：
永久中子电偶极矩（EDM）的测量可能探测CP破坏的超越标准模型（BSM）源。在低能量的CP违反BSM相互作用的参数化的味道保存CP违反运营商的维度高于4。这些算子的核子矩阵元素的QCD计算需要完全重建的来源和大小的不同CP破坏贡献的核子EDM。本文研究了夸克色电偶极矩算符和三胶子Weinberg算符。利用格点量子色动力学非微扰确定这些CP破坏算符的核子矩阵元受到它们的短程行为的阻碍。在重整化下，这些算子与低维算子混合，当接近连续极限时，这会导致晶格间距的幂次发散。利用梯度流研究了qCEDM和Weinberg算子的短距离行为。我们进行短流时间膨胀和确定，在微扰理论中，线性发散项的膨胀系数源于混合与赝标密度和拓扑电荷，确认预期的算子乘积展开。我们介绍了一种新的方法来执行计算在非零流动时间的任意值的外部动量。这种方法允许我们在本文中描述的大部分计算中在四维中工作，避免了与在一般d维中定义$γ_5$相关的复杂性。我们表明，领先的贡献，在外部动量可以复制定义$γ_5$使用的't Hooft-Veltman-Breitenlohner-Maison计划。
英文摘要：
Measurements of a permanent neutron electric dipole moment (EDM) potentially probe Beyond-the-Standard Model (BSM) sources of CP-violation. At low energy the CP-violating BSM interactions are parametrized by flavor-conserving CP-violating operators of dimension higher than four. QCD calculations of the nucleon matrix elements of these operators are required to fully reconstruct the sources and magnitudes of the different CP-violating contributions to the nucleon EDM. Herein we study the quark-chromo electric dipole moment (qCEDM) operator and the three-gluon Weinberg operator. The non-perturbative determination, using lattice QCD, of the nucleon matrix elements of these CP-violating operators is hampered by their short-distance behavior. Under renormalization these operators mix with lower dimensional operators, which induces power divergences in the lattice spacing, as the continuum limit is approached. We study the short-distance behavior of the qCEDM and the Weinberg operators using the gradient flow. We perform a short flow time expansion and determine, in perturbation theory, the expansion coefficients of the linearly-divergent terms stemming from the mixing with the pseudoscalar density and the topological charge, confirming the expectations of the operator product expansion. We introduce a new method to perform calculations at non-zero flow-time for arbitrary values of the external momenta. This method allows us to work in four dimensions for most of the calculations described in this paper, avoiding the complications associated with defining $γ_5$ in generic d dimensions. We show that leading contributions in the external momenta can be reproduced by defining $γ_5$ using the 't Hooft-Veltman-Breitenlohner-Maison scheme.
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