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Register a new userNaturally Light Dirac Neutrinos from $SO(10) times U(1)_psi$
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Authors
Ernest Ma
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A new solution is presented where the right-handed neutrino $ u_R$ in $SO(10)$ pairs up with $ u_L$ to form a naturally light Dirac neutrino. It is based on the framework of $E_6 to SO(10) times U(1)_psi$, then $SO(10) to SU(5) times U(1)_chi$.
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A known mechanism for obtaining naturally light Dirac neutrinos is implemented in the context of $SU(6) to SU(5) times U(1)_N$.
In the decomposition of $SO(10)$ grand unification to $SU(5) times U(1)_chi$, two desirable features are obtained with the addition of one colored fermion octet $Omega$, one electroweak fermion triplet $Sigma$ and one complex scalar triplet $S$ to the particle content of the standard model with two Higgs doublets. They are (1) gauge coupling unification of $SU(3)_C times SU(2)_L times U(1)_Y$ to $SU(5)$, and (2) the automatic (predestined) emergence of dark matter, i.e. $Omega$, $Sigma$ and $S$, with dark parity given by $(-1)^{Q_chi + 2j}$. It suggests that $U(1)_chi$ may well be the underlying symmetry of the dark sector.
$SO(5) times U(1) times SU(3)$ gauge-Higgs unification model inspired by $SO(11)$ gauge-Higgs grand unification is constructed in the Randall-Sundrum warped space. The 4D Higgs boson is identified with the Aharonov-Bohm phase in the fifth dimension. Fermion multiplets are introduced in the bulk in the spinor, vector and singlet representations of $SO(5)$ such that they are implemented in the spinor and vector representations of $SO(11)$. The mass spectrum of quarks and leptons in three generations is reproduced except for the down quark mass. The small neutrino masses are explained by the gauge-Higgs seesaw mechanism which takes the same form as in the inverse seesaw mechanism in grand unified theories in four dimensions.
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.
Signatures of the $SO(5)times U(1)$ gauge-Higgs unification at LHC and future colliders are explored. The Kaluza-Klein (KK) mass spectra of $gamma, Z, Z_R$ and the Higgs self-couplings obey universality relations with the Aharonov-Bohm (AB) phase $theta_H$ in the fifth dimension. The current data at low energies and at LHC indicate $theta_H <0.2$. Couplings of quarks and leptons to KK gauge bosons are determined. Three neutral gauge bosons, the first KK modes $Z_R^{(1)}$, $Z^{(1)}$, and $gamma^{(1)}$, appear as $Z$ bosons in dilepton events at LHC. For $theta_H = 0.114$, the mass and decay width of $Z_R^{(1)}$, $Z^{(1)}$, and $gamma^{(1)}$ are (5.73TeV, 482GeV), (6.07TeV, 342GeV), and (6.08TeV, 886GeV), respectively. For $theta_H = 0.073$ their masses are 8.00TeV$sim$8.61TeV. An excess of events in the dilepton invariant mass should be observed in the $Z$ search at the upgraded LHC at 14TeV.
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