Abstract
We discuss the possibility of unifying in a simple and economical manner the Yukawa couplings of third generation fermions in a non-supersymmetric SO(10) model with an intermediate symmetry breaking, focusing on two possible patterns with intermediate Pati-Salam and minimal left-right groups. For this purpose, we assume a minimal Yukawa sector at high energy, starting with two Higgs bi-doublets at the intermediate scale which then simply reduce to a two Higgs doublet model at the electroweak scale. We first enforce gauge coupling unification at the two-loop level by including the threshold corrections in the renormalization group running which are generated by the heavy fields that appear at the intermediate symmetry breaking scale. We then study the running of the Yukawa couplings of the top quark, bottom quark and tau lepton at two-loops in these two breaking schemes, when the appropriate matching conditions are imposed. We find that the unification of the third family Yukawa couplings can be achieved while retaining a viable spectrum, provided that the ratio of the vacuum expectation values of the two Higgs doublet fields is large, tanβ≈60.
Highlights
The paradigm of grand unification [1,2] is at the heart of particle physics as it exploits the power of symmetries to unify in a most elegant way the electromagnetic, weak and strong interactions of the Standard Model (SM) into a single force [3]
If the mass of this new state is very large, somewhere at a scale of 1010 GeV, the see-saw mechanism [5] could explain the present pattern in the neutrino sector, the baryon asymmetry could be achieved through leptogenesis [6] and a suitable axion [7] could account for dark matter; see Refs. [8,9,10] for reviews
This intermediate scale can naturally be present in SO(10) as the group is of rank five, i.e., larger than the rank of the SM group by one unit, so that the symmetry breaking may occur in three steps, one at the Grand unified theories (GUTs) scale MU, one at this intermediate scale M I and a last one at the electroweak scale
Summary
The paradigm of grand unification [1,2] is at the heart of particle physics as it exploits the power of symmetries to unify in a most elegant way the electromagnetic, weak and strong interactions of the Standard Model (SM) into a single force [3]. One would have an effective two Higgs doublet model (2HDM) of type II [17] at low energies, just as in the MSSM, with vacuum expectation values such that the parameter tan β is large as to obtain the correct hierarchy for the top and bottom quark masses Using this minimal scalar sector, it is possible to make that the renormalization group running of third generation Yukawa couplings in these two breaking schemes, with suitable matching conditions at the intermediate scale for which gauge coupling unification occurs, leads to Yukawa coupling unification at the GUT scale.
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