We report exact analytical expressions relating the fundamental parameters describing the neutralino sector in the context of the left-right supersymmetric model. The method used for such effects is the projector formalism deduced without taking into account the Jarlskog's projector formulas. Also, expressions for the neutralino masses and the neutralino mixing matrix are determined . The results are compared with numerical and analytical ones obtained in similar scenarios in the context of the minimal supersymmetric standard model.

The interaction between a vortex within a finite-thickness type-II superconductor and a magnetic force microscopy tip is studied. By analyzing the expression of the arising lateral force, we show that the superconducting penetration depth may be recovered from experiment, using the so-called Laplace transform inversion method. This entails a vertical displacement experiment. The consideration of lateral scanning modes has allowed us to extend the theory to the more stable Hankel transform inversion method, which eventually becomes a Fourier analysis application. For the case of vortices in two-layered superconductors, we show that magnetic particle manipulation is possible by tuning the configuration of the layers.

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The left-right supersymmetric model contains a right-handed gaugino, as well as several higgsinos, in addition to the minimal supersymmetric model. Thus several CP-noninvariant phases appear in this sector. We analyze their impact on chargino masses and find that only two combinations are physically relevant. We then study the production of charginos in e + e − annihilation and chargino decays into a sneutrino and a lepton, and investigate the effects of CP-phases. We also study the CP-odd asymmetry in the production and subsequent decay at the linear collider with longitudinally polarized beams and find a large enhancement when the decay channel to the right sneutrino is available. The effects of the phases in the left-right supersymmetric chargino sector are different from the minimal supersymmetric standard model, and signals from this sector would be able to distinguish between different gauge symmetries. Charge-parity (CP) violation is one of the least understood phenomena in high energyphysics. In the standard model (SM), CP violation is parametrized by one arbitrary phase in the quark mixing matrix and its value fixed by experimental observations. Models beyond the SM, especially those including supersymmetry, predict several new CP-odd phases. The effects of some of these phases, particularly the ones coming from the soft supersymmetry breaking scalar masses, have been studied extensively [1]. In the minimal supersymmetric standard model (MSSM), these phases need to either be unreasonably small, or the scalar fermion masses unusually large [2].A solution to this so called "SUSY CP-problem" has been suggested by the authors in [3]. By enlarging the supersymmetric gauge sector to be left-right symmetric, parity forces Yukawa couplings to be Hermitean, and mass terms in the superpotential to be real. Thus the CP problem is solved at the right-handed (SU (2) R , or seesaw) scale M ∆ R . If M ∆ R is of the order of the electroweak scale, then no other phase can be generated and the problem is solved. If however M ∆ R is a higher scale, the scenario favored by neutrino masses and grand-unification schemes with left-right models as intermediate steps, this is no longer the case. In some variants of the model, the phases appear only at two loop level and are thus naturally small [3], in others the electroweak phase is generated form the renormalization group equations evolution from the seesaw scale, and the electron dipole moment (EDM) problems persist [4]. The left-right supersymmetric model (LRSUSY) enlarges the minimal supersymmetric standard model (MSSM) gauge symmetry SU(This symmetry allows for the seesaw mechanism within supersymmetry and predicts neutrino masses and mixing naturally. In the supersymmetric sector of the theory, it introduces right-handed gauginos in addition to several higgsinos. We expect this change to be most pronounced in the electroweak chargino sector, where previously forbidden right-right interactions are now allowed to proceed with a strength comparable to left-left interactions....