On Some Geometric Properties of Slice Regular Functions of a Quaternion Variable

The goal of this paper is to introduce and study some geometric properties of slice regular functions of quaternion variable like univalence, subordination, starlikeness, convexity and spirallikeness in the unit ball. We prove a number of results, among which an Area-type Theorem, Rogosinski inequality, and a Bieberbach-de Branges Theorem for a subclass of slice regular functions. We also discuss some geometric and algebraic interpretations of our results in terms of maps from $\mathbb R^4$ to itself. As a tool for subordination we define a suitable notion of composition of slice regular functions which is of independent interest

Coefficient, Distortion and Growth Inequalities for Certain Close-to-Convex Functions

In the present investigation, certain subclasses of close-to-convex functions are investigated. In particular, we obtain an estimate for the Fekete-Szeg\"o functional for functions belonging to the class, distortion, growth estimates and covering theorems

Search for anomalous couplings in the W tb vertex from the measurement of double differential angular decay rates of single top quarks produced in the t-channel with the ATLAS detector

The electroweak production and subsequent decay of single top quarks is determined by the properties of the Wtb vertex. This vertex can be described by the complex parameters of an effective Lagrangian. An analysis of angular distributions of the decay products of single top quarks produced in the t -channel constrains these parameters simultaneously. The analysis described in this paper uses 4.6 fb−1 of proton-proton collision data at √s =7 TeV collected with the ATLAS detector at the LHC. Two parameters are measured simultaneously in this analysis. The fraction f 1 of decays containing transversely polarised W bosons is measured to be 0.37 ± 0.07 (stat.⊕syst.). The phase δ − between amplitudes for transversely and longitudinally polarised W bosons recoiling against left-handed b-quarks is measured to be −0.014π ± 0.036π (stat.⊕syst.). The correlation in the measurement of these parameters is 0.15. These values result in two-dimensional limits at the 95% confidence level on the ratio of the complex coupling parameters g R and V L, yielding Re[g R /V L] ∈ [−0.36, 0.10] and Im[g R /V L] ∈ [−0.17, 0.23] with a correlation of 0.11. The results are in good agreement with the predictions of the Standard Model

Measurement of the dependence of transverse energy production at large pseudorapidity on the hard-scattering kinematics of proton-proton collisions at √s=2.76 TeV with ATLAS

The relationship between jet production in the central region and the underlying-event activity in a pseudorapidity-separated region is studied in 4.0 pb-1 of s=2.76 TeV pp collision data recorded with the ATLAS detector at the LHC. The underlying event is characterised through measurements of the average value of the sum of the transverse energy at large pseudorapidity downstream of one of the protons, which are reported here as a function of hard-scattering kinematic variables. The hard scattering is characterised by the average transverse momentum and pseudorapidity of the two highest transverse momentum jets in the event. The dijet kinematics are used to estimate, on an event-by-event basis, the scaled longitudinal momenta of the hard-scattered partons in the target and projectile beam-protons moving toward and away from the region measuring transverse energy, respectively. Transverse energy production at large pseudorapidity is observed to decrease with a linear dependence on the longitudinal momentum fraction in the target proton and to depend only weakly on that in the projectile proton. The results are compared to the predictions of various Monte Carlo event generators, which qualitatively reproduce the trends observed in data but generally underpredict the overall level of transverse energy at forward pseudorapidity

Search for direct production of charginos and neutralinos in events with three leptons and missing transverse momentum in √s=7 TeV pp collisions with the ATLAS detector

A search for the direct production of charginos and neutralinos in final states with three electrons or muons and missing transverse momentum is presented. The analysis is based on 4.7 fb(-1) of root s = 7 TeV proton-proton collision data delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with Standard Model expectations in three signal regions that are either depleted or enriched in Z-boson decays. Upper limits at 95% confidence level are set in R-parity conserving phenomenological minimal supersymmetric models and in simplified models, significantly extending previous results. (C) 2012 CERN. Published by Elsevier B.V. All rights reserved

Search for pair and single production of new heavy quarks that decay to a Z boson and a third-generation quark in pp collisions at root s=8 TeV with the ATLAS detector

Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited