A sampling algorithm to estimate the effect of fluctuations in particle physics data

Background properties in experimental particle physics are typically estimated using large data sets. However, different events can exhibit different features because of the quantum mechanical nature of the underlying physics processes. While signal and background fractions in a given data set can be evaluated using a maximum likelihood estimator, the shapes of the corresponding distributions are traditionally obtained using high-statistics control samples, which normally neglects the effect of fluctuations. On the other hand, if it was possible to subtract background using templates that take fluctuations into account, this would be expected to improve the resolution of the observables of interest, and to reduce systematics depending on the analysis. This study is an initial step in this direction. We propose a novel algorithm inspired by the Gibbs sampler that makes it possible to estimate the shapes of signal and background probability density functions from a given collection of particles, using control sample templates as initial conditions and refining them to take into account the effect of fluctuations. Results on Monte Carlo data are presented, and the prospects for future development are discussed.Comment: 6 pages, 1 figure. Edited to improve readability in line with the published article. This is based on a condensed version for publication in the Proceedings of the International Conference on Mathematical Modelling in the Physical Sciences, IC-MSQUARE 2012, Budapest, Hungary. A more detailed discussion can be found in the preceding version of this arXiv recor

Search for SUSY in (Leptons +) Jets + E_T^miss final states

We study the observability of the squarks and gluinos in CMS at LHC. Classical E_T^miss + jets final state as well as a number of additional multilepton signatures (0 leptons, 1 lepton, 2 leptons of the same sign, 2 leptons of the opposite sign and 3 leptons) are investigated . The detection of these sparticles relies on the observation of an excess of events over Standard Model background expectations. The study is made in the framework of a minimal SU(5) mSUGRA model as a function of m_0, m_1/2 for 4 sets of model parameters : tan(beta) = 2 or 35 and sign(mu) = +/- 1 and for fixed value of A_0 = 0. The CMS detector response is modelled using CMSJET 4.51 fast MC code (non-GEANT). The results obtained are presented as 5 sigma detection contours in the m_0, m_1/2 planes and with optimized selection cuts in various regions of the parameter space. The result of these investigations is that with integrated luminosity L=10^5 pb^-1 the squark and gluino mass reach is about 2.5 TeV and covers most of the interesting parts of parameter space according to neutralino relic density expectations. The influence of signal and background cross-section uncertainties on the reach contours is estimated. The effect of pile-up on signal and background is also discussed. This effect is found to be insignificant for E_T^miss and single lepton signatures, whilst only a minor deterioration is seen for multilepton final states.Comment: 28 pages, 28 figure

Energy Scaling of Minimum-Bias Tunes

We propose that the flexibility offered by modern event-generator tuning tools allows for more than just obtaining "best fits" to a collection of data. In particular, we argue that the universality of the underlying physics model can be tested by performing several, mutually independent, optimizations of the generator parameters in different physical regions. For regions in which these optimizations return similar and self-consistent parameter values, the model can be considered universal. Deviations from this behavior can be associated with a breakdown of the modeling, with the nature of the deviations giving clues as to the nature of the breakdown. We apply this procedure to study the energy scaling of a class of minimum-bias models based on multiple parton interactions (MPI) and pT-ordered showers, implemented in the Pythia 6.4 generator. We find that a parameter controlling the strength of color reconnections in the final state is the most important source of non-universality in this model.Comment: 17 pages, 3 figures, 4 table

Spectral functions of the half-filled 1D Hubbard chain within the exchange-correlation potential formalism

The spectral functions of the one-band half-filled 1D Hubbard chain are calculated using the exchange-correlation potential formalism developed recently. The exchange-correlation potential is adopted from the exact potential derived from the Hubbard dimer. Within an approximation in which the full Green function is replaced by a non-interacting one, the spectral functions can be calculated analytically. Despite the simplicity of the approximation, the resulting spectra are in favorable agreement with the more accurate results obtained from the dynamic density-matrix renormalization group method. In particular, the calculated band gap as a function of $U$ is in close agreement with the exact gap obtained from the Bethe ansatz. In addition, the formal general solution to the equation of motion of the Green function is presented and the difference between the traditional self-energy approach and the exchange-correlation potential formalism is also discussed and elaborated. A simplified Holstein Hamiltonian is considered to further illustrate the general form of the exchange-correlation potential.Comment: 10 pages, 7 figure

Resolvent estimates for normally hyperbolic trapped sets

We give pole free strips and estimates for resolvents of semiclassical operators which, on the level of the classical flow, have normally hyperbolic smooth trapped sets of codimension two in phase space. Such trapped sets are structurally stable and our motivation comes partly from considering the wave equation for Kerr black holes and their perturbations, whose trapped sets have precisely this structure. We give applications including local smoothing effects with epsilon derivative loss for the Schr\"odinger propagator as well as local energy decay results for the wave equation.Comment: Further changes to erratum correcting small problems with Section 3.5 and Lemma 4.1; this now also corrects hypotheses, explicitly requiring trapped set to be symplectic. Erratum follows references in this versio

Upper bound on the density of Ruelle resonances for Anosov flows

Using a semiclassical approach we show that the spectrum of a smooth Anosov vector field V on a compact manifold is discrete (in suitable anisotropic Sobolev spaces) and then we provide an upper bound for the density of eigenvalues of the operator (-i)V, called Ruelle resonances, close to the real axis and for large real parts.Comment: 57 page

On the Usefulness of Modulation Spaces in Deformation Quantization

We discuss the relevance to deformation quantization of Feichtinger's modulation spaces, especially of the weighted Sjoestrand classes. These function spaces are good classes of symbols of pseudo-differential operators (observables). They have a widespread use in time-frequency analysis and related topics, but are not very well-known in physics. It turns out that they are particularly well adapted to the study of the Moyal star-product and of the star-exponential.Comment: Submitte

Two- and three-particle azimuthal correlations of high-pt charged hadrons in Pb-Au collisions at 158A GeV/c

Azimuthal correlations of hadrons with high transverse momenta serve as a measure to study the energy loss and the fragmentation pattern of jets emerging from hard parton-parton interactions in heavy ion collisions. Preliminary results from the CERES experiment on two- and three-particle correlations in central Pb-Au collisions are presented. A strongly non-Gaussian shape on the away-side of the two-particle correlation function is observed, indicating significant interactions of the emerging partons with the medium. Mechanisms like deflection of the initial partons or the evolution of a mach cone in the medium can lead to similar modifications of the jet structure on the away-side. An analysis based on three-particle correlations is presented which helps to shed light on the origin of the observed away-side pattern.Comment: 4 pages, 2 figures, contribution to the Quark Matter conference 200

Color separate singlets in e+e−e^+e^- annihilation

We use the method of color effective Hamiltonian to study the properties of states in which a gluonic subsystem forms a color singlet, and we will study the possibility that such a subsystem hadronizes as a separate unit. A parton system can normally be subdivided into singlet subsystems in many different ways, and one problem arises from the fact that the corresponding states are not orthogonal. We show that if only contributions of order $1/N_c^2$ are included, the problem is greatly simplified. Only a very limited number of states are possible, and we present an orthogonalization procedure for these states. The result is simple and intuitive and could give an estimate of the possibility to produce color separated gluonic subsystems, if no dynamical effects are important. We also study with a simple MC the possibility that configurations which correspond to "short strings" are dynamically favored. The advantage of our approach over more elaborate models is its simplicity, which makes it easier to estimate color reconnection effects in reactions which are more complicated than the relatively simple $e^+e^-$ annihilation.Comment: Revtex, 24 pages, 7 figures; Compared to the previous version, 1 new figure is added and Monte-Carlo results are re-analyzed, as suggested by the referee; To appear in Phys. Rev.

Spectral projections and resolvent bounds for partially elliptic quadratic differential operators

We study resolvents and spectral projections for quadratic differential operators under an assumption of partial ellipticity. We establish exponential-type resolvent bounds for these operators, including Kramers-Fokker-Planck operators with quadratic potentials. For the norms of spectral projections for these operators, we obtain complete asymptotic expansions in dimension one, and for arbitrary dimension, we obtain exponential upper bounds and the rate of exponential growth in a generic situation. We furthermore obtain a complete characterization of those operators with orthogonal spectral projections onto the ground state.Comment: 60 pages, 3 figures. J. Pseudo-Differ. Oper. Appl., to appear. Revised according to referee report, including minor changes to Corollary 1.8. The final publication will be available at link.springer.co