Abstract:
R-parity-violating supersymmetry with a conserved baryon number B provides a framework for particle physics with lepton number (L) violating interactions. Two important probes of the L-violating physics are neutrino masses and sneutrino-antisneutrino mass-splittings. We evaluate these quantities in the context of the most general CP-conserving, R-parity-violating B-conserving extension of the minimal supersymmetric standard model. In generic three-generation models, three sneutrino-antisneutrino mass splittings are generated at tree-level. In contrast, only one neutrino mass is generated at tree-level; the other two neutrinos acquire masses at one-loop. In many models, the dominant contribution to the radiative neutrino masses is induced by the non-zero sneutrino-antisneutrino mass splitting.

Abstract:
We consider implications of the loop process sneutrino -> gamma gamma in the MSSM with R-parity violation for future experiments, where the sneutrino is produced as the only supersymmetric particle. We present a scenario for the R-parity violating couplings, where this clean decay, although rare with Br(sneutrino -> gamma gamma) ~ 10^{-6}, may be useful for sneutrino detection over a range of sneutrino masses at the LHC. Furthermore, the new sneutrino-gamma-gamma effective coupling may induce detectable sneutrino resonant production in gamma gamma collisions, over a considerably wide mass range. We compare sneutrino -> gamma gamma, gg throughout the paper with the analogous yet quantitatively very different, Higgs -> gamma gamma, gg decays and comment on the loop processes sneutrino -> WW, ZZ.

Abstract:
In supersymmetric models with R-parity violation, sneutrinos may be produced as s-channel resonances at muon colliders. We demonstrate that, for R-parity violating couplings as low as 10^-4, sneutrino resonances may be observed and may be exploited to yield high precision SUSY parameter measurements. The excellent beam energy resolution of muon colliders may also be used to resolve MeV level splittings between CP-even and CP-odd sneutrino mass eigenstates.

Abstract:
We study the single production of sneutrinos with two leptons (or jets) via $\gamma\gamma$ collision in an R-parity ($R_{p}$) violating supersymmetric model. The subsequent decays of the sneutrino are also considered. The single production of sneutrinos may provide a significant test of supersymmetry and $R_p$-violation with flavour conserving and flavour changing final states. If such processes coming from $R_p$ violation are not detected, the parameter space of the model will be strongly constrained at the future Linear Collider.

Abstract:
We study the single production of scalar neutrinos or charginos via $\gamma\gamma$ collision in an R-parity ($R_{p}$) violating supersymmetric model. It may be possible to detect a sneutrino or a chargino at a Linear Collider (LC) in $\gamma \gamma$ operation mode, as a test of supersymmetry and $R_p$-violation. Because of the clean background in LC, stringent constraints on $R_p$ violating parameters can be obtained even if the process cannot be observed at the future Linear Collider.

Abstract:
R-parity violation in the supersymmetric standard model could be the origin of neutrino masses and mixing accounting for the atmospheric and solar neutrino oscillations. More interestingly, this hypothesis may be tested in future colliders by detecting lepton number violating decays of the lightest supersymmetric particle. Here, we present a comprehensive analysis for the determination of sneutrino vacuum expectation values from the one-loop effective scalar potential, and also for the one-loop renormalization of neutrino masses and mixing. Applying our results to theories with gauge mediated supersymmetry breaking, we discuss the effects of the one-loop corrections and how the realistic neutrino mass matrices arise.

Abstract:
We consider new s-channel scalar exchanges in top quark and massive gauge-bosons pair production in e+e- collisions, in supersymmetry with a small lepton number violation. We show that a soft bilinear lepton number violating term in the scalar potential which mixes the Higgs and the slepton fields can give rise to a significant scalar resonance enhancement in e+e- -> ZZ, W+W- and in e+e- -> t t(bar). The sneutrino-Higgs mixed state couples to the incoming light leptons through its sneutrino component and to either the top quark or the massive gauge bosons through its Higgs component. Such a scalar resonance in these specific production channels cannot result from trilinear Yukawa-like R-parity violation alone, and may, therefore, stand as strong evidence for the existence of R-parity violating bilinears in the supersymmetric scalar potential. We use the LEP2 measurements of the WW and ZZ cross-sections to place useful constrains on this scenario, and investigate the expectations for the sensitivity of a future linear collider to these signals. We find that signals of these scalar resonances, in particular in top-pair production, are well within the reach of linear colliders in the small lepton number violation scenario.

Abstract:
We consider the minimal supergravity model (mSUGRA) with one additional R-parity violating operator at the GUT scale. The superparticles mass spectra at the weak scale are generally altered due to the presence of the R-parity violating coupling in the renormalization group equations. We show that a lepton number violating coupling at the GUT scale can lead to a sneutrino as the lightest supersymmetric particle (LSP) in a large region of parameter space consistent with the muon anomalous magnetic moment and other precision measurements. We also give characteristic collider signatures at the LHC.

Abstract:
R parity violation can induce mixing of the supersymmetric Higgs bosons with the sneutrinos at the tree level. We study the effect of this mixing on the decays of Higgs scalars as well as sneutrinos in an effective model where the violation of R parity is included in the minimal supersymmetric model through bilinear lepton number violating superpotential terms. We show that a small violation of R parity can lead to a sizeable branching ratio for the supersymmetric Higgs boson decay mode $H \to \chi \ell$ (where $\chi$ denotes an electroweak gaugino and $\ell$ is either a tau neutrino or a tau lepton). Relevant constraints on R parity violation as well as those coming from SUSY particle searches still allow the decay $H \to \chi \ell$ to compete with the conventional decay $H\ra b \bar{b}$, at least for some ranges of parameters of the model. Moreover, the tau sneutrino will have dominant R parity violating decays to standard model fermions $b \bar{b}$, $\tau^+ \tau^-$ or to the invisible mode $\nu \bar{\nu}$ whenever the phase space for R parity conserving channels is closed.

Abstract:
In R-parity-violating supersymmetric models (with a conserved baryon number), there are no quantum numbers that distinguish the lepton-doublet and down-type Higgs supermultiplets. As a result, the R-parity-violating parameters depend on the basis choice for these superfields, although physical observables are independent of the choice of basis. This paper presents a basis-independent computation of the sneutrino/antisneutrino squared-mass splitting in terms of basis-independent quantities. Techniques are developed for an arbitrary number of sneutrino generations; specific results are provided for the one, two and three generation cases.