Abstract: Motivated by discrete flavour symmetry models, we analyse Spontaneous CP Violation (SCPV) for potentials involving three or six Higgs fi elds (both electroweak doublets and singlets) which fall into irreducible triplet representations of discrete symmetries belonging to the Delta(3n(2)) and Delta(6n(2)) series, including A(4), S-4, Delta(27) and Delta(54). For each case, we give the potential and fi nd various global minima for di ff erent regions of the parameter space of the potential. Using CP-odd basis Invariants that indicate the presence of Spontaneous CP Violation we separate the VEVs into those that do or do not violate CP. In cases where CP is preserved we reveal a CP symmetry of the potential that is preserved by those VEVs, otherwise we display a non-zero CP-odd Invariant. Finally we identify interesting cases where there is Spontaneous Geometrical CP Violation in which the VEVs have geometrical phases.

Abstract: We consider the singular behaviour of QCD scattering amplitudes in kinematical configurations where two or more momenta of the external partons become collinear. At the tree level, this behaviour is known to be controlled by factorization formulae in which the singular collinear factor is universal (process independent). We show that this strict (process-independent) factorization is not valid at one-loop and higher-loop orders in the case of the collinear limit in space-like regions (e. g., collinear radiation from initial-state partons). We introduce a generalized version of all-order collinear factorization, in which the space-like singular factors retain some dependence on the momentum and colour charge of the non-collinear partons. We present explicit results on one-loop and two-loop amplitudes for both the two-parton and multiparton collinear limits. At the level of squared amplitudes and, more generally, cross sections in hadron-hadron collisions, the violation of strict collinear factorization has implications on the non-abelian structure of logarithmically-enhanced terms in perturbative calculations (starting from the next-to-next-to-leading order) and on various factorization issues of mass singularities (starting from the next-to-next-to-next-to-leading order).

Abstract: We consider supersymmetric models in which sneutrinos are viable dark matter candidates. These are either simple extensions of the Minimal Supersymmetric Standard Model with additional singlet superfields, such as the inverse or linear seesaw, or a model with an additional U(1) group. All of these models can accomodate the observed small neutrino masses and large mixings. We investigate the properties of sneutrinos as dark matter candidates in these scenarios. We check for phenomenological bounds, such as correct relic abundance, consistency with direct detection cross section limits and laboratory constraints, among others lepton flavour violating (LFV) charged lepton decays. While inverse and linear seesaw lead to different results for LFV, both models have very similar dark matter phenomenology, consistent with all experimental bounds. The extended gauge model shows some additional and peculiar features due to the presence of an extra gauge boson Z' and an additional light Higgs. Specifically, we point out that for sneutrino LSPs there is a strong constraint on the mass of the Z' due to the experimental bounds on the direct detection scattering cross section.