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Register a new userHidden Sectors from Multiple Line Bundles for the $B-L$ MSSM
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We give a formalism for constructing hidden sector bundles as extensions of sums of line bundles in heterotic $M$-theory. Although this construction is generic, we present it within the context of the specific Schoen threefold that leads to the physically realistic $B-L$ MSSM model. We discuss the embedding of the line bundles, the existence of the extension bundle, and a number of necessary conditions for the resulting bundle to be slope-stable and thus $N=1$ supersymmetric. An explicit example is presented, where two line bundles are embedded into the $SU(3)$ factor of the $E_{6} times SU(3)$ maximal subgroup of the hidden sector $E_{8}$ gauge group, and then enhanced to a non-Abelian $SU(3)$ bundle by extension. For this example, there are in fact six inequivalent extension branches, significantly generalizing that space of solutions compared with hidden sectors constructed from a single line bundle.
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The compactification from the eleven-dimensional Hov{r}ava-Witten orbifold to five-dimensional heterotic M-theory on a Schoen Calabi-Yau threefold is reviewed, as is the specific $SU(4)$ vector bundle leading to the heterotic standard model in the observable sector. Within the context of strongly coupled heterotic M-theory, a formalism for consistent hidden-sector bundles associated with a single line bundle is presented, and a specific line bundle is introduced as a concrete example. Anomaly cancellation and the associated bulk space five-branes are discussed in this context, as is the constraint that the hidden sector bundle be compatible with the slope-stability requirements of the observable sector $SU(4)$ gauge bundle. The further compactification to a four-dimensional effective theory on a linearized BPS double domain wall is then presented to order $kappa_{11}^{4/3}$. Specifically, the generic constraints required for anomaly cancellation and the restrictions imposed by positive squared gauge couplings to order $kappa_{11}^{4/3}$ are presented in detail. Three additional constraints are imposed, one guaranteeing that the $S^{1}/{mathbb{Z}}_{2}$ orbifold length is sufficiently larger than the average Calabi-Yau radius, and two enforcing that the hidden sector be compatible with both the unification mass scale and unified gauge coupling of the $SO(10)$ group in the observable sector. Finally, the expression for the Fayet-Iliopoulos term associated with an anomalous $U(1)$ symmetry is presented and its role in $N=1$ supersymmetry in the low-energy effective theory is discussed. It is shown that $N=1$ supersymmetry can be preserved by cancelling the tree-level and genus-one contributions against each another.
The strongly coupled heterotic M-theory vacuum for both the observable and hidden sectors of the $B-L$ MSSM theory is reviewed, including a discussion of the bundle constraints that both the observable sector $SU(4)$ vector bundle and the a hidden sector bundle induced from a line bundle must satisfy. Gaugino condensation is then introduced within this context, and the hidden sector bundles that exhibit gaugino condensation are presented. The condensation scale is computed, singling out one line bundle whose associated condensation scale is low enough to be compatible with the energy scales available at the LHC. The corresponding region of Kahler moduli space where all bundle constraints are satisfied is presented. The generic form of the moduli dependent $F$-terms due to a gaugino superpotential - which spontaneously break $N=1$ supersymmetry in this sector - is presented and then given explicitly for the unique line bundle associated with the low condensation scale. The moduli dependent coefficients for each of the gaugino and scalar field soft supersymmetry breaking terms are computed leading to a low-energy effective Lagrangian for the observable sector matter fields. We then show that at a large number of points in Kahler moduli space that satisfy all bundle constraints, these coefficients are initial conditions for the renormalization group equations which, at low energy, lead to completely realistic physics satisfying all phenomenological constraints. Finally, we show that a substantial number of these initial points also satisfy a final constraint arising from the quadratic Higgs-Higgs conjugate soft supersymmetry breaking term.
The non-observation of dark matter (DM) by direct detection experiments suggests that any new interaction of DM with the Standard Model (SM) should be very weak. One of the simplest scenarios to achieve this is a dark sector that is charged under a new $U(1)_X$ symmetry, which is kinetically mixed with the SM hypercharge $U(1)_Y$. We briefly review the status of such a minimal setup and analyze in a second step how the picture is altered if also SM fields are charged under the new symmetry. We exemplify this for the case of a gauged $U(1)_{L_mu-L_tau}$ and show that this allows for a simultaneous explanation of the $(g-2)_mu$ excess and the DM relic abundance $Omega_{DM}$. Furthermore, we discuss the potential of four-lepton and two-lepton plus missing energy signatures to test such scenarios.
We study vortex solutions in a theory with dynamics governed by two weakly coupled Abelian Higgs models, describing a hidden sector and a visible sector. We analyze the radial dependence of the axially symmetric solutions constructed numerically and discuss the stability of vortex configurations for different values of the model parameters, studying in detail vortex decay into lower energy configurations. We find that even in a weak coupling regime vortex solutions strongly depend on the parameters of both the visible and hidden sectors. We also discuss on qualitative grounds possible implications of the existence of a hidden sector in connection with superconductivity.
We analyze the dark matter problem in the context of supersymmetric U(1)_{B-L} model. In this model, the lightest neutalino can be the B-L gaugino widetilde {Z}_{B-L} or the extra Higgsinos widetilde{chi}_{1,2} dominated. We compute the thermal relic abundance of these particles and show that, unlike the LSP in MSSM, they can account for the observed relic abundance with no conflict with other phenomenological constraints. The prospects for their direct detection, if they are part of our galactic halo, are also discussed.
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