Study of the renormalization of BRST invariant local composite operators in the U(1) Higgs model
Study of the renormalization of BRST invariant local composite operators in the
U(1)
Higgs model
复制标题
U(1) Higgs模型中BRST不变局部复合算子的重整化研究
DOI：
10.1103/physrevd.102.033003
复制
发表时间：
2020
影响因子：
5
通讯作者：
S. P. Sorella
中科院分区：
文献类型：
--
作者：
M. Capri;I. Justo;L. Palhares;G. Peruzzo;S. P. Sorella
在U（1）Higgs模型中，利用代数重整化方法研究了分别对应于Higgs粒子和质量规范矢量玻色子规范不变描述的两个局部BRST不变复合算符$（O，V\mu）$的重整化性质.他们的重整化$Z$的因素明确评估在一个循环的顺序在$\overline{\text{MS}}$计划，考虑到适当的混合与其他规范不变的运营商。特别地，它证明了算符$V_\mu$与具有相同量子数的规范不变量$\partial_\nu F_{\mu\nu}$混合，产生了一个$2 \times 2$混合矩阵。此外，两个额外的强大的沃德身份存在，使我们能够确定整个集合的Z$的因素进入2\times 2$混合矩阵，以及$Z$因素的运营商O$在一个纯粹的代数方式。提供了对这些沃德恒等式的显式检查。最后得到的设置允许微扰计算的标量和矢量复合算子的任何$n$点相关函数的完整重整化结果。
The renormalization properties of two local BRST invariant composite operators, $(O,V_\mu)$, corresponding respectively to the gauge invariant description of the Higgs particle and of the massive gauge vector boson, are scrutinized in the $U(1)$ Higgs model by means of the algebraic renormalization setup. Their renormalization $Z$'s factors are explicitly evaluated at one-loop order in the $\overline{\text{MS}}$ scheme by taking into due account the mixing with other gauge invariant operators. In particular, it turns out that the operator $V_\mu$ mixes with the gauge invariant quantity $\partial_\nu F_{\mu\nu}$, which has the same quantum numbers, giving rise to a $2 \times 2$ mixing matrix. Moreover, two additional powerful Ward identities exist which enable us to determine the whole set of $Z$'s factors entering the $2 \times 2$ mixing matrix as well as the $Z$ factor of the operator $O$ in a purely algebraic way. An explicit check of these Ward identities is provided. The final setup obtained allows for computing perturbatively the full renormalized result for any $n$-point correlation function of the scalar and vector composite operators.