Angular Dependence of the Radiative Gluon Spectrum and the Energy Loss of Hard Jets in QCD Media

The induced momentum spectrum of soft gluons radiated from a high energy quark propagating through a QCD medium is derived in the BDMPS formalism. A calorimetric measurement for the medium dependent energy lost by a jet with opening angle $\theta_{{\rm cone}}$ is proposed.The fraction of this energy loss with respect to the integrated one appears to be the relevant observable.It exhibits a universal behaviour in terms of the variable $\theta^2_{{\rm cone}} L^3 \hat q$ where $L$ is the size of the medium and $\hat q$ the transport coefficient. Phenomenological implications for the differences between cold and hot QCD matter are discussed.Comment: 13 pages and 7 figures, RevTe

Parton Energy Loss with Detailed Balance

Stimulated gluon emission and thermal absorption in addition to induced radiation are considered for an energetic parton propagating inside a quark- gluon plasma. In the presence of thermal gluons, stimulated emission reduces while absorption increases the parton's energy. The net effect is a reduction of the parton energy loss. Though decreasing asymptotically as $T/E$ with the parton energy, the relative reduction is found to be important for intermediate energies. The modified energy dependence of the energy loss will affect the shape of suppression of moderately high $p_T$ hadrons due to jet quenching in high-energy heavy-ion collisions.Comment: 4 pages in RevTex with 1 postscript figure. Some typos are corrected and new comments are adde

Where is the jet quenching in Pb+Pb collisions at 158 AGeV?

Because of the rapidly falling particle spectrum at large $p_T$ from jet fragmentation at the CERN SPS energy, the high-$p_T$ hadron distribution should be highly sensitive to parton energy loss inside a dense medium as predicted by recent perturbative QCD (pQCD) studies. A careful analysis of recent data from CERN SPS experiments via pQCD calculation shows little evidence of energy loss. This implies that either the life-time of the dense partonic matter is very short or one has to re-think about the problem of parton energy loss in dense matter. The hadronic matter does not seem to cause jet quenching in $Pb+Pb$ collisions at the CERN SPS. High-$p_T$ two particle correlation in the azimuthal angle is proposed to further clarify this issue.Comment: 4 pages with 2 ps figures. Minors changes are made in the text with updated references. Revised version to appear in Phys. Rev. Letter

Exact solutions to the four Goldstone modes around a dark soliton of the nonlinear Schroedinger equation

This article is concerned with the linearisation around a dark soliton solution of the nonlinear Schr\"odinger equation. Crucially, we present analytic expressions for the four linearly-independent zero eigenvalue solutions (also known as Goldstone modes) to the linearised problem. These solutions are then used to construct a Greens matrix which gives the first-order spatial response due to some perturbation. Finally we apply this Greens matrix to find the correction to the dark-soliton wavefunction of a Bose-Einstein condensate in the presence of fluctuations.Comment: 14 pages, 3 figures, submitted to Journal of Physics

One-Dimensional Integrable Spinor BECs Mapped to Matrix Nonlinear Schr\"odinger Equation and Solution of Bogoliubov Equation in These Systems

In this short note, we construct mappings from one-dimensional integrable spinor BECs to matrix nonlinear Schr\"odinger equation, and solve the Bogoliubov equation of these systems. A map of spin-$n$ BEC is constructed from the $2^n$-dimensional spinor representation of irreducible tensor operators of $so(2n+1)$. Solutions of Bogoliubov equation are obtained with the aid of the theory of squared Jost functions.Comment: 2.1 pages, JPSJ shortnote style. Published version. Note and reference adde

Systematic Study of High p_T Hadron Spectra in pp, pA and AA Collisions from SPS to RHIC Energies

High-$p_T$ particle spectra in $p+p$ ($\bar p + p$), $p+A$ and $A+B$ collisions are calculated within a QCD parton model in which intrinsic transverse momentum, its broadening due to initial multiple parton scattering, and jet quenching due to parton energy loss inside a dense medium are included phenomenologically. The intrinsic $k_T$ and its broadening in $p+A$ and $A+B$ collisions due to initial multiple parton scattering are found to be very important at low energies ($\sqrt{s}<50$ GeV). Comparisons with $S+S$, $S+Au$ and $Pb+Pb$ data with different centrality cuts show that the differential cross sections of large transverse momentum pion production ($p_T>1$ GeV/$c$) in $A+B$ collisions scale very well with the number of binary nucleon-nucleon collisions (modulo effects of multiple initial scattering). This indicates that semi-hard parton scattering is the dominant particle production mechanism underlying the hadron spectra at moderate $p_T \stackrel{>}{\sim} 1$ GeV/$c$. However, there is no evidence of jet quenching or parton energy loss. Within the parton model, one can exclude an effective parton energy loss $dE_q/dx>0.01$ GeV/fm and a mean free path $\lambda_q< 7$ fm from the experimental data of $A+B$ collisions at the SPS energies. Predictions for high $p_T$ particle spectra in $p+A$ and $A+A$ collisions with and without jet quenching at the RHIC energy are also given. Uncertainties due to initial multiple scattering and nuclear shadowing of parton distributions are also discussed.Comment: 13 pages in RevTex with 14 figures, the final published version (with some typos corrected

On the Caudrey-Beals-Coifman System and the Gauge Group Action

The generalized Zakharov-Shabat systems with complex-valued Cartan elements and the systems studied by Caudrey, Beals and Coifman (CBC systems) and their gauge equivalent are studies. This includes: the properties of fundamental analytical solutions (FAS) for the gauge-equivalent to CBC systems and the minimal set of scattering data; the description of the class of nonlinear evolutionary equations solvable by the inverse scattering method and the recursion operator, related to such systems; the hierarchies of Hamiltonian structures.Comment: 12 pages, no figures, contribution to the NEEDS 2007 proceedings (Submitted to J. Nonlin. Math. Phys.

Generalized r-matrix structure and algebro-geometric solution for integrable systems

The purpose of this paper is to construct a generalized r-matrix structure of finite dimensional systems and an approach to obtain the algebro-geometric solutions of integrable nonlinear evolution equations (NLEEs). Our starting point is a generalized Lax matrix instead of usual Lax pair. The generalized r-matrix structure and Hamiltonian functions are presented on the basis of fundamental Poisson bracket. It can be clearly seen that various nonlinear constrained (c-) and restricted (r-) systems, such as the c-AKNS, c-MKdV, c-Toda, r-Toda, c-Levi, etc, are derived from the reduction of this structure. All these nonlinear systems have {\it r}-matrices, and are completely integrable in Liouville's sense. Furthermore, our generalized structure is developed to become an approach to obtain the algebro-geometric solutions of integrable NLEEs. Finally, the two typical examples are considered to illustrate this approach: the infinite or periodic Toda lattice equation and the AKNS equation with the condition of decay at infinity or periodic boundary.Comment: 41 pages, 0 figure

High pTp_T Azimuthal Asymmetry in Non-central A+A at RHIC

The high $p_{\rm T}>3$ GeV azimuthal asymmetry, $v_2(p_{\rm T})$, in non-central nuclear collisions at RHIC is shown to be a sensitive measure of the initial parton density distribution of the produced quark-gluon plasma. A generalization of the Gyulassy-Levai-Vitev (GLV) non-abelian energy loss formalism including Bjorken 1+1D expansion as well as important kinematic constraints is used.Comment: 4 pages, Revtex, bbox.sty, 4 eps figures, references added, minor corrections, Phys.Rev.Lett versio

Coupled KdV equations derived from atmospherical dynamics

Some types of coupled Korteweg de-Vries (KdV) equations are derived from an atmospheric dynamical system. In the derivation procedure, an unreasonable $y$-average trick (which is usually adopted in literature) is removed. The derived models are classified via Painlev\'e test. Three types of $\tau$-function solutions and multiple soliton solutions of the models are explicitly given by means of the exact solutions of the usual KdV equation. It is also interesting that for a non-Painlev\'e integrable coupled KdV system there may be multiple soliton solutions.Comment: 19 pages, 2 figure