Referring to Section 3.5 for details of the calculation the result for the diagram depicted in
Fig. 3-2 with fermions on the internal lines is given by
fermionss AAV Nfag3A ln(1/a) 1 ) (1 2), (3-48)
for polarizations nl = n2 A, n3 = V.
Gluons
This calculation has been done for n, = n2 A, n3 = V in the paper [6] and it is very
similar to the fermion calculation. The contribution to charge renormalization is given by:
g3 I K^ [ 2 1 1 2 fg(I
(1pgluons)AAV 4 92a ln(1/a) K_ A 1 t 2 -1 1 2__ + 9)
4 2 m MM I K 1i I M, I M. 1
-(1 2), (3-50)
The first three logarithmically divergent terms in the I summands again represent the
entanglement of infrared and ultraviolet divergences and we will see in section 3.4 how
'!.- v cancel against similar terms from the self energy contribution.
Scalars
Now consider scalars on internal lines and the same external polarizations as before.
Recall that the indices ni in Eq. (2-19) run from 1 to D 2. Let us use indices a, b for
directions 3 to D 2. Then dimensional reduction is implemented by taking p' = 0 for
all i and a. Using these conventions we will be interested in the special case of Eq. (2-19)
with n1 = a, n2 = b and n3 = V
FabV 1 ab 2K (351)
0 873/2 m M1 + (351)