Unification of Gauge Couplings in the Standard Model with Extra Vector-like Families

Abstract: We discuss gauge coupling unification in models with additional 1 to 4 complete vector-like families, and derive simple rules for masses of vector-like fermions required for exact gauge coupling unification. These mass rules and the classification scheme are generalized to an arbitrary extension of the standard model. We focus on scenarios with 3 or more vector-like families in which the values of gauge couplings at the electroweak scale are highly insensitive to the grand unification scale, the unified gauge coupling, and the masses of vector-like fermions. Their observed values can be mostly understood from infrared fixed point behavior. With respect to sensitivity to fundamental parameters, the model with 3 extra vector-like families stands out. It requires vector-like fermions with masses of order 1 TeV - 100 TeV, and thus at least part of the spectrum may be within the reach of the LHC. The constraints on proton lifetime can be easily satisfied in these models since the best motivated grand unification scale is at $\sim 10^{16}$ GeV. The Higgs quartic coupling remains positive all the way to the grand unification scale, and thus the electroweak minimum of the Higgs potential is stable.