This thesis describes a lattice calculation of the matrix elements of the vector and axial-vector currents which are relevant to the semi-leptonic decays <I>D</I> → <I>K</I> and <I>D → K</I><SUP>*</SUP>. The simulation was performed in the quenched approximation to lattice QCD on a 24<SUP>3</SUP> x 48 space-time lattice at <I>β</I> = 6.2, using an <I>O</I>(<I>a</I>)-improved fermionic action. In the limit of zero lepton masses the <I>D</I> → <I>K</I> and <I>D</I> → <I>K</I><SUP>*</SUP> decays are described by four form factors: <I>f<SUB>K</SUB></I><SUP>+</SUP>, <I>V<SUB>K</SUB></I><SUB>*</SUB>, <I>A<SUB>K</SUB></I><SUB>*</SUB><SUP>1</SUP> and <I>A<SUB>K</SUB></I><SUB>*</SUB><SUP>2</SUP> which are dimensionless functions of <I>q</I><SUP>2</SUP>, where <I>q<SUP>u</SUP></I> is the four-momentum transfer. The main results, for the form factors at <I>q</I><SUP>2</SUP> = 0, are as follows: <I>f<SUB>K</SUB><SUP>+</SUP></I>(0) = 0.67<SUP>+0.05 + 0.03</SUP><SUB>-0.03 - 0.04</SUB> <I>V<SUB>K</SUB></I><SUB>*</SUB>(0) = 1.01<SUP>+0.25 + 0.05</SUP><SUB>-0.05 - 0.06</SUB> <I>A<SUB>K</SUB></I><SUB>*</SUB><SUP>1</SUP>(0) = 0.69<SUP>+0.06 + 0.01</SUP><SUB>- 0.03 - 0.05</SUB> <I>A<SUB>K</SUB></I><SUB>*</SUB><SUP>2</SUP>(0) = 0.63<SUP>+0.12 + 0.01</SUP><SUB>-0.12 - 0.05</SUB> where the first set of errors are statistical and the second are an estimate of the systematic error. These results are in good agreement with experiment. The form factors were determined for different <I>q</I><SUP>2</SUP> values; their <I>q</I><SUP>2</SUP> dependence is found to be reasonably well described by a simple pole-dominance model. The form factors corresponding to the semi-leptonic decays <I>D</I> → π and <I>D</I> → <I>? </I> were also computed.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:652278 |
| Date | January 1996 |
| Creators | Hazel, Nicholas Mark |
| Publisher | University of Edinburgh |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/1842/14035 |
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