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arXiv 2007.01770hep-th
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$U(1)$ Higgs模型中BRST不变局域复合算符的重整化研究

Study of the renormalization of BRST invariant local composite operators in the $U(1)$ Higgs model

M. A. L. Capri, I. F. Justo, L. F. Palhares, G. Peruzzo, S. P. Sorella

备注：
36 pages, 6 figures
发表信息：
Phys. Rev. D 102, 033003 (2020)
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摘要：

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域BRST不变复合算符$(O,V_μ)$的重整化性质.考虑到与其他规范不变算子的混合，在$\overline{\text{MS}}$方案中，在单圈阶下明确地计算了它们的重整化$Z$因子.特别是，它证明了运营商$V_μ$与规范不变量$\partial_νF_{μν}$，其中有相同的量子数，产生了一个$2 \times 2$混合矩阵。此外，存在两个额外的强大的沃德身份，使我们能够确定整个集的$Z$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。

英文摘要：

The renormalization properties of two local BRST invariant composite operators, $(O,V_μ)$, 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 $V_μ$ mixes with the gauge invariant quantity $\partial_νF_{μν}$, 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.

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