Perturbative Power Counting,Lowest-Index Operators and Their Renormalization in Standard Model Effective Field Theory

作     者：廖益 马小东 Yi Liao 1,2,3, Xiao-Dong Ma 1

作者机构：School of PhysicsNankai University CAS Key Laboratory of Theoretical PhysicsInstitute of Theoretical Physics Chinese Academy of Sciences Synergetic Innovation Center for Quantum Effects and ApplicationsHunan Normal University 

出 版 物：《Communications in Theoretical Physics》 (理论物理通讯（英文版）)

年 卷 期：2018年第69卷第3期

页      面：285-290页

核心收录：

学科分类：07[理学] 070201[理学-理论物理] 0704[理学-天文学] 0702[理学-物理学] 

基　　金：Supported by the National Natural Science Foundation of China under Grant Nos.11025525,11575089 the CAS Center for Excellence in Particle Physics(CCEPP) 

主　　题：标准模型 理论建模 索引 Lagrangian 正常化 操作员 操作符 相等 

摘      要：We study two aspects of higher dimensional operators in standard model effective field theory.We first introduce a perturbative power counting rule for the entries in the anomalous dimension matrix of operators with equal mass dimension.The power counting is determined by the number of loops and the difference of the indices of the two operators involved,which in turn is defined by assuming that all terms in the standard model Lagrangian have an equal perturbative power.Then we show that the operators with the lowest index are unique at each mass dimension d,i.e.,(H~?H)^(d/2)for even d≥4,and(L^TεH)C(L^TεH)~T(H~?H)^((d-5)/2)for odd d≥5.Here H,L are the Higgs and lepton doublet,andε,C the antisymmetric matrix of rank two and the charge conjugation matrix,respectively.The renormalization group running of these operators can be studied separately from other operators of equal mass dimension at the leading order in power counting.We compute their anomalous dimensions at one loop for general d and find that they are enhanced quadratically in d due to combinatorics.We also make connections with classification of operators in terms of their holomorphic and anti-holomorphic weights.