The B − L MSSM is the MSSM with three right-handed neutrino chiral multiplets and gauged B − L symmetry. The B − L symmetry is broken by the third family right-handed sneutrino acquiring a VEV, thus spontaneously breaking R-parity. Within a natural range of soft supersymmetry breaking parameters, it is shown that a large and uncorrelated number of initial values satisfy all present phenomenological constraints; including the correct masses for the W ± , Z 0 bosons, having all sparticles exceeding their present lower bounds and giving the experimentally measured value for the Higgs boson. For this "valid" set of initial values, there are a number of different LSPs, each occurring a calculable number of times. We plot this statistically and determine that among the most prevalent LSPs are chargino and neutralino mass eigenstates. In this paper, the R-parity violating decay channels of charginos and neutralinos to standard model particles are determined, and the interaction vertices and decay rates computed analytically. These results are valid for any chargino and neutralino, regardless of whether or not they are the LSP. For chargino and neutralino LSPs, we will-in a subsequent series of papers -present a numerical study of their RPV decays evaluated statistically over the range of associated valid initial points. B Mass Matrix elements 54 B.1 Chargino mass matrix 54 B.2 Neutralino mass matrix 55 -1 --4 -In Section 2, we give a brief summary of the B − L MSSM. In particular, the spontaneous breaking of gauged U (1) B−L symmetry by a non-vanishing VEV of the third family right-handed sneutrino is discussed. The associated R-parity violating interactions induced in the Lagrangian are presented in detail. The VEV of the right-handed sneutrino produces a mixing of the third family right-hand neutrino and the three left-handed neutrinos with all fermionic superpartners of the neutral gauge bosons and the up and down neutral Higgsinos. This is presented in Section 3. The general form of this 9 × 9 mass matrix is given, as well as the explicit form of the unitary matrix required to diagonalize it. However, in that section, we focus on the diagonal 3 × 3 left-handed neutrino Majorana submatix m D ν only. The mass eigenvalues of this matrix can be determined from the explicit form of the PMNS mixing matrix as well as the off-diagonal lefthanded neutrino matrix m ν . This latter matrix is a function of the R-parity violating parameters as well as three additional quantities. The result is compared with the experimentally determined mass eigenvalues of both the "normal" and the "inverted" neutrino mass hierarchies. In Section 4, we list all of the presently known experimental data that must be satisfied in any phenomenologically acceptable vacuum. These include the masses of the W ± ,Z 0 electroweak vector bosons, the Higgs mass, the present lower bounds on the SUSY sparticles and so on. Having done this, we present the mass interval in which we will statistically throw all dimensionful parameters of the soft SUSY breaking t...

Observations of the high-redshift Universe using the 21 cm line of neutral hydrogen and complimentary emission lines from the first galaxies promise to open a new door for our understanding of the epoch of reionization. We present predictions for the [C ii] 158 µm line and H i 21 cm emission from redshifts z = 6-9 using high-dynamicrange cosmological simulations combined with semi-analytical models. We find that the CONCERTO experiment should be able to marginally detect the large scale power spectrum of [C ii] emission to redshifts of up to z = 8 (signal-to-noise ratio ∼ 1 at k < 0.1 h/cMpc with 1500 hr of integration). A Stage II experiment similar to CCAT-p should be able to detect [C ii] from even higher redshifts to high significance for similar integration times (signal-to-noise ratio of ∼ 50 at k = 0.2 h/cMpc at z = 6). We study the possibility of combining such future [C ii] measurements with 21 cm measurements using LOFAR and SKA to measure the [C ii]-21cm cross power spectra, and find that a Stage II experiment should be able to measure the cross-power spectrum for k 1 h/cMpc to signal-to-noise ratio of better than 10. We discuss the capability of such measurements to constrain astrophysical parameters relevant to reionization and show that a measurement of the [C ii]-21cm cross power spectrum helps break the degeneracy between the mass and brightness of ionizing sources.

We review the compactification to five‐dimensional heterotic M‐theory on a Schoen Calabi–Yau threefold and the specific SU(4) vector bundle leading to the “heterotic standard model” in the observable sector. Within 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 slope‐stability of both the observable and hidden sector bundles. The further compactification to a four‐dimensional effective theory on a linearized BPS double domain wall is then presented to order κ114/3. Specifically, the generic constraints required for anomaly cancellation and the restrictions imposed by positive squared gauge couplings to order κ114/3 are presented in detail. Three additional constraints are imposed, one guaranteeing that the S1/double-struckZ2 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. As a check on our results, we calculate several quantities to order κ116/3 and show that they remain physically acceptable, and even improve, when computed to higher order.

The R-parity violating decays of both Wino chargino and Wino neutralino LSPs are analyzed within the context of the B − L MSSM "heterotic standard model". These LSPs correspond to statistically determined initial soft supersymmetry breaking parameters which, when evolved using the renormalization group equations, lead to an effective theory satisfying all phenomenological requirements; including the observed electroweak vector boson and Higgs masses. The explicit decay channels of these LSPs into standard model particles, the analytic and numerical decay rates and the associated branching ratios are presented. The decay lengths of these RPV interactions are discussed. It is shown that the vast majority of these decays are "prompt", although a small, but calculable, number correspond to "displaced vertices" of various lengths. It is demonstrated that for a Wino chargino LSP, the NLSP is the Wino neutralino with a mass only slightly higher than the LSP-and vice-versa. As a consequence, we show that both the Wino chargino and Wino neutralino LSP/NLSP R-parity violating decays should be simultaneously observable at the CERN LHC.