Heavy-Light and Doubly-Strange Diquark Spectrum from QCD Laplace Sum-Rules and Diagrammatic Renormalization Methods

In addition to the conventional $q\bar{q}$ and $qqq$ bound states of quarks $q$, exotic hadrons, such as the four-quark $q\bar{q}q\bar{q}$ and the five-quark $qqqq\bar{q}$ bound states, can be constructed by assuming colour confinement in strong interactions. In particular, one of the possible internal structure for a four-quark state is the tetraquark $[qq][\bar{q}\bar{q}]$, where diquarks $[qq]$ and antidiquarks $[\bar{q}\bar{q}]$ are bound due to the colour force. In this thesis, heavy-light $[Qq]$, where $Q\in\{c, b\}$ (charm, bottom) and $q\in\{u,d,s\}$ (up, down, strange), and doubly-strange $[ss]$ diquarks are examined using QCD Laplace sum-rules. The diquark two-point correlation function is renormalized using diagrammatic renormalization methods for QCD correlation functions that are developed and compared to the conventional renormalization method. It is shown that the mixing of composite operators induced by the conventional renormalization approach is avoided by the diagrammatic renormalization method. The strange quark condensate parameter $\kappa=\langle\bar{s}s\rangle/\langle\bar{n}n\rangle$, where $n\in\{u,d\}$, is shown to have an important role on the $[Qs]$ and $[Qn]$ diquark mass splitting.