B-]S-GAMMA DECAY IN SUPERGRAVITY GRAND UNIFICATION AND DARK-MATTER

An analysis of the b --> sgamma is given in supergravity grand unifica tion using the framework of the radiative breaking of the electro-weak symmetry under three separate sets of constraints: 1) neutralino reli c density does not overclose the universe, 2) p-stability constraint, and 3) the combined constraints of p-stability and COBE data. For case 1 it is found that the CLEO II data on the branching ratio already im poses very strong further constraints on dark matter analyses. For cas e 2 the branching ratio is found to lie in the range (1.5-6.3) x 10(-4 ) and thus the data does not at present significantly limit the analys es with p-stability constraint. It is shown that improvements by a fac tor of 3 in the p --> nuBARK+ lifetime will reduce SUSY effects to les s than O(30%) of the Standard Model value. For case 3, the branching r atio lies in the interval (3.1-5.3) x 10(-4), and the SUSY effects lie within (-10%, + 50%) of the SM value. Thus as experimental bounds on B(b --> sgamma) improve, one would need in cases 2 and 3 the next-to-l eading order QCD corrections to disentangle SUSY effects.