Supergravity grand unification, proton decay and cosmological constraints

Abstract

Properties and experimental predictions of a broad class of supergravity grand unified models possessing an SU(5)-type proton decay and R parity are described. Models of this type can be described in terms of four parameters at the Gut scale in addition to those of the Standard Model i.e. m{sub 0} (universal scalar mass), m{sub 1/2} (universal gaugino mass), A{sub 0} (cubic soft breaking parameter) and tan {beta} = /. Thus the 32 SUSY masses can be expressed in terms of m{sub 0}, M{sub 1/2}, A{sub 0} tan {beta} and the as yet unknown t-quark mass M{sub t}. Gut thresholds are examined and a simple model leads to grand unification consistent with p-decay data when 0.114 < {alpha}{sub 3}(M{sub z}) < 0.135, in agreement with current values of {alpha}{sub 3}(M{sub Z}). Proton decay is examined for the superheavy Higgs triplet mass H{sub H3} < 10M{sub G}(M{sub G} {approx_equal} 1.5 {times} 10{sup 16} GeV) and squarks and gluinos lighter than 1 TeV. Throughout most of the parameter space chargino-neutralino scaling relations are predicted to hold: 2m{sub {anti Z}}{sub 1} {congruent} m{sub {anti W}}{sub 1} {congruent} m{sub {anti Z}}{sub 2}, m{sub {anti W}}{sub 1} {approx_equal} (1/4)m{sub {anti g}} (for {mu} > 0) or m{sub {anti W}}{sub 1} {approx_equal} (1/3)m{sub {anti g}} (for {mu} < 0), while m{sub {anti W}}{sub 2} {congruent} m{sub {anti Z}}{sub 3} {congruent} m{sub {anti Z}}{sub 4} {much_gt} m{sub {anti Z}}{sub 1}. Future proton decay experiments combined with LEP2 lead to further predictions, e.g. for the entire parameter space either proton decay should be seen at these or the {anti W}{sub 1} seen at LEP2. Relic density constraints on the {anti Z}{sub 1} further constrain the parameter space e.g. so that m{sub t} < 165 GeV, M{sub h} < 105 GeV, m{sub {anti W}}{sub 1} < 100 GeV and m{sub {anti Z}}{sub 1} < 50 GeV when M{sub H}{sub 3}/M{sub G} < 6.