Short flow-time coefficients of CP -violating operators
Short flow-time coefficients of CP -violating operators
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DOI：
10.1103/physrevd.102.034509
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发表时间：
2020-05
影响因子：
5
通讯作者：
Matthew D. Rizik;C. Monahan;A. Shindler
中科院分区：
文献类型：
--
作者：
Matthew D. Rizik;C. Monahan;A. Shindler
永久中子电偶极矩 (EDM) 的测量可能会探测 CP 破坏的超标准模型 (BSM) 来源。在低能量下，CP 破坏 BSM 相互作用由维数高于四的保味 CP 破坏算子参数化。需要对这些算子的核子矩阵元素进行 QCD 计算，以完全重建对核子 EDM 的不同 CP 破坏贡献的来源和大小。在这里，我们研究了夸克色电偶极矩（qCEDM）算子和三胶子温伯格算子。使用晶格 QCD 对这些 CP 破坏算子的核子矩阵元素进行非微扰测定受到其短距离行为的阻碍。在重整化下，这些算子与低维算子混合，当接近连续极限时，会引起晶格间距的幂发散。我们使用梯度流研究 qCEDM 和 Weinberg 算子的短距离行为。我们执行短流时间展开，并在微扰理论中确定源自与赝标量密度和拓扑电荷混合的线性发散项的展开系数，确认了算子乘积展开的期望。我们引入了一种新方法，可以在非零流动时间下对任意外部动量值进行计算。这种方法允许我们在四个维度上进行本文描述的大多数计算，避免了与在通用 d 维度中定义 $\gamma_5$ 相关的复杂性。我们表明，可以通过使用 't Hooft-Veltman-Breitenlohner-Maison 方案定义 $\gamma_5$ 来重现外部动量的主导贡献。
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 $\gamma_5$ in generic d dimensions. We show that leading contributions in the external momenta can be reproduced by defining $\gamma_5$ using the 't Hooft-Veltman-Breitenlohner-Maison scheme.