This thesis describes a numerical study of weak matrix elements of the vector and axial vector currents relevant to the semi-leptonic and leptonic decays of <I>B</I> and <I>D</I> mesons from Lattice QCD. The simulation was performed in Quenched QCD on a 24<SUP>3</SUP> x 48 lattice at <I>β</I> = 6.2. The fermionic degrees of freedom were calculated using a non-perturbatively <I>O</I>(<I>a</I>) improved action. For a pseudoscalar final state in a semi-leptonic decay, only the vector current contributes and can be parameterised by two form factors which are functions of the momentum transfer squared. The main results for the form factors of the decays <I>B</I> → π at zero momentum transfer are: <I>f</I><SUB>+</SUB> (0) = <I>f</I><SUB>0 </SUB>(0) = 0.31<SUP>+3</SUP><SUB>-3 stat </SUB><SUP>+8</SUP><SUB>-8 sys</SUB><I> </I>The momentum dependence was found to be reasonably modelled by pole dominance models. The decay rate for <I>B</I> → π is calculated and compared to experiment allowing the CKM matrix element <I>V</I><SUB>ub</SUB> to be extracted. <I>V</I><SUB>ub</SUB> = 0.0027<SUP>+2</SUP><SUB>-2 stat </SUB><SUP>+7</SUP><SUB>-7 sys </SUB><SUP>+9</SUP><SUB>-9 exp</SUB><I> </I>The form factors for <I>D</I> → <I>K,</I> π were calculated and the momentum dependence was found to be reasonably modelled by pole dominance. For leptonic decays of pseudoscalar mesons, the axial current is parameterised by the decay constant, for B and D decays the results are <I>f<SUB>B</SUB></I> = 191<SUP>+4</SUP><SUB>-4 stat </SUB><SUP>+22</SUP><SUB>-22 sys</SUB> MeV <I>f<SUB>D</SUB></I> = 203<SUP>+3</SUP><SUB>-2 stat </SUB><SUP>+22</SUP><SUB>-10 sys</SUB> MeV<I> </I>The soft pion relation for the B meson which relates the ratio <I>f<SUB>B</SUB> / f<SUB>π</SUB></I> to <I>f</I><SUB>o</SUB>(<I>q</I><SUP>2</SUP><SUB>max</SUB>), is evaluated and found to be substantially violated.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:657488 |
| Date | January 1999 |
| Creators | Maynard, Christopher Michael |
| Publisher | University of Edinburgh |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/1842/11844 |
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