Theoretical and phenomenological implications of R-parity violation in supersymmetric theories are discussed in the context of particle physics and cosmology. Fundamental aspects include the relation with continuous and discrete symmetries and the various allowed patterns of R-parity breaking. Recent developments on the generation of neutrino masses and mixings within different scenarios of R-parity violation are discussed. The possible contribution of Rparity-violating Yukawa couplings in processes involving virtual supersymmetric particles and the resulting constraints are reviewed. Finally, direct production of supersymmetric particles and their decays in the presence of R-parity-violating couplings is discussed together with a survey of existing constraints from collider experiments.To be submitted to Physics Reports

We analyze the Minimal Supersymmetric extension of the Standard Model that we have after the discovery of the Higgs boson at the LHC, the hMSSM (habemus MSSM?), i.e. a model in which the lighter h boson has a mass of approximately 125 GeV which, together with the non-observation of superparticles at the LHC, indicates that the SUSY-breaking scale MS is rather high, MS≳1 TeV. We first demonstrate that the value Mh≈125 GeV fixes the dominant radiative corrections that enter the MSSM Higgs boson masses, leading to a Higgs sector that can be described, to a good approximation, by only two free parameters. In a second step, we consider the direct supersymmetric radiative corrections and show that, to a good approximation, the phenomenology of the lighter Higgs state can be described by its mass and three couplings: those to massive gauge bosons and to top and bottom quarks. We perform a fit of these couplings using the latest LHC data on the production and decay rates of the light h boson and combine it with the limits from the negative search of the heavier H,A and H± states, taking into account the current uncertainties.

It is notorious that, contrary to all other precision electroweak data, the forwardbackward asymmetry for b quarks A b F B measured in Z decays at LEP1 is nearly three standard deviations away from the predicted value in the Standard Model; significant deviations also occur in measurements of the asymmetry off the Z pole. We show that these discrepancies can be resolved in a variant of the Randall-Sundrum extradimensional model in which the gauge structure is extended to SU(2) L ×SU(2) R ×U(1) X to allow for relatively light Kaluza-Klein excitations of the gauge bosons. In this scenario, the fermions are localized differently along the extra dimension, in order to generate the fermion mass hierarchies, so that the electroweak interactions for the heavy third generation fermions are naturally different from the light fermion ones. We show that the mixing between the Z boson with the Kaluza-Klein excitations allows to explain the A b F B anomaly without affecting (and even improving) the agreement of the other precision observables, including the Z → bb partial decay width, with experimental data. Some implications of this scenario for the ILC are summarized.