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Register a new user$SU(5)times{U(1)}$ models with a vector-like fermion family
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Motivated by experimental measurements indicating deviations from the Standard Model predictions we discuss F-theory inspired models, which, in addition to the three chiral generations contain a vector-like complete fermion family. The analysis takes place in the context of $SU(5)times U(1)$ GUT embedded in an $E_8$ covering group which is associated with the (highest) geometric singularity of the elliptic fibration. In this context, the $U(1)$ is a linear combination of four abelian factors subjected to appropriate anomaly cancellation conditions. Furthermore, we require universal $U(1)$ charges for the three chiral families and different ones for the corresponding fields of the vector-like representations. Under the aforementioned assumptions, we find 192 such models which can be classified into five distinct categories with respect to their specific GUT properties. We exhibit representative examples for each such class and construct the superpotential couplings and the fermion mass matrices. We explore the implications of the vector-like states in low energy phenomenology including the predictions regarding the B-meson anomalies. The r^ole of R-parity violating terms appearing in some particular models of the above construction is also discussed.
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We study low energy implications of F-theory GUT models based on $SU(5)$ extended by a $U(1)$ symmetry which couples non-universally to the three families of quarks and leptons. This gauge group arises naturally from the maximal exceptional gauge symmetry of an elliptically fibred internal space, at a single point of enhancement, $E_8supset SU(5)times SU(5)supset SU(5)times U(1)^4$. Rank-one fermion mass textures and a tree-level top quark coupling are guaranteed by imposing a $Z_2$ monodromy group which identifies two abelian factors of the above breaking sequence. The $U(1)$ factor of the gauge symmetry is an anomaly free linear combination of the three remaining abelian symmetries left over by $Z_2$. Several classes of models are obtained, distinguished with respect to the $U(1)$ charges of the representations, and possible extra zero modes coming in vector-like representations. The predictions of these models are investigated and are compared with the LHC results and other related experiments. Particular cases interpreting the B-meson anomalies observed in LHCb and BaBar experiments are also discussed.
$SO(5) times U(1) times SU(3)$ 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.
We show that by adding a vector-like 5+5bar pair of matter fields to the spectrum of the minimal renormalizable SUSY SU(5) theory the wrong relations for fermion masses can be corrected, while being predictive and consistent with proton lifetime limits. Threshold correction from the vector-like fields improves unification of gauge couplings compared to the minimal model. It is found that for supersymmetric spectra lighter than 3 TeV, which would be testable at the LHC, at least some of the nucleon decay modes should have partial lifetimes shorter than about 2.10^34 yrs., which is within reach of ongoing and proposed experiments.
The Cabibbo-Kobayashi-Maskawa (CKM) mixing matrix and flavor-changing neutral currents (FCNCs) in the quark sector are examined in the GUT inspired $SO(5) times U(1) times SU(3)$ gauge-Higgs unification in which the 4D Higgs boson is identified with the Aharonov-Bohm phase in the fifth dimension. Gauge invariant brane interactions play an important role for the flavor mixing in the charged-current weak interactions. The CKM matrix is reproduced except that the up quark mass needs to be larger than the observed one. FCNCs are naturally suppressed as a consequence of the gauge invariance, with a factor of order $10^{-6}$. It is also shown that induced flavor-changing Yukawa couplings are extremely small.
The electroweak phase transition in GUT inspired $SO(5) times U(1) times SU(3)$ gauge-Higgs unification is shown to be of weakly first-order and occurs at $T = T_c^{ rm EW} sim 163 ,$GeV, which is very similar to the behavior in the standard model in perturbation theory. There appears a new phase at higher temperature. $SU(2)_L times U(1)_Y$ ($ theta_H=0$) and $SU(2)_R times U(1)_{Y}$ ($ theta_H= pi$) phases become almost degenerate above $T sim m_{rm KK}$ where $m_{rm KK}$ is the Kaluza-Klein mass scale typically around 13TeV and $theta_H$ is the Aharonov-Bohm phase along the fifth dimension. The two phases become degenerate at $T = T_c^{rm LR} sim m_{rm KK}$. As the temperature drops in the evolution of the early universe the $SU(2)_R times U(1)_{Y}$ phase becomes unstable. The tunneling rate from the $SU(2)_R times U(1)_{Y}$ phase to the $SU(2)_L times U(1)_Y$ phase becomes sizable and a first-order phase transition takes place at $T=2.5 sim 2.6,$TeV. It is shown that the $W$ boson, $Z$ boson and photon, with $theta_H$ varying from 0 to $pi$, are transformed to gauge bosons in the $SU(2)_R times U(1)_{Y}$ phase. Gauge couplings and wave functions of quarks, leptons and dark fermions in the $SU(2)_R times U(1)_{Y}$ phase are determined.
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