论文标题
$ u（1）$ higgs模型中BRST不变的本地复合运算符的重新规则化的研究
Study of the renormalization of BRST invariant local composite operators in the $U(1)$ Higgs model
论文作者
论文摘要
在$ u（1）$ higgs模型中仔细检查了两个本地BRST不变的复合算子$（O，V_μ）$的$（O，V_μ）$，分别与Higgs粒子的规格不变描述相对应。通过$ \ Overline {\ text {ms}} $方案，通过与其他规格不变运算符的混合在一起，以一环订单的一环订单来显式评估它们的重归其化$ z $因素。特别是，事实证明，运算符$v_μ$与规格不变数量$ \partial_νf_{μν} $混合在一起，该量子具有相同的量子数，从而产生了$ 2 \ times 2 $混合矩阵。此外，存在两个其他强大的病房身份，使我们能够确定进入$ 2 \ times 2 $混合矩阵的整个$ z $的因素以及以纯代数方式的操作员$ o $的$ z $系数。提供了这些病房身份的明确检查。获得的最终设置允许对标量和矢量复合运算符的任何$ n $ - 点相关函数进行扰动地计算完整的重新归一化结果。
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.
