SUSY GUTs under Siege : Proton Decay

TL;DR

The paper addresses whether SO(10) SUSY GUTs can withstand stringent proton decay constraints. It shows that proton decay is dominated by dimension-five operators from color triplet Higgsino exchange, with rates governed by the effective mass $\tilde{M}_t$, the sparticle spectrum via a Loop Factor, and nonperturbative lattice matrix elements $\alpha_{lat}$ and $\beta_{lat}$. Using a specific SO(10) model with a $U(2)\times U(1)^n$ family symmetry and SUSY boundary conditions at $M_G$, the authors derive upper bounds on $\tilde{t}\tilde{M}_t$ from gauge coupling unification and compare predictions to Super-Kamiokande limits. The results imply very heavy first-two-generation sfermions and possibly only third-generation sparticles accessible at the LHC, placing significant pressure on minimal SUSY GUTs unless proton decay is suppressed.

Abstract

SO(10) supersymmetric grand unified theories [SUSY GUTs] provide a beautiful framework for physics beyond the standard model. Experimental measurements of the three gauge couplings are consistent with unification at a scale $M_G \sim 3 \times 10^{16}$ GeV. In addition predictive models for fermion masses and mixing angles have been found which fit the low energy data, including the recent data for neutrino oscillations. SO(10) boundary conditions can be tested via the spectrum of superparticles. The simplest models also predict neutron and proton decay rates. In this paper we discuss nucleon decay rates and obtain reasonable upper bounds. A clear picture of the allowed SUSY spectra as constrained by nucleon decay is presented.