The R-parity violating decays of charginos and neutralinos in the B-L MSSM

Abstract

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...

R-parity violating decays of Bino neutralino LSPs at the LHC

“…The absolute value of each soft mass is confined to be in the interval (2.2) presented above. Using RGE calculations discussed in detail in [8,30], we run the mass parameters and physical couplings of the theory down from the scale M I -where the B − L MSSM emerges after the spontaneous breaking of an SO(10) GUT theory-through the soft SUSY breaking scale to lower energies. However, not all sets of random throws are physically viable at low energy.…”

“…Therefore, with the RPV extension, the gauge eigenstate basis is enlarged from 3 and the neutralino mass matrix becomes 9 × 9. After diagonalization, the three generations of left-handed neutrinos receive non-zero Majorana masses, a process carefully outlined in [30,31]. The original six neutralino eigenstates, on the other hand, each receive a negligibly small RPV contribution containing the three left-handed neutrinos.…”

“…The matrices U, V and N matrices rotate the gaugino eigenstates into the neutralino and chargino mass eigenstates. They are presented in Appendices B.1 and B.2 of [30]. Note that in all cases in Appendix A and B above, we sum over j = 1, 2, 3.…”

“…In fact, it is the most likely LSP to occur for any viable initial conditions. It seems well-motivated, therefore, to apply the results of [30] to the Bino and to determine its decay modes to standard model particles, and the associated decay rates and branching ratios-as well as the relationship of these decays to the neutrino mass hierarchy. However, an important new phenomenon occurs for the Bino which is unique among all chargino and neutralino LSPs.…”

“…Finally, the analysis in this paper uses the notation and formalism for the B − L MSSM presented in a series of papers [8,30]. The reader is referred specifically to [30] for the precise notation and formalism particularly relevant to the definition and decay processes of the Bino LSP. For clarity, we have summarized the relevant notation in Appendix A of this paper.…”