SHOULD SPARTICLE MASSES UNIFY AT THE GUT SCALE?

Abstract

Gauge and Yukawa (for the third family) coupling unification seem to be the best predictions of the grand-unified theories (GUTs). In supersymmetric GUTs, one also expects that the sparticle masses unify at the GUT scale (for sparticles embedded in the same GUT multiplet). I show under what circumstances GUTs do not lead to sparticle mass unification. In particular, I give examples of SU(5) and SO(10) SUSY GUTs in which squarks and sleptons of a family have different tree-level masses at the unification scale. The models have interesting relations between Yukawa couplings. For example, I present an SO(10) GUT that allows for a large ratio of the top to bottom Yukawas, accounting for the large $m_t /m_b$. The splittings can also be induced in the Higgs soft masses and accommodate the electroweak breaking.