Nonnegative Trigonometric Sums

AbstractWe obtain estimates for ∑|k|≤N|ck|2 and ∑|k|≤N|ck|4, when ∑|k|≤Nckeitkx≥0, t0=0, and c0=1. It is shown that∑k=−NN|ck|4≤M/b+1and∑k=−NN|ck|2≤(2N+1)(M/b+1),where M=max|tk| and b=min{|tj|:j≠0}. When the cks are known to be nonnegative, the inequality∑k=−NN|ck|2≤M/b+1is established

Global Analysis with SNO: Toward the Solution of the Solar Neutrino Problem

We perform a global analysis of the latest solar neutrino data including the SNO result on the CC-event rate. This result further favors the LMA solution of the solar neutrino problem. The best fit values of parameters we find are: \Delta m^2 = (4.8 - 5.0)10^{-5} eV^2, tan^2 \theta = 0.35 - 0.38, f_B = 1.08 - 1.12, and f_{hep} = 1 - 4. With respect to this best fit the LOW solution is accepted at 90% C.L.. The Vacuum oscillation solution with \Delta m^2 = 1.4 10^{-10} eV^2, gives good fit of the data provided that the boron neutrino flux is substantially smaller than the SSM flux (f_B \sim 0.5). The SMA solution is accepted only at 3\sigma level. We find that vacuum oscillations to sterile neutrino, VAC(sterile), with f_B \sim 0.5 also give rather good global fit of the data. All other sterile solutions are strongly disfavored. We check the quality of the fit by constructing the pull-off diagrams of observables. Predictions for the day-night asymmetry, spectrum distortion and NC/CC ratio at SNO are calculated. In the best fit points of the global solutions we find: A_{DN}^{CC} \approx (7 - 8)% for LMA, \sim 3% for LOW, and (2 - 3)% for SMA. It will be difficult to see the distortion of the spectrum expected for LMA as well as LOW solutions. However, future SNO spectral data can significantly affect the VAC and SMA solutions. We also calculate expectations for the BOREXINO rate.Comment: 35 pages, latex, 9 figures; results of analysis slightly changed due to different treatment of the hep neutrino flux; predictions for NC/CC ratio and Borexino rate adde

High Energy Neutrino Signals of Four Neutrino Mixing

We evaluate the upward shower and muon event rates for two characteristic four neutrino mixing models for extragalactic neutrinos, as well as for the atmospheric neutrinos, with energy thresholds of 1 TeV, 10 TeV and 100 TeV. We show that by comparing the shower to muon event rates, one can distinguish between oscillation and no-oscillation models. By measuring shower and muon event rates for energy thresholds of 10 TeV and 100 TeV, and by considering their ratio, it is possible to use extragalactic neutrino sources to determine the type of four-flavor mixing pattern. We find that one to ten years of data taking with kilometer-size detector has a very good chance of providing valuable information about the physics beyond the Standard Model.Comment: version accepted for publication in Phys. Rev.

Angular momenta creation in relativistic electron-positron plasma

Creation of angular momentum in a relativistic electron-positron plasma is explored. It is shown that a chain of angular momentum carrying vortices is a robust asymptotic state sustained by the generalized nonlinear Schrodinger equation characteristic to the system. The results may suggest a possible electromagnetic origin of angular momenta when it is applied to the MeV epoch of the early Universe.Comment: 20 pages, 6 figure

Saturn's icy satellites and rings investigated by Cassini - VIMS. III. Radial compositional variability

In the last few years Cassini-VIMS, the Visible and Infared Mapping Spectrometer, returned to us a comprehensive view of the Saturn's icy satellites and rings. After having analyzed the satellites' spectral properties (Filacchione et al. (2007a)) and their distribution across the satellites' hemispheres (Filacchione et al. (2010)), we proceed in this paper to investigate the radial variability of icy satellites (principal and minor) and main rings average spectral properties. This analysis is done by using 2,264 disk-integrated observations of the satellites and a 12x700 pixels-wide rings radial mosaic acquired with a spatial resolution of about 125 km/pixel. The comparative analysis of these data allows us to retrieve the amount of both water ice and red contaminant materials distributed across Saturn's system and the typical surface regolith grain sizes. These measurements highlight very striking differences in the population here analyzed, which vary from the almost uncontaminated and water ice-rich surfaces of Enceladus and Calypso to the metal/organic-rich and red surfaces of Iapetus' leading hemisphere and Phoebe. Rings spectra appear more red than the icy satellites in the visible range but show more intense 1.5-2.0 micron band depths. The correlations among spectral slopes, band depths, visual albedo and phase permit us to cluster the saturnian population in different spectral classes which are detected not only among the principal satellites and rings but among co-orbital minor moons as well. Finally, we have applied Hapke's theory to retrieve the best spectral fits to Saturn's inner regular satellites using the same methodology applied previously for Rhea data discussed in Ciarniello et al. (2011).Comment: 44 pages, 27 figures, 7 tables. Submitted to Icaru

Dark Energy and Neutrino CPT Violation

In this paper we study the dynamical CPT violation in the neutrino sector induced by the dark energy of the Universe. Specifically we consider a dark energy model where the dark energy scalar derivatively interacts with the right-handed neutrinos. This type of derivative coupling leads to a cosmological CPT violation during the evolution of the background field of the dark energy. We calculate the induced CPT violation of left-handed neutrinos and find the CPT violation produced in this way is consistent with the present experimental limit and sensitive to the future neutrino oscillation experiments, such as the neutrino factory.Comment: 10 pages, 2 figures. Typos corrected and references added. To be published in EPJ

Vortex merger near a topographic slope in a homogeneous rotating fluid

This work is a contribution to the PHYSINDIEN research program. It was supported by CNRS-RFBR contract PRC 1069/16-55-150001.The effect of a bottom slope on the merger of two identical Rankine vortices is investigated in a two dimensional, quasi-geostrophic, incompressible fluid. When two cyclones initially lie parallel to the slope, and more than two vortex diameters away from the slope, the critical merger distance is unchanged. When the cyclones are closer to the slope, they can merge at larger distances, but they lose more mass into filaments, thus weakening the efficiency of merger. Several effects account for this: the topographic Rossby wave advects the cyclones, reduces their mutual distance and deforms them. This along shelf wave breaks into filaments and into secondary vortices which shear out the initial cyclones. The global motion of fluid towards the shallow domain and the erosion of the two cyclones are confirmed by the evolution of particles seeded both in the cyclone sand near the topographic slope. The addition of tracer to the flow indicates that diffusion is ballistic at early times. For two anticyclones, merger is also facilitated because one vortex is ejected offshore towards the other, via coupling with a topographic cyclone. Again two anticyclones can merge at large distance but they are eroded in the process. Finally, for taller topographies, the critical merger distance is again increased and the topographic influence can scatter or completely erode one of the two initial cyclones. Conclusions are drawn on possible improvements of the model configuration for an application to the ocean.PostprintPeer reviewe

Clustering of dark matter tracers: generalizing bias for the coming era of precision LSS

On very large scales, density fluctuations in the Universe are small, suggesting a perturbative model for large-scale clustering of galaxies (or other dark matter tracers), in which the galaxy density is written as a Taylor series in the local mass density, delta, with the unknown coefficients in the series treated as free "bias" parameters. We extend this model to include dependence of the galaxy density on the local values of nabla_i nabla_j phi and nabla_i v_j, where phi is the potential and v is the peculiar velocity. We show that only two new free parameters are needed to model the power spectrum and bispectrum up to 4th order in the initial density perturbations, once symmetry considerations and equivalences between possible terms are accounted for. One of the new parameters is a bias multiplying s_ij s_ji, where s_ij=[nabla_i nabla_j \nabla^-2 - 1/3 delta^K_ij] delta. The other multiplies s_ij t_ji, where t_ij=[nabla_i nabla_j nabla^-2 - 1/3 delta^K_ij](theta-delta), with theta=-(a H dlnD/dlna)^-1 nabla_i v_i. (There are other, observationally equivalent, ways to write the two terms, e.g., using theta-delta instead of s_ij s_ji.) We show how short-range (non-gravitational) non-locality can be included through a controlled series of higher derivative terms, starting with R^2 nabla^2 delta, where R is the scale of non-locality (this term will be a small correction as long as k^2 R^2 is small, where k is the observed wavenumber). We suggest that there will be much more information in future huge redshift surveys in the range of scales where beyond-linear perturbation theory is both necessary and sufficient than in the fully linear regime.Comment: 24 pg., 5 fi

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 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

Jet size dependence of single jet suppression in lead-lead collisions at sqrt(s(NN)) = 2.76 TeV with the ATLAS detector at the LHC

Measurements of inclusive jet suppression in heavy ion collisions at the LHC provide direct sensitivity to the physics of jet quenching. In a sample of lead-lead collisions at sqrt(s) = 2.76 TeV corresponding to an integrated luminosity of approximately 7 inverse microbarns, ATLAS has measured jets with a calorimeter over the pseudorapidity interval |eta| < 2.1 and over the transverse momentum range 38 < pT < 210 GeV. Jets were reconstructed using the anti-kt algorithm with values for the distance parameter that determines the nominal jet radius of R = 0.2, 0.3, 0.4 and 0.5. The centrality dependence of the jet yield is characterized by the jet "central-to-peripheral ratio," Rcp. Jet production is found to be suppressed by approximately a factor of two in the 10% most central collisions relative to peripheral collisions. Rcp varies smoothly with centrality as characterized by the number of participating nucleons. The observed suppression is only weakly dependent on jet radius and transverse momentum. These results provide the first direct measurement of inclusive jet suppression in heavy ion collisions and complement previous measurements of dijet transverse energy imbalance at the LHC.Comment: 15 pages plus author list (30 pages total), 8 figures, 2 tables, submitted to Physics Letters B. All figures including auxiliary figures are available at http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/HION-2011-02