三胶子张量算符反常量纲的计算

Calculation of Anomalous Dimension of Three-Gluon Tensor Operators

计算了两个与量子数为JPC=1-+ 的胶球流算符密切相关的三胶子张量算符Ωαβ1=Gαa ,μGμb ,νGνβcfabc和Ωαβ2 =gαβGσa ,μGμb ,νGνc,σfabc的重整化矩阵和反常量纲矩阵 .在Lorentz规范下 ,计算算符Ωαβi 去外腿三点Green函数 (顶点动量不为零 )发散项的过程中 ,到 g2s 级为止 ,没有发现其它规范不变的算符参与混合 .在定义 Ωαβ1=Ωαβ1- 14Ωαβ2 后 ,求得最小减除方案 (MS)下 (空间维数D =4+2) Ωαβ1的重整化系数 (物理部分 )为Z Ω1 =1+g2sCA(4π) 2 76 +O(g4 s) . Ωαβ1的反常量纲 (物理部分 )是一个规范无关量 ,为γ Ω1 =g2sCA(4π) 273.

The renormalization coefficient matrix and anomalous dimension matrix of two three gluon tensor operator Ω αβ 1=G α a,μ G μ b,ν G νβ c f abc and Ω αβ 2 =g αβ G σ a,μ G μ b,v G ν c,σ f abc ,which are closely related to the glueball current operator with quantum number J PC =1 -+ , were calculated. The divergent terms of amputated three point Green function of Ω αβ i (nonzero momentum transfer) in Lorentz gauge were calculated explicitly up to g 2 s order,and no other gauge invaraiant operators were found to mix with them. Defining αβ 1 =Ω αβ 1-14Ω αβ 2, the physical part of renormalization coefficient matrix of αβ 1 in minimum subtraction scheme with space dimension D=4+2 is Z 1 =1+g 2 s C A(4 π ) 276+O(g 4 s). The Physical part of anomalous dimension matrix of αβ 1 is gauge invariant, and γ 1 =g 2 s C A(4 π ) 2 73