detailed expressions we get
dq exp a kl(Pi -p)2+ -P? (k2 ki)(-p3 )2_)
1 1 kl,k2
{ r / \ r / \1- 11
Tr (7"7) P P -P +ag P3 _P P 2
2 KM -1 / /1 M (16i
ag(7 P3 -P + P P3
2m M.- I I m 1 M.( \
a ( 7 2 7 ) P i P rP 3 i ) + a g P 3 P P 2] ( 3 1 2 6 )
Notice that this is the expression associated with fermion arrows running counterclockwise
around the loop. The other diagram contributes the same amount as this one. Also,
this expression is for k, > 0, the other time ordering k, < 0 is obtained by making the
substitution pl +- P2 as in the gluon calculation of the paper [6]. We now proceed much as
in that calculation by completing the square in the exponent of Eq. (3-126) and shifting
momentum
Ml- 'f q tIr + t2+ a6 H
11 klk2 ( 2 q H _
Tr 2 ___ X i (7 X ) + g 3
Tr 1 (M 1) M (Mi-1) H I(. 1) m
t n2
(X2 (2[t) 2_/+g 2 (3-127)
2 A (M-1)(pf. 1) (M. 1) M
with
3 tlKT t2K+ tlKT (
X1 + t2 + 6 Mlq", X' 6 + t +, 6 = + M 3-128)
S- kl k2 k2 kl (19
1 k2T' k3 (3-129)
a tlt3P + 1t 2 2 3 2
H a tIt3p= + t2p + W3P3 (3-130)
2m tI + t2 + 3