125071872
Exact solutions of perfect fluid hydrodynamics: Theory and applications in high-energy experiments
Some exact and explicit solutions of the relativistic hydrodynamical equations are reviewed in context of high-energy heavy ion physics. Hydrodynamics is a powerful tool to describe the experimentally observed features (e.g. scaling laws) in the final state of high-energy collisions. Hydrodynamical solutions (both exact, analytic and numerical) can then be used to draw consequences on the initial state or the equation of state of the created matter. These findings can help to reach the ultimate goal of heavy-ion physics, the mapping of the phase structure of the strong interaction. In this paper we discuss exact and phenomenologically relevant solutions of hydrodynamics, and hint at some applications of them. We detail one important application: the estimation of the initial energy density from the observed final state.
119143405
Detailed description of accelerating, simple solutions of relativistic perfect fluid hydrodynamics
In this paper we describe in full details a new family of recently found exact solutions of relativistic, perfect fluid dynamics. With an ansatz that generalizes the well-known Hwa-Bjorken solution we obtain a wide class of new exact, explicit, and simple solutions, which have a remarkable advantage as compared to presently known exact and explicit solutions: they do not lack acceleration. They can be utilized for the description of the evolution of the matter created in high energy heavy ion collisions. Because these solutions are accelerating, they provide a more realistic picture than the well-known Hwa-Bjorken solution, and give more insight into the dynamics of the matter. We exploit this by giving an advanced simple estimation of the initial energy density of the produced matter in high energy collisions, which takes acceleration effects, i.e., the work done by the pressure, and the modified change of the volume elements, into account. We also give an advanced estimation of the life-time of the reaction. Our new solutions can also be used to test numerical hydrodynamical codes reliably. In the end, we also give an exact, 1+1 dimensional, relativistic hydrodynamical solution, where the initial pressure and velocity profile is arbitrary, and we showmore » that this general solution is stable for perturbations.« less
15716297
New exact solutions of relativistic hydrodynamics
A new class of simple and exact solutions of relativistic hydrodynamics is presented, and the consequences are explored in data analysis. The effects of longitudinal work and acceleration are taken into account in an advanced estimate of the initial energy density and the life-time of the reaction.
119105321
New family of exact and rotating solutions of fireball hydrodynamics
A new class of analytic, exact, rotating, self-similar and surprisingly simple solutions of non-relativistic hydrodynamics are presented for a three-dimensionally expanding, spheroidally symmetric fireball. These results generalize earlier, non-rotating solutions for ellipsoidally symmetric fireballs with directional, three-dimensional Hubble flows. The solutions are presented for a general class of equations of state that includes the lattice QCD equations of state and may feature inhomogeneous temperature and corresponding density profiles.
16863322
Multi-boson correlations using wave-packets II
Abstract.
We investigate the analytically solvable pion-laser model, and generalize it to arbitrary multiplicity distributions.
We show that this kind of extension of the model is possible, but less interesting, than the already known one.
30878089
Accelerating solutions of perfect fluid hydrodynamics for initial energy density and life-time measurements in heavy ion collisions
A new class of accelerating, exact, explicit and simple solutions of relativistic hydrodynamics is presented. Since these new solutions yield a finite rapidity distribution, they lead to an advanced estimate of the initial energy density and life-time of high energy heavy ion collisions. Accelerating solutions are also given for spherical expansions in arbitrary number of spatial dimensions.
15038835
From quark gluon plasma to a perfect fluid of quarks and beyond
With high energy heavy ion collisions one tries to create a new forms of matter that is similar to the one present at the birth of our Universe. Recent development on flow pattern, initial energy-density and freeze-out temperature shows that most likely this new form of matter is in a deconfined state, has colored degrees of freedom and is more fluid-like than gas-like. In present paper we calculate estimations on the physical properties of this new-old matter. “We simply do not yet know enough about the physics of elementary particles to be able to calculate the properties of such a melange with any confidence. ...Thus our ignorance of microscopic physics stands as a veil, obscuring our view of the very beginning.”
7896037
Existence and Properties of the $f_0(665)$ State and Chiral Symmetry
On the basis of a simultaneous description of the isoscalar s-wave of $\pi\pi$ scattering (from the threshold up to 1.9 GeV) and of $\pi\pi\to K\bar{K}$ process (from the threshold to $\sim$ 1.4 GeV) in the model-independent approach, it is shown that there exists the $f_0(665)$ state with properies of the $\sigma$-meson, the glueball nature of $f_0(1500)$ is indicated, and the $f_0(1370)$ is assigned mainly to $s{\bar s}$ state. The coupling constants of the observed states with $\pi\pi$ and $K\bar{K}$ systems and scattering lengths $a_0^0(\pi\pi)$ and $a_0^0(K\bar{K})$ are calculated. The existence of the $f_0(665)$ state and the obtained $\pi\pi$-scattering length ($a_0^0\approx 0.27 m_{\pi^+}^{-1}$) seem to suggest the linear realization of chiral symmetry.
121038747
EFFECTIVE CHIRAL LAGRANGIANS, THE QUARK MODEL OF SUPERCONDUCTIVITY TYPE AND THE PROBLEM OF P-A DIAGONALIZATION
The vertices appearing after the inclusion of P-A transitions and a subsequent diagonalization of the chiral Lagrangian are analyzed in the quark model of superconductivity type. These vertices can conditionally be divided into physical and nonphysical ones. It is shown that if the Pauli-Villars regularization is used, the contribution of the latter can be eliminated from the description of the physical processes. This is in full agreement with the experimental data.
14996935
Scalar mesons in a chiral quark model with glueball
Ground-state scalar isoscalar mesons and a scalar glueball are described in a U(3) × U(3) chiral quark model of the Nambu-Jona-Lasinio (NJL) type with’ t Hooft interaction. The latter interaction produces singlet-octet mixing in the scalar and pseudoscalar sectors. The glueball is introduced into the effective meson Lagrangian as a dilaton on the base of scale invariance. The mixing of the glueball with scalar isoscalar quarkonia and amplitudes of their decays into two pseudoscalar mesons are shown to be proportional to current quark masses, vanishing in the chiral limit. Mass spectra of the scalar mesons and the glueball and their main modes of strong decay are described.
121460518
Chiral properties of low-energy matrix elements of local four-quark operators
The chiral properties of low-energy matrix elements of four-quark operators describing the weak vertices in the effective Lagrangian of weak interactions are investigated. A constituent quark diagram technique for the derivation of “soft” pion low-energy theorems is proposed. The technique is applied to the calculation of the⌆-term operator correlator in the low-energy theorem of the penguin-operator matrix elements.