Cosmological constraints on R-parity violation from neutrino decay

If the neutrino mass is non-zero, as hinted by several experiments, then R-parity-violating supersymmetric Yukawa couplings can drive a heavy neutrino decay into lighter states. The heavy neutrino may either decay radiatively into a lighter neutrino, or it may decay into three light neutrinos through a Z-mediated penguin. For a given mass of the decaying neutrino, we calculate its lifetime for the various modes, each mode requiring certain pairs of R-parity-violating couplings be non-zero. We then check whether the calculated lifetimes fall in zones allowed or excluded by cosmological requirements. For the latter case, we derive stringent new constraints on the corresponding products of R-parity-violating couplings for given values of the decaying neutrino mass.Comment: 13 pages, Latex, uses axodraw.sty; version to appear in Physical Review

Quantum Gravity Effects in Black Holes at the LHC

We study possible back-reaction and quantum gravity effects in the evaporation of black holes which could be produced at the LHC through a modification of the Hawking emission. The corrections are phenomenologically taken into account by employing a modified relation between the black hole mass and temperature. The usual assumption that black holes explode around $1$TeV is also released, and the evaporation process is extended to (possibly much) smaller final masses. We show that these effects could be observable for black holes produced with a relatively large mass and should therefore be taken into account when simulating micro-black hole events for the experiments planned at the LHC.Comment: 14 pages, 8 figures, extended version of hep-ph/0601243 with new analysis of final products, final version accepted for publication in J. Phys.

Leptonic CP Violation in Supersymmetric Standard Model

We point out the possibility of spontaneous and hard CP-violation in the scalar potential of R-parity broken supersymmetric Standard Model. The existence of spontaneous CP-violation depends crucially on the R-parity breaking terms in the superpotential and, in addition, on the choice of the soft supersymmetry breaking terms. Unlike in theories with R-parity conservation, it is natural, in the context of the present model, for the sneutrinos to acquire (complex) vacuum expectation values. In the context of this model we examine here the global implications, like the strength of the CP-violating interactions and the neutrino masses.Comment: REVTEX, 15 page

How generic is cosmic string formation in SUSY GUTs

We study cosmic string formation within supersymmetric grand unified theories. We consider gauge groups having a rank between 4 and 8. We examine all possible spontaneous symmetry breaking patterns from the GUT down to the standard model gauge group. Assuming standard hybrid inflation, we select all the models which can solve the GUT monopole problem, lead to baryogenesis after inflation and are consistent with proton lifetime measurements. We conclude that in all acceptable spontaneous symmetry breaking schemes, cosmic string formation is unavoidable. The strings which form at the end of inflation have a mass which is proportional to the inflationary scale. Sometimes, a second network of strings form at a lower scale. Models based on gauge groups which have rank greater than 6 can lead to more than one inflationary era; they all end by cosmic string formation.Comment: 31 pages, Latex, submitted to PR

Simple Dynamics on the Brane

We apply methods of dynamical systems to study the behaviour of the Randall-Sundrum models. We determine evolutionary paths for all possible initial conditions in a 2-dimensional phase space and we investigate the set of accelerated models. The simplicity of our formulation in comparison to some earlier studies is expressed in the following: our dynamical system is a 2-dimensional Hamiltonian system, and what is more advantageous, it is free from the degeneracy of critical points so that the system is structurally stable. The phase plane analysis of Randall-Sundrum models with isotropic Friedmann geometry clearly shows that qualitatively we deal with the same types of evolution as in general relativity, although quantitatively there are important differences.Comment: an improved version, 34 pages, 9 eps figure

Supersymmetry without R-Parity and without Lepton Number

We investigate Supersymmetric models where neither R parity nor lepton number is imposed. Neutrino masses can be kept highly suppressed compared to the electroweak scale if the $\mu$-terms in the superpotential are aligned with the SUSY-breaking bilinear $B$-terms. This situation arises naturally in the framework of horizontal symmetries. The same symmetries suppress the trilinear R parity violating terms in the superpotential to an acceptable level.Comment: 18 pages, harvma

Non-perturbative renormalization of QCD

In these lectures, we discuss different types of renormalization problems in QCD and their non-perturbative solution in the framework of the lattice formulation. In particular the recursive finite size methods to compute the scale-dependence of renormalized quantities is explained. An important ingredient in the practical applications is the Schr\"odinger functional. It is introduced and its renormalization properties are discussed. Concerning applications, the computation of the running coupling and the running quark mass are covered in detail and it is shown how the $\Lambda$-parameter and renormalization group invariant quark mass can be obtained. Further topics are the renormalization of isovector currents and non-perturbative Symanzik improvement.Comment: 49 pages, lectures at Schladming-9