论文标题
从几何形状的标准模型有效野外理论重新归一化
Renormalization of the Standard Model Effective Field Theory from Geometry
论文作者
论文摘要
$ s $ -Matrix元素在Lagrangian的现场重新定义下是不变的。它们由几何量（例如标量和量规场的场空间歧管的曲率）确定。我们提出了一种形式主义，其中标量和仪表场一起进行处理，并在两种类型的磁场的组合空间上进行度量。标量和量规散射幅度由此组合空间的Riemann Curvature $ r_ {ijkl} $给出，并带有指数$ i，j，k，l $，根据外部粒子的类型为标量或量规指数。一环差异也可以根据组合空间的几何不变性来计算，这极大地简化了重新归一化组方程的计算。我们将形式主义应用于标准模型有效田间理论（SMEFT），并计算偶数骨算子的重新归一化组方程将其计算为质量8。
$S$-matrix elements are invariant under field redefinitions of the Lagrangian. They are determined by geometric quantities such as the curvature of the field-space manifold of scalar and gauge fields. We present a formalism where scalar and gauge fields are treated together, with a metric on the combined space of both types of fields. Scalar and gauge scattering amplitudes are given by the Riemann curvature $R_{ijkl}$ of this combined space, with indices $i,j,k,l$ chosen to be scalar or gauge indices depending on the type of external particle. One-loop divergences can also be computed in terms of geometric invariants of the combined space, which greatly simplifies the computation of renormalization group equations. We apply our formalism to the Standard Model Effective Field Theory (SMEFT), and compute the renormalization group equations for even-parity bosonic operators to mass dimension eight.
