content_image/323214.jpg content_image/323213.jpg content_image/323212.jpg
time ordered product, which can be evaluated using Wick’s theorem (1.16): 

<img src='content_image/323214.jpg'>

Note that the first term in Eq. (1.106) corresponds to a disconnected diagram and can be ignored. The second term in Eq. (1.106) is the O ( g $^{0}$) contribution to the n = 0 Wilson coefficient in the OPE. That is, the second term represents the leading-order perturbative contribution to the correlation function (1.105). The third and fourth terms in Eq. (1.106) involve the normal ordered product of two quark fields at distinct locations. Ultimately, the normal ordered products will be related to condensate contributions, i.e. terms in the OPE with n > 0. The propagators that multiply these terms will lead to the corresponding Wilson coefficients. 

Note that because of the limit the definition of the perturbative expansion (1.19), the vacuum expectation value of these terms is taken using | Ω 〉 . For instance, the fourth term in Eq. (1.106) involves the vacuum expectation value 

<img src='content_image/323213.jpg'>

The first term in this expansion can be identified with the quark condensate 〈 ¯ qq 〉 (1.101). The second term is problematic because it involves the derivative ∂$_{µ}$ and hence is not gauge invariant. Ultimately the higher order terms in this expansion will be related to higher dimensional condensates, which are gauge invariant by definition. Therefore the expansion in Eq. (1.107) must be performed in a gauge invariant fashion. This can be achieved using fixed-point gauge techniques [95], or equivalently using plane wave methods [16]. Here we will use fixed-point gauge, where the gluon field satisfies 

<img src='content_image/323212.jpg'>

