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Register a new userEmbedding Flipped SU(5) into SO(10)
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We embed the flipped SU(5) models into the SO(10) models. After the SO(10) gauge symmetry is broken down to the flipped SU(5) times U(1)_X gauge symmetry, we can split the five/one-plets and ten-plets in the spinor mathbf{16} and mathbf{bar{16}} Higgs fields via the stable sliding singlet mechanism. As in the flipped SU(5) models, these ten-plet Higgs fields can break the flipped SU(5) gauge symmetry down to the Standard Model gauge symmetry. The doublet-triplet splitting problem can be solved naturally by the missing partner mechanism, and the Higgsino-exchange mediated proton decay can be suppressed elegantly. Moreover, we show that there exists one pair of the light Higgs doublets for the electroweak gauge symmetry breaking. Because there exist two pairs of additional vector-like particles with similar intermediate-scale masses, the SU(5) and U(1)_X gauge couplings can be unified at the GUT scale which is reasonably (about one or two orders) higher than the SU(2)_L times SU(3)_C unification scale. Furthermore, we briefly discuss the simplest SO(10) model with flipped SU(5) embedding, and point out that it can not work without fine-tuning.
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We explore proton decay in a class of realistic supersymmetric flipped $SU(5)$ models supplemented by a $U(1)_R$ symmetry which plays an essential role in implementing hybrid inflation. Two distinct neutrino mass models, based on inverse seesaw and type I seesaw, are identified, with the latter arising from the breaking of $U(1)_R$ by nonrenormalizable superpotential terms. Depending on the neutrino mass model an appropriate set of intermediate scale color triplets from the Higgs superfields play a key role in proton decay channels that include $p rightarrow (e^{+},mu^+), pi^0$, $p rightarrow ( e^+,mu^{+}), K^0 $, $p rightarrow overline{ u}, pi^{+}$, and $p rightarrow overline{ u}, K^+ $. We identify regions of the parameter space that yield proton lifetime estimates which are testable at Hyper-Kamiokande and other next generation experiments. We discuss how gauge coupling unification in the presence of intermediate scale particles is realized, and a $Z_4$ symmetry is utilized to show how such intermediate scales can arise in flipped $SU(5)$. Finally, we compare our predictions for proton decay with previous work based on $SU(5)$ and flipped $SU(5)$.
We study the feasibility of realizing supersymmetric new inflation model, introduced by Senoguz and Shafi in [1], for $SU(5)$ and flipped $SU(5)$ models of grand unified theories (GUTs). This realization requires an additional $U(1)_R times Z_{n}$ symmetry for its successful implementation. The standard model (SM) gauge singlet scalar components of $24_H$ and $10_H$ GUT Higgs superfields are respectively employed to realize successful inflation in $SU(5)$ and flipped $SU(5)$ models. The predictions of the various inflationary observables lie within the recent Planck bounds on the scalar spectral index, $n_s$, for $n geq 5$ in $SU(5)$ model and for $n geq 6$ in flipped $SU(5)$ model. In particular, the tensor to scalar ratio $r$ and the running of spectral index $d n_s/ dln k$ are negligibly small and lie in the range, $10^{-12} lesssim r lesssim 10^{-8}$ and $10^{-9} lesssim dn_s/dln k lesssim 10^{-3}$, for realistic values of $n$. In numerical estimation of the various predictions, we fix the gauge symmetry breaking scale, $M$, around $2 times 10^{16}$ GeV. The issue of gauge coupling unification in $R$-symmetric $SU(5)$ is evaded by adding vectorlike families with mass splitting within their multiplets. The dilution of monopoles beyond the observable limit is naturally achieved in the breaking of $SU(5)$ gauge symmetry during inflation. A realistic scenario of reheating with non-thermal leptogenesis is employed for both models. The predicted range of reheat temperature within Planck bounds, $3 times 10^{7}text{ GeV }lesssim T_r lesssim 2 times 10^{9}$ GeV, is safe from the gravitino problem for the gravitino mass, $m_{3/2} gtrsim 10$ TeV. Finally, the $U(1)_R times Z_{n}$ symmetry is also observed to play a crucial role in suppressing the various fast proton decay operators.
Recently, there are two hints arising from physics beyond the standard model. One is a possible energy loss mechanism due to emission of very weakly interacting light particles from white dwarf stars, with a coupling strength ~ 0.7x10^{-13}, and another is the high energy positrons observed by the PAMELA satellite experiment. We construct a supersymmetric flipped-SU(5) model, SU(5)xU(1)_X with appropriate additional symmetries, [U(1)_H]_{gauge}x[U(1)_RxU(1)_Gamma]_{global}xZ_2, such that these are explained by a very light electrophilic axion of mass 0.5 meV from the spontaneously broken U(1)_Gamma and two component cold dark matters from Z_2 parity. We show that in the flipped-SU(5) there exists a basic mechanism for allowing excess positrons through the charged SU(2) singlet leptons, but not allowing anti-proton excess due to the absence of the SU(2) singlet quarks. We show the discovery potential of the charged SU(2) singlet E at the LHC experiments by observing the electron and positron spectrum. With these symmetries, we also comment on the mass hierarchy between the top and bottom quarks.
In this paper, $E_6$ and especially $E_7$ GUT are considered in the F-theory setting in view of the free fermionic construction of the $4D$ heterotic string. In particular, the NAHE-Based LRS model of cite{Cleaver:2000ds, Cleaver:2002ps} is revisited as an illustration where the starting point was taken to be the $N=4$, $E_7 times E_7 times SO(16)$ which through the use of boundary condition basis vectors is reduced to obtain the flipped $SO(10)$ GUT symmetry. We also seek to extend the results of cite{Faraggi:2002ah} in the case of the flipped $SU(5)$ to home in on the flipped $SO(10)$ vacua from the Horv{a}va-Witten theory where the $E_8$ gauge group on the observable sector decomposes as $E_{8}supset E_{6}times SU(3)$ with $E_{6}$ being the gauge group of the effective field theory. We find for the $E_{6}$ GUT symmetry, solutions of type A and solutions of type B where the Hirzebruch surfaces are considered for the base contrary to cite{Faraggi:2002ah} where flipped $SU(5)$ vacua were studied and only solutions of type B were found. Moreover, no solutions are found in the case of the base being the del Pezzo surfaces. Furthermore, this goes hand in hand with the heterotic, low-energy string-derived effective model discussed in cite{Ashfaque:2016psv,Ashfaque:2016ydg}.
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.
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