Burford, Darren Ross (1996) Hadronic physics in lattice QCD. University of Southampton, Doctoral Thesis.
Abstract
In this work we consider how hadronic physics can be probed within the framework of lattice QCD. By considering a 'first stage' calculation one can hope to show viability and accuracy of numerical lattice simulations. Equally the analysis of an involved calculation will hope to show the usefulness of the lattice to extract important physics to complement and probe beyond other methods. Here we firstly look at the semileptonic decays of B mesons; how to extract predictions confidently. Secondly we use the first principle to examine the effect of a proposed improvement to numerical simulations.
We present a method of analysing the form factors in B → πlV̅;l and B → K*γ decays which allows us to obtain information on the q2 dependence of both form factors at the B scale. Using this we examine a series of fits based on pole-dominance subject to both constraints on the form factors and consistency checks on the q2 and 1/M extrapolations. For the B → πlV̅;l decay we show that fits to of f+ to a simple pole may not be consistent with the q2 behaviour of f0. Other pole-like behaviours for the form factors, that do show consistency, lead to a possible factor of two uncertainty in the decay rate and hence in the value of |VubZ|2 deduced from it. For B → K*γ, although unable to favour one pole-like model our method of extrapolation in q2 and 1/M satisfies the consistency checks which were not obeyed in previous analysis of this data.
We examine the effect of the method of tadpole improvement on the O(a) improved action of B. Sheikholeslami and R. Wohlert. We examine the light spectrum of β = 6.2 using the same set of 60 gauge configurations for both the non-tadpole and tadpole-improved actions. We see little effect of tadpole improvement except for the perturbative prediction of kcrit and pertubative matching of fπ. We present results for the tadpole-improved action using a larger set of 190 configurations which allows the use of multi-state fits to the two-point functions. Together these improve our results towards, though not in agreement with, experiment.
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