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Register a new userSuperstring standard model from Z_{12-I} orbifold compactification with and without exotics, and effective R-parity
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We construct a supersymmetric standard model in the context of the $Z_{12-I}$ orbifold compactification of the heterotic string theory. The gauge group is $SU(3)_ctimes SU(2)_Ltimes U(1)_Ytimes U(1)^4times[SO(10)times U(1)^3]$. We obtain three chiral families, $3times{Q,d^c,u^c,L,e^c, u^c}$, and Higgs doublets. There are numerous neutral singlets many of which can have VEVs so that low energy phenomenology on Yukawa couplings can be satisfied. In one assignment (Model E) of the electroweak hypercharge, we obtain the string scale value of $sin^2theta_W^0={3/8}$ and another exactly massless {it exphoton} (in addition to the photon) coupling to exotic particles only. There are color triplet and anti-triplet exotics, $alpha$ and $bar{alpha}$, $SU(2)_L$ doublet exotics, $delta$ and $bar{delta}$, and $SU(3)_ctimes SU(2)_L$ singlet but $Y={2/3},-{1/3},-{2/3},{1/3}$ exotics, $xi,eta,bar{xi}, bar{eta}$. We show that all these vector-like exotics achieve heavy masses by appropriate VEVs of neutral singlets. One can find an effective R-parity between light (electroweak scale) particles so that proton and the LSP can live sufficiently long. In another assignment (Model S) of the electroweak hypercharge, there does not appear any exotic particle but $sin^2theta_W^0={3/14}$.
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In string compactifications, frequently there appears the anomalous U(1) gauge symmetry which belonged to E8$times$E8 of the heterotic string. This anomalous U(1) gauge boson obtains mass at the compactification scale, just below $10^{18,}$GeV, by absorbing one pseudoscalar (corresponding to the model-independent axion) from the second rank anti-symmetric tensor field $B_{MN}$. Below the compactification scale, there results a global symmetry U(1)$_{rm anom}$ whose charge $Q_{rm anom}$ is the original gauge U(1) charge. This is the most natural global symmetry, realizing the invisible axion. This global symmetry U(1)$_{rm anom}$ is suitable for a flavor symmetry. In the simplest compactification model with the flipped SU(5) grand unification, we calculate all the low energy parameters in terms of the vacuum expectation values of the standard model singlets.
The strategy for assigning $Z_{4R}$ parity in the string compactification is presented. For the visible sector, an anti-SU(5) (flipped-SU(5)) grand unification (GUT) model with three families is used to reduce the number of representations compared to the number in the minimal supersymmetric standard models (MSSMs). The SO(32) heterotic string is used to allow a large nonabelian gauge group SU($N$), $Nge 9$, for the hidden sector such that the number of extra U(1) factors is small. A discrete subgroup of the gauge U(1)s is defined as the $Z_{4R}$ parity. Spontaneous symmetry breaking of anti-SU(5) GUT is achieved by the vacuum expectation values of two index antisymmetric tensor Higgs fields ${bf 10}_{+1}$ and $overline{bf 10}_{-1}$ that led to our word `anti-SU(5). In the illustrated example, the multiplicity 3 in one twisted sector allows the permutation symmetry $S_3$ that leads us to select the third family members and one MSSM pair of the Higgs quintets.
We construct a supersymmetric standard model in the context of the Z_{12-I} orbifold compactification of the E_8 x E_8 heterotic string theory. The gauge group is SU(3)_c x SU(2)_L x U(1)_Y x U(1)^4 x [SO(10) x U(1)^3] with sin^2theta_W = 3/8. We obtain three families of SO(10) spinor-like chiral matter states, and Higgs doublets. All other extra states are exactly vector-like under the standard model gauge symmetry. There are numerous standard model singlets, many of which get VEVs such that only the standard model gauge symmetry survives and desired Yukawa couplings can be generated at lower energies. In particular, all vector-like exotic states achieve superheavy masses and the R-parity can be preserved.
From the current ATLAS and CMS results on Higgs boson mass and decay rates, the NMSSM is obviously better than the MSSM. To explain the fine-tuning problems such as gauge hiearchy problem and strong CP problem in the SM, we point out that supersymmetry does not need to provide a dark matter candidate, i.e., R-parity can be violated. Thus, we consider three kinds of the NMSSM scenarios: in Scenarios I and II R-parity is conserved and the lightest neutralino relic density is respectively around and smaller than the observed value, while in Scenario III R-parity is violated. To fit all the experimental data, we consider the chi^2 analyses, and find that the Higgs boson mass and decay rates can be explained very well in these Scenarios. Considering the small chi^2 values and fine-tuning around 2-3.7% (or 1-2%), we obtain the viable parameter space with light (or relatively heavy) supersymmetric particle spectra only in Scenario III (or in Scenarios I and II). Because the singlino, Higgsinos, and light stop are relatively light in general, we can relax the LHC supersymmetry search constraints but the XENON100 experiment gives a strong constraint in Scenarios I and II. In all the viable parameter space, the anomalous magnetic moment of the muon (g_{mu} - 2)/2 are generically small. With R-parity violation, we can increase (g_{mu} - 2)/2, and avoid the contraints from the LHC supersymmetry searches and XENON100 experiment. Therefore, Scenario III with R-parity violation is more natural and realistic than Scenarios I and II.
R-parity conservation is an {it ad hoc} assumption in the most popular version of the supersymmetric standard model. Most studies of models which do allow for R-parity violation have been restricted to various limiting scenarios. The single-VEV parametrization used in this paper provides a workable framework to analyze phenomenology of the most general theory of SUSY without R-parity. We perform a comprehensive study of leptonic phenomenology at tree-level. Experimental constraints on various processes are studied individually and then combined to yield regions of admissible parameter space. In particular, we show that large R-parity violating bilinear couplings are not ruled out, especially for large $tanbeta$.
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