content_image/322025.jpg content_image/322024.jpg content_image/322022.jpg content_image/322021.jpg content_image/322020.jpg
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 

<img src='content_image/322025.jpg'>

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. 

<img src='content_image/322024.jpg'>

This integral can be evaluated with the aid of the following identity [97]: 

<img src='content_image/322022.jpg'>

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 

<img src='content_image/322021.jpg'>

Using this and making the change of variables p = k − xq , 

<img src='content_image/322020.jpg'>

