Search

Weak decays of beautiful mesons can be used to probe the validity of our best model of particle physics: the Standard Model. In this thesis, I use specialised techniques to overcome practical challenges associated with the large mass of valence b quarks to study a selection of decays of B mesons with Lattice Quantum Chromodynamics. After introducing these modern methods, I report on my progress on calculating the vector current form factors for B_c to D_s. This decay is allowed at the one-loop level and so my vector current form factors will be used, along with future analysis of the tensor form factor, to describe the short-distance physics of this transition. I then present a comprehensive calculation of the B_c to B_s(d) vector current form factors based on a non-relativistic field theory approach for the bottom quark. I conclude by comparing my results with another calculation that uses an alternative approach for the heavy valence quark, an important test of our best lattice techniques. Combining data from this study with my calculation, I give the first prediction of the decay rates Γ (B_c⁺ to B_s⁰ ̅ℓ νℓ) and Γ (B_c⁺ to B⁰ ̅ℓ νℓ) from lattice QCD. Next, exploratory work on the long-distance contributions of charmonia on the flavour-changing neutral current process B to K is discussed. Difficulties with intermediate states that lead to divergences in the corresponding correlation function are addressed by again using the non-relativistic approach for the b quark. Finally, I digress from weak decays to explore applications of the Sherman-Morrison-Woodbury formula within the framework of lattice QCD. I find computational efficiencies in determining the inverse and the determinant of quark matrices. Potential applications are discussed.

This thesis consists of two parts that have contributed to a new meson spectroscopy program, MesonEx, which is currently taking place in Hall B of the upgraded Thomas Jefferson National Accelerator Facility (JLab) in the USA. The first, hardware part, presents design, testing, construction and calibration of a fast-timing scintillation Hodoscope for a new Forward Tagger detector, that has been installed inside the upgraded CEBAF Large Acceptance Spectrometer (CLAS12) which is situated in the Hall B of JLab. The Forward Tagger is a key apparatus for measurement of quasi-real photoproduction of mesons in the MesonEx, and a necessary device for other new hadron spectroscopy programs. The second, software and analysis part, presents contributions to the general HAdron SPEctroscopy CenTre (HASPECT) analysis framework, that has been developed in preparation for the MesonEx data analysis. The software contribution consists of finalizing HASPECT simulation and analysis chains in a model-independent way, and developing a mass-independent partial wave analysis procedure. This procedure has been tested via analysis of the γ p → p K+ K- channel from the g11a CLAS data, in the photon energy range Eγ = 3:0 - 3:8 GeV and momentum transfer squared range -t = 0:6 - 0:7 (GeV/c2)2. The first result of this analysis is the differential cross section for the ϕ(1020) resonance photoproduction. This result has been compared with a previous analysis result, and a good agreement has validated the developed analysis procedure. Furthermore, S, P and D partial waves have been extracted from the data set, using the same procedure, and ambiguous solutions for these partial waves have been calculated, using the method of Barrelet zeros which is for the first time applied to photoproduction of the K+ and K- mesons on the proton. Distributions of the calculated solutions have been compared with the fit results. It is found that the physical solution contains contributions of the ϕ(1020) in the P-wave and the a2(1320) in the D-wave.

This thesis is concerned with the properties of two classes of exotic hadron: hy- brid mesons, in which an excitation of the gluonic field causes distinction from the conventional mesons and can give rise to JPC quantum numbers not available to a qq̄ state; and pentaquarks, where the usual baryonic qqq structure is supplemented by a qq̄ pair, potentially giving the state an exotic flavour structure. In the hybrid meson sector, we work within the flux-tube model and extend upon an observation made by Isgur that the oscillations of the flux-tube can have dynamical effects upon the quarks living on the ends of the tube. We reverse the logic by allowing oscillations of the quarks caused by interactions with currents to excite modes in the flux-tube and hence hybrid mesons. Electromagnetic, weak and pionic currents are all applied, allowing us to make predictions about the radiative and hadronic decays of hybrid mesons and their production rates in exclusive hadronic decays of the B-meson. Such predictions are of interest to past, present and future experiments at E852, the B-factories and Jefferson Lab. In light of the possible observation of a pentaquark state, the Θ+ , we investigate some phenomenological consequences of certain models proposed to describe this state and attempt to justify one such model within a quark model framework. Jaffe and Wilczek's model for pentaquarks predicts in addition to the 10 [note: with a horizontal line above] with JP=½ , a 10 [note: with a horizontal line above] with JP=3/2+, the multiplets being initially degenerate. Within a dynamical model we are able to calculate the spin-orbit splitting between them and find it to not be large. We also consider the effect of a near degenerate 8 on the states in a pentaquark 10 [note: with a horizontal line above] , outlining a set of characteristic decay systematics that may be used in the search for non-flavour-exotic pentaquarks. In a constituent quark model with colour-spin interactions it is found to be possible to accommodate a Jaffe-Wilczek-like Θ+ with a rather low mass, while simultaneously describing the Δ-N splitting.