and similarly for Fpb^. The evaluation of the diagram is analogous to the previous
calculations and the result corresponding to (3-48) is
(icalars)AAV N nag3 KA Mi-1
(palarsAAV ln(l/a) ^ f (1/ .) (1 2). (3-52)
47r2M M I
1
3.4 Discussion of Results
The physical coupling can be measured by i V/-ZF, the renormalized vertex function,
where F is the proper vertex and Zi is the wave function renormalization for leg i. To one
loop we write this in terms of our quantities as:
Y + Fo -(Zi 1), (3-53)
i
where F0o is the tree level vertex and F, is our one loop result for the vertex:
p^AAV fiermions + pgluons + pscalars (3 54)
L /3 P3+ M-1 2 1 1 F(1/1f.) (t 0-25)
4 w nM + 1 + + +
411 1 m. i1 1
Because of how loops are treated in the Lightcone World Sheet formalism we are
motivated to combine the one loop vertex result and the wave function renormalization
for a fixed position of the solid line representing the loop. In other words we renormalize
,Ju,"flu on the world sheet. To clarify this, note the three different ways to insert a one loop
correction to the cubic vertex at fixed I on the world sheet, as in Fig. 3-3. Notice that
k k k2
k k2
kO0
k k-
k = k i k k. k -k2
k = 0
k 0
I M1 if. 1 M1 if. 1 M1 if.
Figure 3-3: One loop diagrams for fixed I in the Lightcone World Sheet.