we can write Now, consider the integral To evaluate this integral we will use the following identity [110, 118] The integration variable α is called an alpha parameter and serves a similar purpose to the Feynman parameters introduced earlier. The resulting k$_{1}$ and k$_{2}$ loop integrals can be evaluated using the integral [118] Doing this, the result is The functions D ( α ) and Q ( α , a$_{1}$ , a$_{2}$ ) are 67 Q ( α$_{i}$ , a$_{1}$ , a$_{2}$ ) = [( α$_{1}$ + α$_{2}$ ) ( α$_{3}$ + α$_{4}$ ) α$_{5}$ + α$_{1}$α$_{2}$ ( α$_{3}$ + α$_{4}$ ) + α$_{3}$α$_{4}$ ( α$_{1}$ + α$_{2}$ )] q 2 + ( a$_{1}$ · q ) Q$_{1}$ + ( a$_{2}$ · q ) Q$_{2}$ + a 2 $_{1}$Q 2 11 + a 2 $_{2}$Q 2 22 + ( a$_{1}$ · a$_{2}$ ) Q$_{12}$ , (2.52) D ( α ) = α$_{5}$ ( α$_{1}$ + α$_{2}$ + α$_{3}$ + α$_{4}$ ) + ( α$_{1}$ + α$_{3}$ ) ( α$_{2}$ + α$_{4}$ ) , (2.51) G ( d ) $^{(}$q 2 ) = i 2 − d (4 π ) d 5 ∏ i =1 1 i n$_{i}$ Γ ( n$_{i}$ ) ∫ ∞ 0 dα$_{i}$ [ D ( α )] d 2 α n$_{i}$ − 1 i exp$^{[}$ i$^{(}$ Q ( α$_{i}$ , a$_{1}$ , a$_{2}$ ) D ( α ) − 5 ∑ j =1 α$_{j}$m 2 j )] . (2.50) ∫ d $^{d}$k exp $^{[}$i $^{(}$Ak 2 + 2 q · k )] = i [ π iA$^{]}$$^{d}$ 2 exp$^{[}$ − iq 2 A ] . (2.49) 1 ( k 2 − m $^{2}$) n = 1 i $^{n}$Γ ( n ) ∫ ∞ 0 dα α n − $^{1}$exp $^{[}$iα $^{(}$k 2 − m 2 )] . (2.48) G ( d ) $^{(}$q 2 ) = ∫ d $^{d}$k$_{1}$ (2 π ) d ∫ d $^{d}$k$_{2}$ (2 π ) d exp [ i ( a$_{1}$ · k$_{1}$ + a$_{2}$ · k$_{2}$ )] c n$_{1}$ 1 c n$_{2}$ 2 c n$_{3}$ 3 c n$_{4}$ 4 c n$_{5}$ 5 . (2.47) T$_{µ}$$_{1}$$_{...µ}$$_{r}$$_{λ}$$_{1}$$_{...λ}$$_{s}$ = 1 i r + s ∂ ∂a µ$_{1}$ 1 . . . ∂ ∂a µ$_{r}$ 1 ∂ ∂a λ$_{1}$ 2 . . . ∂ ∂a λ$_{s}$ 2 exp [ i ( a$_{1}$ · k$_{1}$ + a$_{2}$ · k$_{2}$ )]$^{∣}$ ∣ ∣ a$_{1}$ = a$_{2}$ =0 . (2.46)