On the viability of SUSY GUTs with Yukawa unification: the crucial role of FCNCs

The hypothesis of “grand unification” – namely, that the strengths of the three Standard Model (SM) gauge couplings unify at some energy scale – is not only appealing in itself, but allows also to address structural questions that in the SM remain unanswered, like the gauge quantum number assignments. This hypothesis is also supported by the measured low-energy values of the SM gauge couplings, if one supposes that above the Fermi scale MEW the SM becomes supersymmetric: the predictions for the three couplings get closer at higher scales and eventually unify at a scaleMG of about 3×10 16 GeV. Supersymmetry (SUSY) itself allows to keep the huge ratio MG/MEW natural beyond tree level. The above ideas may be a red herring or else a major clue to the structure of fundamental interactions at scales that will probably never be tested at colliders. The second possibility looks favored by the (excellent) degree to which coupling unification works: this motivates the construction of grand unified theories (GUTs) and the quest for further tests thereof. The cornerstone predictions of SUSY GUTs are [1], besides (i.) gauge coupling unification at MG, (ii.) the existence of SUSY throughout the energy interval between MG and MEW, and (iii.) proton decay. Concerning the latter, while a positive signal is generically expected to be behind the corner, a precise prediction is a highly modeldependent issue, depending in particular on whether the SUSY GUT under consideration is realized in 4 dimensions or via orbifold constructions [2]. Turning to (ii.), the expectation of low-energy SUSY, the question of the predicted pattern of SUSY masses is, again, a model-dependent one, because of the unknown mechanism of SUSY breaking and of the form that Yukawa couplings assume at the high scale, in the first place. To make progress, one assumes universalities in soft SUSY-breaking terms at MG, which can then be motivated in specific SUSY-breaking scenarios. A very elegant additional assumption, potentially testable in the SM fermion masses and mixings, is that of Yukawa unification (YU) at the GUT scale. It is motivated by the fact that, due to the higher degree of symmetry, matter fields must sit in appropriate representations of the gauge group, thereby sharing a common Yukawa coupling. Since this simple picture can be spoiled by e.g. the presence of higher-dimensional interactions, the crucial question is whether YU may leave any low-energy remnant at all. While for the light fermion generations this is definitely not the case, for the third generation it remains an open and appealing possibility. The latter immediately singles out SO(10) as the potentially most predictive case, in that it is the simplest group allowing to relate all third generation fermion masses to one another.