This paper introduces a random statistical scan over the high-energy initial parameter space of the minimal SUSY B − L model -denoted as the B − L MSSM. Each initial set of points is renormalization group evolved to the electroweak scale -being subjected, sequentially, to the requirement of radiative B − L and electroweak symmetry breaking, the present experimental lower bounds on the B − L vector boson and sparticle masses, as well as the lightest neutral Higgs mass of ∼125 GeV. The subspace of initial parameters that satisfies all such constraints is presented, shown to be robust and to contain a wide range of different configurations of soft supersymmetry breaking masses. The lowenergy predictions of each such "valid" point -such as the sparticle mass spectrum and, in particular, the LSP -are computed and then statistically analyzed over the full subspace of valid points. Finally, the amount of fine-tuning required is quantified and compared to the MSSM computed using an identical random scan. The B − L MSSM is shown to generically require less fine-tuninng.

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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...

The structure of the B-L minimal supersymmetric Standard Model (MSSM) theoryspecifically, the relevant mass scales and soft supersymmetric breaking parameters -is discussed. The space of initial soft parameters is explored at the high scale using random statistical sampling subject to a constraint on the range of dimensionful parameters. For every chosen initial point, the complete set of renormalization group equations is solved. The low energy results are then constrained to be consistent with present experimental data. It is shown that a large set of initial conditions satisfy these constraints and lead to acceptable low energy particle physics. Each such initial point has explicit predictions, such as the exact physical sparticle spectrum which is presented for two such points. There are also statistical predictions for the masses of the sparticles and the LSP species which are displayed as histograms. Finally, the fine-tuning of the μ parameter -which is always equivalent to or smaller than in the MSSM -is discussed.An ad hoc Z 2 symmetry -R-parity is invoked in the minimal supersymmetric Standard Model (MSSM) to eliminate certain dimension four operators, which, if present, would induce unobserved rapid proton decay. This leads to the important question: is there a natural explanation for R-parity? Note that R-parity is contained as a finite subgroup of the Abelian group U(1) B-L , and that U(1) B−L can be imposed as a global symmetry of both the MSSM and the right-handed neutrino extended MSSM. One expects, however, that a continuous symmetry of the Lagrangian will appear in its local form; that is, as a gauge symmetry. It has long been known that the MSSM is anomalous under this local symmetry, whereas ‡ Corresponding author 1550085-1 B. A. Ovrut, A. Purves & S. Spinnerthe MSSM extended by three right-handed neutrino chiral multiplets with gauged U(1) B-L -henceforth referred to as the B-L MSSM is anomaly free and renormalizable. Furthermore, it is the minimal such theory. If the gauged U(1) B-L symmetry can be spontaneously broken, then the B-L MSSM gives a natural explanation for the suppression of dimension four proton decay, that is, it is forbidden by gauge invariance rather than by an ad hoc finite symmetry. This makes the B-L MSSM very attractive from both a theoretical and phenomenological perspective.The B-L MSSM was introduced from a "bottom-up" phenomenological point of view in Refs. 1 and 2. It was also found from a "top-down" viewpoint to be the low-energy theory associated with a class of smooth vacua of the E 8 × E 8 heterotic superstring. 3-5 In addition, it was shown 6-8 that the "soft" supersymmetry breaking operators associated with this low-energy theory can radiatively induce -via a nonvanishing vacuum expectation value for a right-handed sneutrino -the breakdown of the U(1) B-L symmetry. Since the sneutrino has odd B-L charge, R-parity is spontaneously broken at a scale that is naturally consistent with both electroweak breaking and the bounds on proton decay. In Ref. 9, an analysis ...

The existence of R-parity in supersymmetric models can be naturally explained as being a discrete subgroup of gauged baryon minus lepton number (B − L). The most minimal supersymmetric B − L model triggers spontaneous R-parity violation, while remaining consistent with proton stability. This model is well-motivated by string theory and makes several interesting, testable predictions.Furthermore, R-parity violation contributes to neutrino masses, thereby connecting the neutrino sector to the decay of the lightest supersymmetric particle (LSP). This paper analyzes the decays of third generation squark LSPs into a quark and a lepton. In certain cases, the branching ratios into charged leptons reveal information about the neutrino mass hierarchy, a current goal of experimental neutrino physics, as well as the θ 23 neutrino mixing angle. Furthermore, optimization of leptoquark searches for this scenario is discussed. Using currently available data, the lower bounds on the third generation squarks are computed.

The MSSM with right-handed neutrino supermultiplets, gauged B − L symmetry and a non-vanishing sneutrino expectation value is the minimal theory that spontaneously breaks R-parity and is consistent with the bounds on proton stability and lepton number violation. This minimal B − L MSSM can have a colored/charged LSP, of which a stop LSP is the most amenable to observation at the LHC. We study the R-parity violating decays of a stop LSP into a bottom quark and charged leptons-the dominant modes for a generic "admixture" stop. A numerical analysis of the relative branching ratios of these decay channels is given using a wide scan over the parameter space. The fact that R-parity is violated in this theory by a vacuum expectation value of a sneutrino links these branching ratios directly to the neutrino mass hierarchy. It is shown how a discovery of bottom-charged lepton events at the LHC can potentially determine whether the neutrino masses are in a normal or inverted hierarchy, as well as determining the θ 23 neutrino mixing angle. Finally, present LHC bounds on these leptoquark signatures are used to put lower bounds on the stop mass.

It is shown that in the phenomenologically realistic supersymmetric B − L MSSM theory, a linear combination of the neutral, up Higgs field with the third family left-and right-handed sneutrinos can play the role of the cosmological inflaton. Assuming that supersymmetry is softly broken at a mass scale of order 10 13 GeV, the potential energy associated with this field allows for 60 e-foldings of inflation with the cosmological parameters being consistent with all Planck2015 data. The theory does not require any non-standard coupling to gravity and the physical fields are all sub-Planckian during the inflationary epoch. It will be shown that there is a "robust" set of initial conditions which, in addition to satisfying the Planck data, simultaneously are consistent with all present LHC phenomenological requirements.

In previous work, we presented a statistical scan over the soft supersymmetry breaking parameters of the minimal SUSY B − L model. For specificity of calculation, unification of the gauge parameters was enforced by allowing the two Z 3 × Z 3 Wilson lines to have mass scales separated by approximately an order of magnitude. This introduced an additional "left-right" sector below the unification scale. In this paper, for three important reasons, we modify our previous analysis by demanding that the mass scales of the two Wilson lines be simultaneous and equal to an "average unification" mass M U . The present analysis is 1) more "natural" than the previous calculations, which were only valid in a very specific region of the Calabi-Yau moduli space, 2) the theory is conceptually simpler in that the left-right sector has been removed and 3) in the present analysis the lack of gauge unification is due to threshold effects -particularly heavy string thresholds, which we calculate statistically in detail. As in our previous work, the theory is renormalization group evolved from M U to the electroweak scale -being subjected, sequentially, to the requirement of radiative B − L and electroweak symmetry breaking, the present experimental lower bounds on the B − L vector boson and sparticle masses, as well as the lightest neutral Higgs mass of ∼125 GeV. The subspace of soft supersymmetry breaking masses that satisfies all such constraints is presented and shown to be substantial.