Calculation of Anomalous Dimension of Three-Gluon Tensor Operators

Abstract：

The renormalization coefficient matrix and anomalous dimension matrix of two three gluon tensor operator Ωαβ1=Gαa,μ Gμb,ν Gνβc f_abc and Ωαβ2=gαβ Gσa,μ Gμb,v Gνc,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 Ωαβi (nonzero momentum transfer) in Lorentz gauge were calculated explicitly up to g2s order,and no other gauge invaraiant operators were found to mix with them. Defining αβ1=Ωαβ 1-14Ωαβ2, the physical part of renormalization coefficient matrix of αβ1 in minimum subtraction scheme with space dimension D=4+2 is Z1=1+g 2s C A(4 π)276+O(g4s). The Physical part of anomalous dimension matrix of αβ1 is gauge invariant, and γ1=g2 sCA(4π)273