operator must renormalize multiplicatively. The publication above (Ref. [70]) determines the renormalization factor of the scalar $^{(}$J P = 0 + ) diquark operator to second (two-loop) order in the strong coupling α . This builds upon the work of Ref. [42], which gives the scalar diquark renormalization factor to first order. The renormalization factor of the scalar diquark operator can be determined by considering the correlation function where J d is the scalar diquark operator (5.1) and colour indices have been omitted for brevity. The correlation function can be calculated using the perturbative expansion (1.19) in mo- mentum space with the external quark propagators amputated. Because we are calculating a renormalization factor which is momentum independent, the diquark operator inserted into Eq. (5.2) can be taken to have zero momentum without loss of generality. We will use the MS renormalization scheme which is mass independent so we can work in the chiral limit, ignoring the quark masses in Eq. (5.2). The bare and renormalized correlation functions are related by As discussed in Chapter 1, the scalar diquark renormalization factor Z$_{d}$ is the additional renormalization factor that is required in order to evaluate the limit in Eq. (5.3). This relationship can be used to calculate the scalar diquark operator renormalization factor Z$_{d}$ to any order in the coupling α . In order to calculate scalar diquark operator renormalization factor, it is helpful to exploit the similarity between the scalar diquark and scalar meson operators. The scalar meson 89 5.2 Results Γ d = 〈 Ω | T $^{[}$Q ( x ) J $^{d}$(0) q ( y ) $^{]}$| Ω 〉 , (5.2) Γ d $_{R}$( q ; m$_{R}$ , a$_{R}$ , α$_{R}$ ) = lim ϵ → 0 $^{[}$Z$_{d}$ Z − 1 $_{2F}$Γ d B ( q ; m$_{B}$ , a$_{B}$ , α$_{B}$ ) ] . (5.3)