Universal couplings in two-body strong and electromagnetic meson decays

The strong and electromagnetic interactions of the ground state hadrons have, since the early 1970's, been known to comply with the tree level approximations given by effective Lagrangians. In more recent years the weak decays of heavy hadrons have been successfully calculated by use of the Heavy Quark Effective Theory (HQET). It is suited to hadrons containing a heavy quark (c, b, t) with light quark partner(s) (u, d, s) and uses the approximation that the hadron momentum is carried by the heavy quark. This resembles a group theoretical approach of constructing relativistic hadron wavefunctions in the mid 1960's, based on U(2N1f) ‚Äöv§v= U(2Nf) ‚Äöv§vá U(4Nf ) symmetry group, producing wavefunctions whose structure implies that the constituent quarks must be moving collinearly and with the same velocity as the hadron. If one quark is much heavier than the others then it will have most of the momentum, as is the case for HQET. The main difference between the schemes is in the treatment of the light quark momentum, but this is a higher order correction leading only to minor changes. Given the similarity between the models, but with the present favouritism shown for HQET, we re-investigate the U(4Nf) scheme because of its many - advantages. Firstly, since the scheme is a spin extension of the SU(Nf) symmetry, the known mesons (including excited states) are classified into spin-flavour supermultiplets which naturally leads to the reduction of the number of free parameters compared to simple flavour SU(Nf). Secondly, the scheme's interaction Lagrangian is applicable to two-body strong decays with one only needing a single coupling constant for each parent orbital angular momentum state. Vector meson dominance is easily incorporated to enable study of the electromagnetic processes. In this thesis the U(4Nf) x 0(3, 1)L scheme has been applied to the twobody strong and radiative decays of ground and excited mesons (from L = 0 to L = 3). We use known decay widths and meson masses to calculate the universal coupling constant involved. Uniformity in the value of supports the supposed supersymmetry. There is high quality experimental data on the ground states decays and our analysis finds reasonably constant coupling, but there is some small symmetry breaking associated with the parent meson mass. Nonetheless, the breaking is quantifiable and leads to predictions for the D* and B* decay rates and branching fractions. From the less accurate experimental data available on excited decays we find good uniformity in the results, especially when taking into account the uniquely large number of processes considered in this work. Thus I have determined that the U(4Nf) scheme appears well suited to describing meson interactions and their excitations and should be useful in studying the weak interactions after appropriate manipulation, as well. As a contrast to U(4Nf) we develop a quark triangle scheme involving a Feynman graph which provides quark level universal couplings to account for the symmetry breaking effects of unequal quark masses. Due to its complexity it is only applied to the ground state radiative decays, but with considerable success and over a range of processes far exceeding any similar work. Also, whereas other research has used approximations in the derivation of the decay amplitude, ours is exact and lends itself to study of all applicable channels regardless of the mesons involved. Unfortunately it is difficult to apply the method to higher excitations as the quark triangle involved is divergent, and so techniques of renormalization would have to be used.