Chapter 4 Heavy-Light Diquark mass predictions 4.1 Introduction The research in this chapter is based upon the following publication: The manuscript above (Ref. [71]) uses QSR to determine the masses of diquarks with J P = 0 $^{±}$, 1 ± that are composed of one heavy (charm or bottom) quark and one light quark. As described in Chapter 1, many of the heavy quarkonium-like states have been interpreted as four-quark states. These can be realized as weakly bound molecular states, or as tightly bound tetraquarks composed of diquark clusters. Heavy quarkonium-like four-quark states have been widely studied using QSR (see Ref. [94] for a review). A universal feature of these approaches has been the use of currents containing four quark fields, which are in either the molecule or tetraquark configurations where Q and q denote heavy and light quark fields, respectively. The Dirac matrices Γ and ˜ Γ are related to the quantum numbers of the hadrons probed by each current. The composite operator in the round brackets in Eq. (4.1) is a current that couples to heavy-light mesons, while that in the square brackets is a current that couples to heavy-light diquarks. However, the two currents in Eq. (4.1) are not truly independent because they can be transformed 82 J$_{molecule}$ = ( ¯ Q Γ Q $^{)}$(¯ q Γ q ) , J$_{tetraquark}$ = $^{[}$¯ Q ˜ Γ¯ q $^{] [}$Q ˜ Γ q ] , (4.1) • R.T. Kleiv, T.G. Steele, Ailin Zhang, and Ian Blokland, Heavy-light diquark masses from QCD sum rules and constituent diquark models of tetraquarks, Phys. Rev. D87 (2013) 125018.