content_image/300358.jpg
## Chapter 5 

## Scalar Diquark Operator Renormalization 

## 5.1 Introduction 

The research in this chapter is based upon the publication: 

• R.T. Kleiv and T.G. Steele, Two-loop QCD renormalization and anomalous dimension of the scalar diquark operator, J. Phys. G38 (2011) 025001. 

In QSR calculations hadronic states are probed by currents which are composite local operators constructed from quark and gluon fields. As discussed in Chapter 1, composite operators can mix under renormalization with operators of lower dimension and the same quantum numbers. This presents a significant challenge to extending QSR studies to higher orders. However, some composite operators are protected from this mixing by the fact that there are no lower dimensional operators with which they could mix. Such operators must renormalize multiplicatively, and the renormalization factor can be determined using the methods described in Chapter 1. Therefore it is much easier to perform higher order QSR analyses using operators that do not mix under renormalization. 

An example of a composite operator that does not mix under renormalization is the scalar diquark operator, which is given by 

<img src='content_image/300358.jpg'>

where the notation used here is identical to that of Eq. (4.3). The current couples to diquarks with J P = 0 $^{+}$. However, because diquarks have a net colour there are no lower dimensional operators that could mix with the scalar diquark current (5.1). Therefore, the scalar diquark 

