Precise Predictions of Grand Unified Gauge Theories.
Abstract
The strong, weak, and electromagnetic interactions can be unified into a grand unified theory (GUT), a local gauge theory with a single coupling constant. The large disparity between the observed coupling constants of the strong, weak and electromagnetic interactions implies that the gauge symmetry of the GUT must be broken at a very large energy, of 0(10('1416) GeV), and it is therefore difficult to find precise predictions of GUT's. Some predictions can be made, however, by making use of the renormalization group equations, which relate the values of masses and coupling constants at low energies to those at high energies. In this thesis, we examine the predictions, in detail, of the simplest GUT, based on the group SU(5). Among these are the proton lifetime, the weak mixing angle (which is related to the ratio of the weak to electromagnetic coupling constants) and the bquark mass. We calculate these quantities including twoloop contributions, Higgs and threshold effects, etc. The most precise prediction is that of the weak mixing angle. It is noted that the most accurate determination of the mixing angle, and thus the most accurate test of SU(5), can be made from measurement of the masses of the weak vector bosons (the W and Z). Using higher order expressions for these masses in terms of the mixing angle, we calculate the W and Z masses in SU(5). By considering the effects of heavy colored scalars on the renormalization group equations, it is shown that the simplest form of SU(5) is the only GUT which makes very precise predictions. If one assumes that the symmetry breakdown in the standard model of electroweak interactions is due to quantum corrections, then the mass of the scalar boson predicted in the model is calculable and is around 10 GeV. The mass is very sensitive to the value of the mixing angle, and its measurement could also be a precise test of SU(5). Also, as this mass is very near the bottomonium (upsilon) states, a precise prediction for the mass could indicate the best method of detection of the scalar. We calculate the mass of the scalar including higher order ((alpha)('2)) corrections. Ingredients in the calculation are the effective potential up to two loops and the vector propagator, scalar propagator and coupling constants up to one loop. For the predicted value of the mixing angle in SU(5), the scalar mass is 10.8 (+OR ) .3 GeV, which is above the states of bottomonium. A measurement of the mass, under the above assumption, will yield the value of the mixing angle to an accuracy of less than 1%, and would thus be a precise test of SU(5).
 Publication:

Ph.D. Thesis
 Pub Date:
 1980
 Bibcode:
 1980PhDT........98S
 Keywords:

 Physics: Elementary Particles and High Energy;
 Electromagnetism;
 Particle Theory;
 Theoretical Physics;
 Bosons;
 Coupling;
 Electromagnetic Interactions;
 Quantum Theory;
 Quarks;
 Weak Energy Interactions;
 Communications and Radar