From the time of its introduction, the standard model has become a very well established model in particle physics. In fact, no experiment so far has shown any violation of this model. Still, there are some unsatisfying aspects and open questions that this model cannot explain. For instance, the standard model may require as many as 21 input parameters. Among these are the coefficients of the Cabibbo-Kobayashi-Maskawa matrix. This is a 3¡Á3 matrix, where the square of the absolute value of its matrix elements, |Vqq¡¯|^2, is proportional to the probability for a transition from a quark of flavour q to a quark of flavour q¡¯. We can get information about this matrix by comparing theoretical calculations of decay probabilities to different final states with experimental data from decay of particles containing a heavy quark, for example a D-meson.
What we have done in this thesis is to look at the decay process D -> V + ¦Ã, and calculated the amplitudes and decay widths for the process, including the gluon condensate to first order. D is here a heavy-light D-meson, containing a heavy c-quark and one light quark (u, d or s). ¦Ã is a photon and V is a vector meson consisting of only light quarks (i.e. V = ¦Ñ, ¦Ø, ¦Õ or K*). In order to do these calculations we used the heavy light chiral quark model and the chiral quark model for vector mesons. In these models we treated the c-quark as a heavy particle, and disregarded terms including 1/mc, as these where considered being small in the theory. As the mass of the c-quark is in the range 1,15 ¨C 1,35 GeV and our energy cutoff was chosen to be ¦« = 1 GeV, this could give rise to uncertainties and inaccuracies in the theory.
We then turned to a specific process; D0 -> (K-bar)*0 + ¦Ã. This process we approximated as a point interaction using Fermi theory, and used Wilson coefficients to account for the effects of the heavy particle. From this we found that the non-factorizable part of the decay process was slightly dominating over the factorizable one. We next used the VSA factorization limit to split the D0 -> (K-bar)*0 + ¦Ã process to two parts; one which annihilated the D-meson and one which created the vector meson. We then calculated M = iL, where L is the Lagrangian, for these two types of diagrams separately, with gluons and photons coupled to them when necessary. This gave nine diagrams of the annihilation type and 26 of the creation type. Later these two types of diagrams were combined into a total of 33 full diagrams, and from these we calculated the amplitudes and decay widths, and compared them to experimental data.
What we found from these calculations was that our results for the decay widths where too low (from a factor 137 to 30 times lower) compared to the experimental values. An attempt to adjust any of the parameters used to gain a better value of the decay width, did only result in unphysical values of the adjusted parameters for the process we were looking at. One reason for this, that we discussed, was the value of the factor h_V and how the decay width was affected by the use of the formula for h_V, compared to using only the numerical value for it. Apparently the decay width became very sensitive to the value of the gluon condensate when using the equation for h_V, and a slight change in the gluon condensate value (within its uncertainty limits) gave the correct value for the specific process that we were looking at. However, although it also gave clearly less deviation in the decay widths for the other processes we studied (D0 -> ¦Ñ0 + ¦Ã, D0 -> ¦Ø + ¦Ã and D0 -> ¦Õ + ¦Ã ), it did not gave the correct values for all of them, probably meaning that the problem is more complex. The same situation occurred when we looked specifically at the decay width as a function of the constituent quark mass.
An attempt to combine the two, i.e. finding the optimal values of the gluon condensate and the constituent quark mass, by plotting the decay width as a function of these two, showed that it was not possible. Using our data and numerical values of the other parameters, it seemed that we were only able to adjust one of the parameters (condensate or quark mass) once the other had been specified, if we wanted the correct value of the decay width when using the formula for h_V. These small adjustments in the gluon condensate or the mass to get the experimentally correct decay width, was not possible to do when the value for h_V was explicitly put equal to its numerical value 6.
We also looked at the Cabibbo-Kobayashi-Maskawa matrix elements, and tried in different ways to extract their values from our results. One of these ways was to calculate the ratio between different CKM matrix elements by looking at ratios between different decay widths. This approach turned out to give results that agreed quite well with experimental values. Unfortunately, lack of experimental data reduced the number of ratios we could calculate.