namely 4 − 2 n . Typically, we will be interested in the behaviour of this integral near d = 4, which can be determined by setting d = 4 + 2 ϵ and expanding around ϵ = 0. However, we will refrain from doing so until Section 2.6. By itself, this integral is not particularly useful in QCD sum rule analyses because it has no momentum dependence. However, it is extraordinarily useful as a means for deriving more complicated integrals. Now consider the one-loop integral which is depicted in Fig. 2.3. This integral is reminiscent of a quark self-energy contribution, therefore it is called a self-energy integral. This integral can be evaluated with the aid of the following identity [97]: The variable x is called a Feynman parameter. This identity can be used to combine the two propagators in (2.14) so that the integral can be performed using the result (2.13). For instance, let A = ( k − q ) 2 − m $^{2}$, α = n$_{2}$ , B = k $^{2}$, and β = n$_{1}$ , then we can write Using this and making the change of variables p = k − xq , 56 B ( d ; n$_{1}$ , 0 ; n$_{2}$ , m ) = Γ( n$_{1}$ + n$_{2}$ ) Γ( n$_{1}$ )Γ( n$_{2}$ ) ∫ 1 0 dx x n$_{2}$ − $^{1}$(1 − x ) n$_{1}$ 1 µ d − 4 ∫ d $^{d}$p (2 π ) d 1 [ p 2 − ( xm 2 − x (1 − x ) q $^{2}$) ] n$_{1}$ + n$_{2}$ , (2.17) Ax + B (1 − x ) = x ( k 2 + q 2 − 2 k · q − m $^{2}$) + (1 − x ) k 2 = ( k − xq ) 2 − $^{[}$xm 2 − x (1 − x ) q 2 ] . (2.16) 1 A $^{α}$Bβ = Γ( α + β ) Γ( α )Γ( β ) ∫ 1 0 dx x α − $^{1}$(1 − x ) β − 1 [ Ax + B (1 − x )] α + β . (2.15) Figure 2.3: Feynman diagram representing the B -type self-energy integral. B ( d ; n$_{1}$ , 0 ; n$_{2}$ , m ) = 1 µ d − 4 ∫ d $^{d}$k (2 π ) d 1 k 2 n$_{1}$ [ ( k − q ) 2 − m 2 ] n$_{2}$ , (2.14)