arXiv subjects
Publications and source records attributed to G. Papp.
We study, in a pQCD calculation augmented by nuclear effects, the jet energy loss needed to reproduce the pi^0 spectra in Au+Au collisions at large p_T, measured by PHENIX at RHIC. The transverse width of the parton momentum distributions (intrinsic-k_T) is used phenomenologically to obtain a reliable baseline pp result. Jet quenching is applied to the nuclear spectra (including shadowing and multiscattering) to fit the data.
High-p_T pion and kaon production is studied in relativistic proton-proton, proton-nucleus, and nucleus-nucleus collisions in a wide energy range. Cross sections are calculated based on perturbative QCD, augmented by a phenomenological transverse momentum distribution of partons (``intrinsic k_T''). An energy dependent width of the transverse momentum distribution is extracted from pion and charged hadron production data in proton-proton/proton-antiproton collisions. Effects of multiscattering and shadowing in the strongly interacting medium are taken into account. Enhancement of the transverse momentum width is introduced and parameterized to explain the Cronin effect. In collisions between heavy nuclei, the model over-predicts central pion production cross sections (more significantly at higher energies), hinting at the presence of jet quenching. Predictions are made for proton-nucleus and nucleus-nucleus collisions at RHIC energies.
In ultrarelativistic heavy-ion collisions, in the 2 GeV$<p_\perp<$ 6 GeV transverse momentum region, the soft and semi-hard multiple scattering of the incoming nucleons in the nuclear medium results in the broadening of the expected hadronic (e.g. pion) $p_\perp$ spectra relative to proton-proton ($pp$) collisions. Thus, higher transverse-momentum regions are populated than in $pp$ collisions. In a perturbative QCD based calculation we include the intrinsic transverse momentum ($k_\perp$) of the partons in the nucleon (determined from $pp$ collisions), augmented by the extra broadening obtained via a systematic analysis of proton-nucleus ($pA$) collisions in the energy range 17$<\sqrt{s}<$ 39 AGeV. The original polynomial spectra are modified, and a nearly exponential spectrum appears in the region 2$\lesssim p_\perp\lesssim 3.5$ GeV. At present RHIC energies ($\sqrt{s}=$130 AGeV), the slope of the calculated spectra is reminiscent of that of fluid-dynamical descriptions, but lacks any thermal origin. We determine and discuss the size of the modifications originating in multiple scattering, which lead to this state of affairs.
The predicted quenching of jets in A+A at RHIC energies has been discovered by STAR and PHENIX in preliminary data reported at this conference. We apply the GLV theory of QCD radiative energy loss to estimate the opacity, L/λ_g, of the gluon plasma produced in Au+Au collisions at 130 AGeV. We show that (in contrast to the factor of two Cronin enhancement of π^0 found at the SPS by WA98) the factor of 5-8 suppression of p_T \sim 2-4 GeV π^0 reported by PHENIX can be accounted for with an effective static plasma opacity L/λ_g \approx 3-4.
We suggest that Free Random Variables, represented here by large random matrices with spectral Levy disorder, may be relevant for several problems related to the modeling of financial systems. In particular, we consider a financial covariance matrix composed of asymmetric and free random Levy matrices. We derive an algebraic equation for the resolvent and solve it to extract the spectral density. The free eigenvalue spectrum is in remarkable agreement with the one obtained from the covariance matrix of the SP500 financial market.
In a given market, financial covariances capture the intra-stock correlations and can be used to address statistically the bulk nature of the market as a complex system. We provide a statistical analysis of three SP500 covariances with evidence for raw tail distributions. We study the stability of these tails against reshuffling for the SP500 data and show that the covariance with the strongest tails is robust, with a spectral density in remarkable agreement with random Levy matrix theory. We study the inverse participation ratio for the three covariances. The strong localization observed at both ends of the spectral density is analogous to the localization exhibited in the random Levy matrix ensemble. We discuss two competitive mechanisms responsible for the occurrence of an extensive and delocalized eigenvalue at the edge of the spectrum: (a) the Levy character of the entries of the correlation matrix and (b) a sort of off-diagonal order induced by underlying inter-stock correlations. (b) can be destroyed by reshuffling, while (a) cannot. We show that the stocks with the largest scattering are the least susceptible to correlations, and likely candidates for the localized states. We introduce a simple model for price fluctuations which captures behavior of the SP500 covariances. It may be of importance for assets diversification.
We consider a covariance matrix composed of asymmetric and free random Levy matrices. We use the results of free random variables to derive an algebraic equation for the resolvent and solve it to extract the spectral density. For an appropriate choice of asymmetry and Levy index ($α/2=3/4$) the free eigenvalue spectrum is in remarkable agreement with the one obtained from the covariance matrix of the SP500 financial market. Our results are of interest to a number of stochastic systems with power law noise.
We discuss a Pareto macro-economy (a) in a closed system with fixed total wealth and (b) in an open system with average mean wealth and compare our results to a similar analysis in a super-open system (c) with unbounded wealth. Wealth condensation takes place in the social phase for closed and open economies, while it occurs in the liberal phase for super-open economies. In the first two cases, the condensation is related to a mechanism known from the balls-in-boxes model, while in the last case to the non-integrable tails of the Pareto distribution. For a closed macro-economy in the social phase, we point to the emergence of a ``corruption'' phenomenon: a sizeable fraction of the total wealth is always amassed by a single individual.
Using the theory of free random variables (FRV) and the Coulomb gas analogy, we construct stable random matrix ensembles that are random matrix generalizations of the classical one-dimensional stable Lévy distributions. We show that the resolvents for the corresponding matrices obey transcendental equations in the large size limit. We solve these equations in a number of cases, and show that the eigenvalue distributions exhibit Lévy tails. For the analytically known Lévy measures we explicitly construct the density of states using the method of orthogonal polynomials. We show that the Lévy tail-distributions are characterized by a novel form of microscopic universality.
The diabatic approach to collective nuclear motion is reformulated in the local-density approximation in order to treat the normal modes of a spherical nuclear droplet analytically. In a first application the adiabatic isoscalar modes are studied and results for the eigenvalues of compressional (bulk) and pure surface modes are presented as function of density and temperature inside the droplet, as well as for different mass numbers and for soft and stiff equations of state. We find that the region of bulk instabilities (spinodal regime) is substantially smaller for nuclear droplets than for infinite nuclear matter. For small densities below 30% of normal nuclear matter density and for temperatures below 5 MeV all relevant bulk modes become unstable with the same growth rates. The surface modes have a larger spinodal region, reaching out to densities and temperatures way beyond the spinodal line for bulk instabilities. Essential experimental features of multifragmentation, like fragmentation temperatures and fragment-mass distributions (in particular the power-law behavior) are consistent with the instability properties of an expanding nuclear droplet, and hence with a dynamical fragmentation process within the spinodal regime of bulk and surface modes (spinodal decomposition).
Higher-order pQCD corrections play an important role in the reproduction of data at high transverse momenta in the energy range 20 GeV $ \leq \sqrt{s} \leq 200$ GeV. Recent calculations of photon and pion production in $pp$ collisions yield detailed information on the next-to-leading order contributions. However, the application of these results in proton-nucleus and nucleus-nucleus collisions is not straightforward. The study of nuclear effects requires a simplified understanding of the output of these computations. Here we summarize our analysis of recent calculations, aimed at handling the NLO results by introducing process and energy-dependent $K$ factors.
We compare and discuss the dependence of a polynomial truncation of the effective potential used to solve exact renormalization group flow equation for a model with fermionic interaction (linear sigma model) with a grid solution. The sensitivity of the results on the underlying cutoff function is discussed. We explore the validity of the expansion method for second and first-order phase transitions.
For the linear sigma model with quarks we derive renormalization group flow equations for finite temperature and finite baryon density using the heat kernel cutoff. At zero temperature we evolve the effective potential to the Fermi momentum and compare the solutions of the full evolution equation with those in the mean field approximation. We find a first order phase transition either from a massive constituent quark phase to a mixed phase, where both massive and massless quarks are present, or from a metastable constituent quark phase at low density to a stable massless quark phase at high density. In the latter solution, the formation of droplets of massless quarks is realized even at low density.
The stability of hot expanded nuclear droplets against small bulk and surface oscillations is examined and possible consequences for multifragmentation are discussed.
We establish a general relation between the diagonal correlator of eigenvectors and the spectral Green's function for non-hermitian random-matrix models in the large-N limit. We apply this result to a number of non-hermitian random-matrix models and show that the outcome is in good agreement with numerical results.
An extensive comparison of the recent experimental data published by the FOPI collaboration at GSI with the results of a relativistically covariant formulation of a QMD code is presented. For most of the quantities we find agreement with the experimental results showing that the derived force has a reasonable momentum dependence.
We show that at the critical point of chiral random matrix models, novel scaling laws for the inverse moments of the eigenvalues are expected. We evaluate explicitly the pertinent microscopic spectral density, and found it in agreement with numerical calculations. We suggest that similar sum rules are of relevance to QCD at the critical temperature, and even above if the transition is amenable to a Landau-Ginzburg description.
Using the Gell-Mann-Oakes-Renner (GOR) relation and semi-classical arguments, we show that the bulk quark spectrum in QCD exhibits a variety of regimes including the ergodic one described by random matrix theory. We analyze the quark spectral form-factor in the diffusive and ballistic regime. We suggest that a class of chiral transitions in QCD is possibly of the metal-insulator type, with a universal spectral statistics at the mobility edge.