SuperB production,matter stability and gauge hierarchy in SUSY GUTs

We analyze the connections between the problems of the cosmological baryon asymmetry (CBA), matter stability and mass hierarchy in supersymmetric Grand Unified models. We show that the typical delay of the phase transition in supersymmetric theories as well as a natural solution to the triplet-doublet Higgs hierarchy problem imply baryon production after the Grand Unification phase transition which in a wide class of SUSY GUTs takes place atT～10⁹–10¹⁰ GeV. Light Higgs colour triplets as a means of producing the CBA are discussed in detail. An alternative mechanism involving a singlet superfield is proposed leading to striking consequences in proton decay with the appearance of (B+L) conserving modes with a muon and a kaon in the final state:n→μ^? K ⁺,p μ ^2212;π⁺ K ⁺ and a lifetime of 10³¹ years.