Convergence of generalized conjugate partial sums of Fourier series

Generalized conjugate partial sums of Fourier series are used to find jumps of functions. The rate of convergence is studied and sharp results are obtained

Early search for supersymmetric dark matter models at the LHC without missing energy

We investigate early discovery signals for supersymmetry at the Large Hadron Collider without using information about missing transverse energy. Instead we use cuts on the number of jets and isolated leptons (electrons and/or muons). We work with minimal supersymmetric extensions of the standard model, and focus on phenomenological models that give a relic density of dark matter compatible with the WMAP measurements. An important model property for early discovery is the presence of light sleptons, and we find that for an integrated luminosity of only 200--300 pb$^{-1}$ at a center-of-mass energy of 10 TeV models with gluino masses up to $\sim 700$ GeV can be tested.Comment: 28 pages, 12 figures; published versio

Second-order corrections to mean field evolution for weakly interacting Bosons. I

Inspired by the works of Rodnianski and Schlein and Wu, we derive a new nonlinear Schr\"odinger equation that describes a second-order correction to the usual tensor product (mean-field) approximation for the Hamiltonian evolution of a many-particle system in Bose-Einstein condensation. We show that our new equation, if it has solutions with appropriate smoothness and decay properties, implies a new Fock space estimate. We also show that for an interaction potential $v(x)= \epsilon \chi(x) |x|^{-1}$, where $\epsilon$ is sufficiently small and $\chi \in C_0^{\infty}$, our program can be easily implemented locally in time. We leave global in time issues, more singular potentials and sophisticated estimates for a subsequent part (part II) of this paper

Bounds for anisotropic Carleson operators

We prove weak $(2,2)$ bounds for maximally modulated anisotropically homogeneous smooth multipliers on $\mathbb{R}^n$. These can be understood as generalizing the classical one-dimensional Carleson operator. For the proof we extend the time-frequency method by Lacey and Thiele to the anistropic setting. We also discuss a related open problem concerning Carleson operators along monomial curves.Comment: 26 page

Local smoothing for scattering manifolds with hyperbolic trapped sets

We prove a resolvent estimate for the Laplace-Beltrami operator on a scattering manifold with a hyperbolic trapped set, and as a corollary deduce local smoothing. We use a result of Nonnenmacher-Zworski to provide an estimate near the trapped region, a result of Burq and Cardoso-Vodev to provide an estimate near infinity, and the microlocal calculus on scattering manifolds to combine the two.Comment: 16 pages. Published version available at http://www.springerlink.com/content/r663321331243288/?p=5ad2fe4778a742e4949de2030a409358&pi=1

Asymptotic Lower Bounds for a class of Schroedinger Equations

We shall study the following initial value problem: \begin{equation}{\bf i}\partial_t u - \Delta u + V(x) u=0, \hbox{} (t, x) \in {\mathbf R} \times {\mathbf R}^n, \end{equation} $$u(0)=f,$$ where $V(x)$ is a real short--range potential, whose radial derivative satisfies some supplementary assumptions. More precisely we shall present a family of identities satisfied by the solutions to the previous Cauchy problem. As a by--product of these identities we deduce some uniqueness results and a lower bound for the so called local smoothing which becomes an identity in a precise asymptotic sense.Comment: 24 pages. to appear on Comm. Math. Phy

Single hadron response measurement and calorimeter jet energy scale uncertainty with the ATLAS detector at the LHC

The uncertainty on the calorimeter energy response to jets of particles is derived for the ATLAS experiment at the Large Hadron Collider (LHC). First, the calorimeter response to single isolated charged hadrons is measured and compared to the Monte Carlo simulation using proton-proton collisions at centre-of-mass energies of sqrt(s) = 900 GeV and 7 TeV collected during 2009 and 2010. Then, using the decay of K_s and Lambda particles, the calorimeter response to specific types of particles (positively and negatively charged pions, protons, and anti-protons) is measured and compared to the Monte Carlo predictions. Finally, the jet energy scale uncertainty is determined by propagating the response uncertainty for single charged and neutral particles to jets. The response uncertainty is 2-5% for central isolated hadrons and 1-3% for the final calorimeter jet energy scale.Comment: 24 pages plus author list (36 pages total), 23 figures, 1 table, submitted to European Physical Journal

Search for squarks and gluinos in events with isolated leptons, jets and missing transverse momentum at s√=8 TeV with the ATLAS detector

The results of a search for supersymmetry in final states containing at least one isolated lepton (electron or muon), jets and large missing transverse momentum with the ATLAS detector at the Large Hadron Collider are reported. The search is based on proton-proton collision data at a centre-of-mass energy s√=8 TeV collected in 2012, corresponding to an integrated luminosity of 20 fb−1. No significant excess above the Standard Model expectation is observed. Limits are set on supersymmetric particle masses for various supersymmetric models. Depending on the model, the search excludes gluino masses up to 1.32 TeV and squark masses up to 840 GeV. Limits are also set on the parameters of a minimal universal extra dimension model, excluding a compactification radius of 1/R c = 950 GeV for a cut-off scale times radius (ΛR c) of approximately 30

Measurement of the cross-section and charge asymmetry of WW bosons produced in proton-proton collisions at s=8\sqrt{s}=8 TeV with the ATLAS detector

This paper presents measurements of the $W^+ \rightarrow \mu^+\nu$ and $W^- \rightarrow \mu^-\nu$ cross-sections and the associated charge asymmetry as a function of the absolute pseudorapidity of the decay muon. The data were collected in proton--proton collisions at a centre-of-mass energy of 8 TeV with the ATLAS experiment at the LHC and correspond to a total integrated luminosity of 20.2~\mbox{fb^{-1}}. The precision of the cross-section measurements varies between 0.8% to 1.5% as a function of the pseudorapidity, excluding the 1.9% uncertainty on the integrated luminosity. The charge asymmetry is measured with an uncertainty between 0.002 and 0.003. The results are compared with predictions based on next-to-next-to-leading-order calculations with various parton distribution functions and have the sensitivity to discriminate between them.Comment: 38 pages in total, author list starting page 22, 5 figures, 4 tables, submitted to EPJC. All figures including auxiliary figures are available at https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/STDM-2017-13