The two-loop scalar diquark operator renormalization factor given in Eq. (5.6) can be used to extend existing QSR studies of diquarks to higher order. It is possible that these higher order corrections could have a significant effect on QSR mass predictions for diquarks. Note that the renormalization factor was calculated in the MS renormalization scheme, where all quark flavours renormalize in the same way. Therefore the renormalization factor determined in Ref. [70] applies to all scalar diquark operators, regardless of the flavour of the quarks composing the diquark operator. In Chapter 4, mass predictions were determined for heavy- light diquarks with J P = 0 ± , 1 $^{±}$. The unknown renormalization factors for the pseudoscalar (0 $^{−}$), axial vector (1 $^{+}$) and vector (1 $^{−}$) diquark operators were determined by utilizing the one-loop relationship between diquark and quark meson operators established in this chapter. 

Although this research presented in this chapter is not directly relevant to the heavy quarkonium-like states, it has been applied in the QSR study of heavy-light diquarks in Chapter 4. The renormalization of the diquark current is an essential aspect of the renor- malization methodology used in Chapter 4. In order to calculate the two-loop scalar diquark operator renormalization factor, a large number of loop integrals must be calculated. Because the MS renormalization scheme is mass independent, these integrals can be evaluated in the chiral limit. The loop integration methods discussed in Chapter 2 are needed in order to evaluate these integrals. Finally, the result presented here for the two-loop scalar diquark renormalization factor could permit higher order QSR studies of scalar diquarks. 

## 5.3 Published Article 

The two-loop scalar diquark renormalization paper was published in the Journal of Physics G in 2011. Note that a corrigendum correcting a minor error was published in the same journal in 2012. Links to the preprint, published article and corrigendum are included below. 

• R.T. Kleiv and T.G. Steele, Two-loop QCD renormalization and anomalous dimension of the scalar diquark operator, J. Phys. G38 (2011) 025001; Corrigendum ibid J. Phys. G39 (2012) 039501, arXiv:1010.2971 [hep-ph]. 

