论文标题
在标准模型有效现场理论中的Dimension-9操作员基础的明确构造
An explicit construction of the dimension-9 operator basis in the standard model effective field theory
论文作者
论文摘要
我们在标准模型有效字段理论中系统地研究了尺寸-9的运算符，该理论仅包含标准模型字段并尊重其规格对称性。在Hilbert系列方法的帮助下，根据其Lepton和Baryon数字及其现场内容对运营商进行分类，我们明确构建了运营商的基础。我们通过采用各种运动学和代数关系来删除冗余的操作员，包括零件，运动方程，舒顿身份，迪拉克矩阵和fierz身份以及比安奇身份的集成。我们通过分析其风味对称关系来确认对独立运营商进行计数。所有操作员都违反了Lepton或Baryon的数字或两者兼而有之，因此是非热者。包括Hermitian共轭操作员，有$ 384 |^{Δl= \ pm 2} _ {ΔB= 0} +10 |^{Δl= 0} _ {ΔB= \ pm 2} +4 |^{Δl= \ pm3} 1} _ {ΔB= \ pm1} $ operators operators nOwe nOwing Fermion Generations，$ 44874 |^{Δl= \ pm 2} _ {ΔB= 0} +2862 |^{Δl= 0} _ {Δl= 0} 2} +486 |^{Δl= \ pm3} _ {Δb= \ pm1} +42234 |^{Δl= \ pm 1} _ {Δb= \ mp1} $操作员在三代效率转介给$δB$δB$ neup and lep and lep and lep and lep and lep时。我们的结果为与Dimension-9运算符相关的一致现象学研究提供了一个起点。
We investigate systematically dimension-9 operators in the standard model effective field theory which contains only standard model fields and respects its gauge symmetry. With the help of the Hilbert series approach to classifying operators according to their lepton and baryon numbers and their field contents, we construct the basis of operators explicitly. We remove redundant operators by employing various kinematic and algebraic relations including integration by parts, equations of motion, Schouten identities, Dirac matrix and Fierz identities, and Bianchi identities. We confirm counting of independent operators by analyzing their flavor symmetry relations. All operators violate lepton or baryon number or both, and are thus non-Hermitian. Including Hermitian conjugated operators there are $384|^{ΔL=\pm 2}_{ΔB=0}+10|^{ΔL=0}_{ΔB=\pm 2}+4|^{ΔL=\pm3}_{ΔB=\pm1}+236|^{ΔL=\mp 1}_{ΔB=\pm1}$ operators without referring to fermion generations, and $44874|^{ΔL=\pm 2}_{ΔB=0}+2862|^{ΔL=0}_{ΔB=\pm 2}+486|^{ΔL=\pm3}_{ΔB=\pm1}+42234|^{ΔL=\pm 1}_{ΔB=\mp1}$ operators when three generations of fermions are referred to, where $ΔL,~ΔB$ denote the net lepton and baryon numbers of the operators. Our result provides a starting point for consistent phenomenological studies associated with dimension-9 operators.
