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Register a new userUnification of Gauge Couplings in the E(6)SSM
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P. Athron
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We argue that in the two-loop approximation gauge coupling unification in the exceptional supersymmetric standard model can be achieved for any phenomenologically reasonable value of strong gauge coupling at the electroweak scale consistent with the experimentally measured central value.
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The standard model extended by three vector-like families with masses of order 1 TeV -- 100 TeV allows for unification of gauge couplings. The values of gauge couplings at the electroweak scale are highly insensitive to fundamental parameters. The grand unification scale is large enough to avoid the problem with fast proton decay. The electroweak minimum of the Higgs potential is stable.
In gauge-Higgs unification the 4D Higgs boson appears as a part of the fifth dimensional component of gauge potentials, namely as a fluctuation mode of the Aharonov-Bohm phase in the extra dimension. The $SO(5) times U(1) times SU(3)$ gauge-Higgs unification gives nearly the same phenomenology as the standard model (SM) at low energies. It predicts KK excited states of photon, $Z $ boson, and $Z_R$ boson ($Z$ bosons) around 7 - 8 TeV. Quarks and leptons couple to these $Z$ bosons with large parity violation, which leads to distinct interference effects in $e^+ e^- rightarrow mu^+ mu^-, q , bar q$ processes. At 250 GeV ILC with polarized electron beams, deviation from SM can be seen at the 3 - 5 sigma level even with 250 fb$^{-1}$ data, namely in the early stage of ILC. Signals become stronger at higher energies. Precision measurements of interference effects at electron-positron colliders at energies above 250 GeV become very important to explore physics beyond the standard model.
We analize the impact of two-loop renormalization group equations on the $SU(3)_ctimes SU(2)_wtimes U(1)_Y$ gauge couplings unification in various supersymmetric theories. In general the presence of superfields in higher representation than the doublet spoil the gauge couplings unification at one-loop. The situation is more interesting when the renormalization group equations are calculated at two-loop. In this case we show that the unification of the gauge couplings can be achieved for models with triplet superfield(s). In the analysis of the models with triplet superfield(s) we show that the dimensionless couplings do not have a Landau pole in their evolution at high energies but they run to a nontrivial ultraviolet fixed point.
We discuss gauge coupling unification in models with additional 1 to 4 complete vector-like families, and derive simple rules for masses of vector-like fermions required for exact gauge coupling unification. These mass rules and the classification scheme are generalized to an arbitrary extension of the standard model. We focus on scenarios with 3 or more vector-like families in which the values of gauge couplings at the electroweak scale are highly insensitive to the grand unification scale, the unified gauge coupling, and the masses of vector-like fermions. Their observed values can be mostly understood from infrared fixed point behavior. With respect to sensitivity to fundamental parameters, the model with 3 extra vector-like families stands out. It requires vector-like fermions with masses of order 1 TeV - 100 TeV, and thus at least part of the spectrum may be within the reach of the LHC. The constraints on proton lifetime can be easily satisfied in these models since the best motivated grand unification scale is at $sim 10^{16}$ GeV. The Higgs quartic coupling remains positive all the way to the grand unification scale, and thus the electroweak minimum of the Higgs potential is stable.
All lowest-order amplitudes for e+e- --> 4f+gamma are calculated including five anomalous quartic gauge-boson couplings that are allowed by electromagnetic gauge invariance and the custodial SU(2)_c symmetry. Three of these anomalous couplings correspond to the operators L_0, L_c, and L_n that have been constrained by the LEP collaborations in WWgamma production. The anomalous couplings are incorporated in the Monte Carlo generator RACOONWW. Moreover, for the processes e+e- --> 4f+gamma RACOONWW is improved upon including leading universal electroweak corrections such as initial-state radiation. The discussion of numerical results illustrates the size of the leading corrections as well as the impact of the anomalous quartic couplings for LEP2 energies and at 500GeV.
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