content_image/315290.jpg content_image/315287.jpg content_image/315288.jpg
operator renormalizes as 

<img src='content_image/315290.jpg'>

where Z$_{m}$ corresponds to the quark mass renormalization factor in the MS scheme and this expression is valid to all orders in the coupling α . The renormalization factor Z$_{m}$ is given to O ( α $^{2}$) in Ref. [97]. Equivalently, the scalar meson operator renormalization factor can be calculated directly using the relation 

<img src='content_image/315287.jpg'>

where Γ s is a correlation function similar to that in Eq. (5.2), except with a zero momentum insertion of J s rather than J $^{d}$. Because the scalar diquark (5.1) and scalar meson (5.4) oper- ators are very similar in structure, the correlation functions given in Eqs. (5.3) and (5.5) are closely related. In fact, to any order in perturbation theory, each diagram contributing to the scalar diquark correlation function is proportional to a corresponding diagram contributing to the scalar meson operator. This relationship and the known two loop expression for the scalar meson operator renormalization factor provide a useful benchmark for the direct calculation of the scalar diquark renormalization factor via Eq. (5.3). At one-loop order, there is only one diagram that contributes to each correlation function, so the one-loop renormalization factors are proportional. However, at two-loop order there are eleven Feynman diagrams that contribute to each correlation function. Thus the simple proportionality between the scalar diquark and scalar meson operator renormalization factors does not persist at two-loop level. The complete expression for the two-loop scalar diquark renormalization factor in the MS scheme is determined to be 

<img src='content_image/315288.jpg'>

where a is the covariant gauge parameter, n$_{f}$ is the number of quark flavours and dimensional regularization with d = 4 + 2 ϵ has been used. 

