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Register a new userExtended MSSM in Supersymmetric $rm{SO}(10)$ Grand Unification
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Sibo Zheng
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We apply the perturbative grand unification due to renormalization to distinguish TeV-scale relics of supersymmetric $rm{SO}(10)$ scenarios. With rational theoretical constraints taken into account, we find that for the breaking pattern of either $rm{SU}(5)$ or Pati-Salam only extra matter $mathbf{16}$ supermultiplet of $SO(10)$ can appear at TeV scale, apart from MSSM spectrum.
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We present a new possibility for achieving doublet-triplet splitting naturally in supersymmetric SO(10) grand unified theories. It is based on a missing partner mechanism which is realized with the 126 + 126-bar Higgs superfields. These Higgs fields, which are also needed for generating Majorana right-handed neutrino masses, contain a pair of color triplets in excess of weak doublets. This feature enables us to remove the color triplets from the low energy spectrum without fine-tuning. We give all the needed ingredients for a successful implementation of the missing partner mechanism in SO(10) and present explicit models wherein the Higgs doublet mass is protected against possible non-renormalizable corrections to all orders. We also show how realistic fermion masses can be generated in this context.
Low-energy supersymmetric models such as MSSM, NMSSM and MSSM with vectorlike fermion are consistent with perturbative unification. While the non-minimal extensions naturally explain Higgs mass and dark matter in the low energy region, it is unclear how seriously they are constrained in the ultraviolet region. Our study shows that $i)$, In the case of embedding MSSM into $rm{SU}(5)$, the fit to SM fermion masses requires a singlet $S$, which leads to unviable embedding of NMSSM into $rm{SU}(5)$ because such $S$ feeds singlet $N$ a mass of order unification scale as well. $ii)$, Similar result holds in the case of embedding NMSSM into $rm{SO}(10)$, where $S$ is replaced by some Higgs fields responsible for $rm{SO}(10)$ breaking. $iii)$, On the contrary, for the embedding of MSSM with $16$-dimensional vectorlike fermions into $rm{SO}(10)$, the Higgs field responsible for the vectorlike mass of order TeV scale can evade those problems the singlet $N$ encounters because of an intermediate mass scale in the $126$-dimensional Higgs field.
It is shown how grand unification can occur in models which are partly supersymmetric. The particle states which are composite do not contribute to the running of gauge couplings above the compositeness scale, while the elementary states contribute the usual large logarithmns. This introduces a new differential running contribution to the gauge couplings from partly composite SU(5) matter multiplets. In particular, for partly supersymmetric models, the incomplete SU(5) elementary matter multiplets restore gauge coupling unification even though the usual elementary gaugino and Higgsino contributions need not be present.
In a class of gauged $U(1)$ extended Standard Models (SMs), the breaking of the $U(1)$ symmetry is not only a source for Majorana masses of right-handed (RH) neutrinos crucial for the seesaw mechanism, but also a source of stochastic gravitational wave (GW) background. Such $U(1)$ extended models are well-motivated from the viewpoint of grand unification. In this paper, we discuss a successful ultraviolet completion of a $U(1)$ extended SM by an $SO(10)$ grand unified model through an intermediate step of $SU(5) times U(1)$ unification. With a parameter set that is compatible with the $SO(10)$ grand unification, we find that a first-order phase transition associated with the $U(1)$ symmetry breaking can be strong enough to generate GWs with a detectable size of amplitude. We also find that the resultant GW amplitude reduces and its peak frequency becomes higher as the RH neutrino masses increase.
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 start with a two Higgs doublet model at the electroweak scale and assume a minimal Yukawa sector at the high energy scales. We first enforce gauge coupling unification at the two-loop level by including the threshold corrections in the renormalisation 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, $tanbeta approx 60$.
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