ALEPH Four-Jet Excess, RbR_b and R−R-Parity Violation

We review briefly the indications for some relatively light superpartners based on the ~$R_b$ ~anomaly and discuss the dependence of the potential increase in $R_b$ on the assumption about ~$R-$parity (non)conservation. We point out that the exotic 4-jet events reported by ALEPH may constitute a signal for supersymmetry with such a light spectrum and with explicitly broken $R-$parity. A parton level simulation shows that production of a pair of light charginos with their subsequent baryon-number violating decays (either through a stop or through a neutralino) could possibly give rise to this excess. The decay \chi^- \ra \tilde{t}_R^\ast b \ra d s b with m_{\chi^-_1} \sim 60 \gev and m_{\tilde t} \sim 52 \gev leads to signatures very close to the experimental observations.Comment: 17 pages, submited as uuencoded gz-compressed .tar file containing LATEX file and figures. Some typos fixed and the important error in the caption of Fig. 7 correcte

Lepton non-universality in BB decays and fermion mass structure

We consider the possibility that the neutral-current $B$ anomalies are due to radiative corrections generated by Yukawa interactions of quarks and leptons with new vector-like quark and lepton electroweak doublets and new Standard Model singlet scalars. We show that the restricted interactions needed can result from an underlying Abelian family symmetry and that the same symmetry can give rise to an acceptable pattern of quark and charged lepton masses and mixings, providing a bridge between the non-universality observed in the B-sector and that of the fermion mass matrices. We construct two simple models, one with a single singlet scalar in which the flavour changing comes from quark and lepton mixing and one with an additional scalar in which the flavour changing can come from both fermion and scalar mixing. We show that for the case the new quarks are much heavier than the new leptons and scalars the $B$ anomalies can be due to box diagrams with couplings in the perturbative regime consistent with the bounds coming from $B_s- \bar B_s$, $K- \bar K$ and $D- \bar D$ mixing as well as other lepton family number violating processes. The new states can be dark matter candidates and, in the two scalar model with a light scalar of O(60) GeV and vector-like lepton of O(100) GeV, there can be a simultaneous explanation of the B-anomalies, the muon anomalous magnetic moment and the dark matter abundance.Comment: Replacement contains few additional reference

Unification in models with replicated gauge groups

We examine unification of gauge couplings in four dimensional renormalizable gauge theories inspired by the latticized (deconstructed) SM or MSSM in five dimensions. The models are based on replicated gauge groups, spontaneously broken to the diagonal subgroup. The analysis is performed at one-loop level, with the contribution from the heavy vector bosons included, and compared with the analogous results in the SM or MSSM. Unification at or above the diagonal breaking scale is discussed. We find that in the considered class of extensions of the SM(MSSM) unification is possible for a wide range of unification scales and with the similar accuracy as in the SM(MSSM). Unification above the diagonal breaking scale is particularly attractive: it is a consequence of the SM(MSSM) unification, but with the unification scale depending on the number of replications of the gauge group.Comment: 19 pages, 3 figure

Quantum Isometrodynamics

Classical Isometrodynamics is quantized in the Euclidean plus axial gauge. The quantization is then generalized to a broad class of gauges and the generating functional for the Green functions of Quantum Isometrodynamics (QID) is derived. Feynman rules in covariant Euclidean gauges are determined and QID is shown to be renormalizable by power counting. Asymptotic states are discussed and new quantum numbers related to the "inner" degrees of freedom introduced. The one-loop effective action in a Euclidean background gauge is formally calculated and shown to be finite and gauge-invariant after renormalization and a consistent definition of the arising "inner" space momentum integrals. Pure QID is shown to be asymptotically free for all dimensions of "inner" space $D$ whereas QID coupled to the Standard Model fields is not asymptotically free for D <= 7. Finally nilpotent BRST transformations for Isometrodynamics are derived along with the BRST symmetry of the theory and a scetch of the general proof of renormalizability for QID is given.Comment: 38 page

Causal Fermion Systems: A Quantum Space-Time Emerging from an Action Principle

Causal fermion systems are introduced as a general mathematical framework for formulating relativistic quantum theory. By specializing, we recover earlier notions like fermion systems in discrete space-time, the fermionic projector and causal variational principles. We review how an effect of spontaneous structure formation gives rise to a topology and a causal structure in space-time. Moreover, we outline how to construct a spin connection and curvature, leading to a proposal for a "quantum geometry" in the Lorentzian setting. We review recent numerical and analytical results on the support of minimizers of causal variational principles which reveal a "quantization effect" resulting in a discreteness of space-time. A brief survey is given on the correspondence to quantum field theory and gauge theories.Comment: 23 pages, LaTeX, 2 figures, footnote added on page

The Minimal Landau Background Gauge on the Lattice

We present the first numerical implementation of the minimal Landau background gauge for Yang-Mills theory on the lattice. Our approach is a simple generalization of the usual minimal Landau gauge and is formulated for general SU(N) gauge group. We also report on preliminary tests of the method in the four-dimensional SU(2) case, using different background fields. Our tests show that the convergence of the numerical minimization process is comparable to the case of a null background. The uniqueness of the minimizing functional employed is briefly discussed.Comment: 5 pages, 1 tabl