Coupling constants and unification

The first part of this work gives a general background for the ideas involved in the research presented in this thesis. Coupling constants, Renor-malisation Group Equation, Grand Unified Theories (GUTs) and Super symmetry (SUSY) are briefly introduced. Following this, we analyse the unification parameters M(_GUT) and l/α(_GUT) as functions of the number of fermion families (F) and Higgs boson multiplets (S). Analytical and numerical solutions to the leading and next-to-leading order evolution equation for the couplings a, are obtained. This is done in the context of the Standard Model embedded in SU(5), SUSY SU(5) and L-R SO(IO). In all these GUTs, the first order analytical approach proves itself a useful probe to examine the structure of M(_GUT) and l/α(_GUT) in terms of the variables F and S. General trends remain the same after including second order corrections to the evolution equations. Recent precision data for the coupling constants allow more definitive conclusions to be reached. We find that restrictions on the unification parameters constrain F and S in such a way that SU(5) is ruled out by constraints on 5 (in agreement with previous results), F is severely limited in SUSY SU(5) and, unlike SUSY SU(5), an acceptable unification scenario can still be obtained when Higgs bosons are ignored in L-R SO(IO). The structures of the latter two GUTs are found to be very different although some features are common to both