J/ψJ/\psi production in Au+Au/Cu+Cu collisions at sNN\sqrt{s}_{NN}=200 GeV and the threshold model

Using the QGP motivated threshold model, where all the $J/\psi$'s are suppressed above a threshold density, we have analyzed the preliminary PHENIX data on the centrality dependence of nuclear modification factor for $J/\psi$'s in Cu+Cu and in Au+Au collisions, at RHIC energy, $\sqrt{s}_{NN}$=200 GeV. Centrality dependence of $J/\psi$ suppression in Au+Au collisions are well explained in the model for threshold densities in ranges of 3.6-3.7 $fm^{-2}$. $J/\psi$ suppression in Cu+Cu collisions on the other hand are not explained in the model.Comment: 6 pages, 5 figure

Conical flow due to partonic jets in central Au+Au collisions

In jet quenching, a hard QCD parton, before fragmenting into a jet of hadrons, deposits a fraction of its energy in the medium, leading to suppressed production of high-$p_T$ hadrons. The process can generate shock waves. We study the distortion of Mach shock waves due to jet quenching in central Au+Au collisions and its effect on particle production. Finite fluid velocity and inhomogeneity of the medium can distort the Mach shock front significantly such that the inside shock front disappear and the outside shock front is opened up. We also show that the STAR data on azimuthal distribution of background subtracted secondaries, associated with high $p_T$ trigger, are reasonably well explained by the excess pions produced due to partonic energy loss.Comment: 4 pages, 4 figure

Transverse energy distributions and J/ψJ/\psi production in Pb+Pb collisions

We have analyzed the latest NA50 data on transverse energy distributions and $J/\psi$ suppression in Pb+Pb collisions. The transverse energy distribution was analysed in the geometric model of AA collisions. In the geometric model, fluctuations in the number of NN collisions at fixed impact parameter are taken into account. Analysis suggests that in Pb+Pb collisions, individual NN collisions produces less $$, than in other AA collisions. The nucleons are more transparent in Pb+Pb collisions. The transverse energy dependence of the $J/\psi$ suppression was obtained following the model of Blaizot et al, where charmonium suppression is assumed to be 100% effective above a threshold density. With fluctuations in number of NN collisions taken into account, good fit to the data is obtained, with a single parameter, the threshold density.Comment: Revised version with better E_T fit. 4 pages, 2 figure

Effects of jet quenching on the hydrodynamical evolution of quark-gluon plasma

We study the effects of jet quenching on the hydrodynamical evolution of the quark-gluon plasma (QGP) fluid created in a heavy-ion collision. In jet quenching, a hard QCD parton, before fragmenting into a jet of hadrons, deposits a fraction of its energy in the medium, leading to suppressed production of high-pT hadrons. Assuming that the deposited energy quickly thermalizes, we simulate the subsequent hydrodynamic evolution of the QGP fluid. For partons moving at supersonic speed, v_p > c_s, and sufficiently large energy loss, a shock wave forms leading to conical flow [1]. The PHENIX Collaboration recently suggested that observed structures in the azimuthal angle distribution [2] might be caused by conical flow. We show here that conical flow produces different angular structures than predicted in [1] and that, for phenomenologically acceptable values of parton energy loss, conical flow effects are too weak to explain the structures seen by PHENIX [2].Comment: 4 pages, 3 figures. Last figure changed, now showing angular distribution of pions instead of photons. Added comments on "lost jets" and pT-dependence of angular correlation

Differentially Private Model Selection with Penalized and Constrained Likelihood

In statistical disclosure control, the goal of data analysis is twofold: The released information must provide accurate and useful statistics about the underlying population of interest, while minimizing the potential for an individual record to be identified. In recent years, the notion of differential privacy has received much attention in theoretical computer science, machine learning, and statistics. It provides a rigorous and strong notion of protection for individuals' sensitive information. A fundamental question is how to incorporate differential privacy into traditional statistical inference procedures. In this paper we study model selection in multivariate linear regression under the constraint of differential privacy. We show that model selection procedures based on penalized least squares or likelihood can be made differentially private by a combination of regularization and randomization, and propose two algorithms to do so. We show that our private procedures are consistent under essentially the same conditions as the corresponding non-private procedures. We also find that under differential privacy, the procedure becomes more sensitive to the tuning parameters. We illustrate and evaluate our method using simulation studies and two real data examples

Learning Arbitrary Statistical Mixtures of Discrete Distributions

We study the problem of learning from unlabeled samples very general statistical mixture models on large finite sets. Specifically, the model to be learned, $\vartheta$, is a probability distribution over probability distributions $p$, where each such $p$ is a probability distribution over $[n] = \{1,2,\dots,n\}$. When we sample from $\vartheta$, we do not observe $p$ directly, but only indirectly and in very noisy fashion, by sampling from $[n]$ repeatedly, independently $K$ times from the distribution $p$. The problem is to infer $\vartheta$ to high accuracy in transportation (earthmover) distance. We give the first efficient algorithms for learning this mixture model without making any restricting assumptions on the structure of the distribution $\vartheta$. We bound the quality of the solution as a function of the size of the samples $K$ and the number of samples used. Our model and results have applications to a variety of unsupervised learning scenarios, including learning topic models and collaborative filtering.Comment: 23 pages. Preliminary version in the Proceeding of the 47th ACM Symposium on the Theory of Computing (STOC15

J/ψJ/\psi production in Au+Au collisions at RHIC and the nuclear absorption

It is shown that a QCD based nuclear absorption model, with few parameters fixed to reproduce experimental $J/\psi$ yield in 200 GeV pp/pA and 450 GeV pA collisions can explain the preliminary PHENIX data on the centrality dependence of $J/\psi$ suppression in Cu+Cu collisions at RHIC energy, $\sqrt{s_{NN}}$=200 GeV. However, the model does not give satisfactory description to the preliminary PHENIX data on the centrality dependence of $J/\psi$ suppression in Au+Au collisions. The analysis suggest that in Au+Au collisions, $J/\psi$ are suppressed in a medium unlike the medium produced in SPS energy nuclear collisions or in RHIC energy Cu+Cu collisions.Comment: Revised version, published in Phys. Rev. C 74(2006)044907. PHENIX preliminary data on the centrality dependence of nuclear modification factor for $J/\psi$ in Cu+Cu and in Au+Au are analysed. 6 pages, 5 figure

Di-jet hadron pair correlation in a hydrodynamical model with a quenching jet

In jet quenching, a hard QCD parton, before fragmenting into a jet of hadrons, deposits a fraction of its energy in the medium, leading to suppressed production of high-$p_T$ hadrons. Assuming that the deposited energy quickly thermalizes, we simulate the subsequent hydrodynamic evolution of the QGP fluid. Hydrodynamic evolution and subsequent particle emission depend on the jet trajectories. Azimuthal distribution of excess $\pi^-$ due to quenching jet, averaged over all the trajectories, reasonably well reproduce the di-hadron correlation as measured by the STAR and PHENIX collaboration in central and in peripheral Au+Au collisions.Comment: 5 pages, 4 figures. Some minor corrections are made in the revised manuscrip

Deconfinement and the Hagedorn Transition in String Theory

Superseded and extended in hep-th/0105110 and hep-th/0208112.Comment: Superseded and extended in hep-th/0105110 and hep-th/020811