Writing out the terms from interchanging I +-> 2 in this expression. and simplifying we
obtain
F^ .3KA In + In -4 ( (A)+ (AI)+ ( 37)
1 8 M 12 1
+3 2 "
In ( 2( (M ( t 2 + 1)
3 K A2 3 1 n 4 ( 1n V 2
ln ___ _(__(_.'_)-__,(_._))_+__ (-11 '''+ F,,-IL)I ,
i2 l
In "- I II n P2 4 (nM r 4 ) I 4 in In
I pn+ 9M) I In
In~ 8In -11 ( 3')j}3
where the final expression, valid at large A, I, i has been arranged so that the auv
divergence appears symmetrically among the three legs of the vertex.
Putting everything together, the l:: :litude for the vertex function to one loop is
given in the continuum limit by
p ^AAV A {i S (1 2)}
16- i21 1 M 9'
_In + In 4 (In A] + + -
pp pi 9
In 41 n +( +-1 1(3 .)