Model independent shape analysis of correlations in 1, 2 or 3 dimensions

A generic, model-independent method for the analysis of the two-particle short-range correlations is presented, that can be utilized to describe e.g. Bose-Einstein (HBT or GGLP), statistical, dynamical or other short-range correlation functions. The method is based on a data-motivated choice for the zero-th order approximation for the shape of the correlation function, and on a systematic determination of the correction terms with the help of complete orthonormal set of functions. The Edgeworth expansion is obtained for approximately Gaussian, the Laguerre expansion for approximately exponential correlation functions. Multi-dimensional expansions are also introduced and discussed.Comment: Latex, 15 pages, uses epsfig.sty elsart.sty, misprints correcte

Simple analytic solution of fireball hydrodynamics

A new family of simple analytic solutions of hydrodynamics is found for non-relativistic, rotationally symmetric fireballs assuming an ideal gas equation of state. The solution features linear flow profile and a non-trivial transverse temperature profile. The radial temperature gradient vanishes only in the collisionless gas limit. The Zimanyi-Bondorf-Garpman solution and the Buda-Lund parameterization of expanding hydrodynamical sources are recovered as special cases. The results are applied to predict new features of proton-proton correlations and spectra data at 1.93 AGeV Ni + Ni reactions.Comment: Latex, Revte

Buda-Lund hydro model for ellipsoidally symmetric fireballs and the elliptic flow at RHIC

The ellipsoidally symmetric extension of Buda-Lund hydrodynamic model is shown here to yield a natural description of the pseudorapidity dependence of the elliptic flow $v_2(\eta)$, as determined recently by the PHOBOS experiment for Au+Au collisions at $\sqrt{s_{NN}} = 130$ and 200 GeV. With the same set of parameters, the Buda-Lund model describes also the transverse momentum dependence of $v_2$ of identified particles at mid-rapidity. The results confirm the indication for quark deconfinement in Au+Au collisions at RHIC, obtained from a successful Buda-Lund hydro model fit to the single particle spectra and two-particle correlation data, as measured by the BRAHMS, PHOBOS, PHENIX and STAR collaborations.Comment: 16 pages, 2 figures, 1 table added, discussion extended and an important misprint in the caption of Fig. 1 is correcte

New analytic solutions of the non-relativistic hydrodynamical equations

New solutions are found for the non-relativistic hydrodynamical equations. These solutions describe expanding matter with a Gaussian density profile. In the simplest case, thermal equilibrium is maintained without any interaction, the energy is conserved, and the process is isentropic. More general solutions are also obtained that describe explosions driven by heat production, or contraction of the matter caused by energy loss.Comment: 6 pages, LaTeX. Submitted to Physics Letters B. Shortened from 9 pages, errors corrected in the "More general solutions" sectio

Scaling properties of spectra in new exact solutions of rotating, multi-component fireball hydrodynamics

We describe fireballs that rehadronize from a perfect fluid of quark matter, characterized by the lattice QCD equation of state, to a chemically frozen, multi-component mixture, that contains various kinds of observable hadrons. For simplicity and clarity, we apply a non-relativistic approximation to describe the kinematics of this expansion. Unexpectedly, we identify a secondary explosion that may characterize fireball hydrodynamics at the QCD critical point. After rehadronization, the multi-component mixture of hadrons keeps on rotating and expanding together, similarly to a single component fluid. After kinetic freeze-out, the effective temperature $T_{i}$ of the single-particle spectra of hadron type $h_i$ is found to be a sum of the kinetic freeze-out temperature $T_f$ (that is independent of the hadron type $h_i$) and a term proportional to the mass $m_i$ of hadron type $h_i$. The coefficient of proportionality to $m_i$ is also found to be independent of the hadron type $h_i$ but be dependent on the radial flow and vorticity of collective dynamics.Comment: 12 pages, 2 figures, 6 tables, invited talk of G. Kasza at the 10th Bolyai-Gauss-Lobachevsky conference, Gy\"ongy\"os, Hungary, Aug. 21-25, 2017. Submitted for a publication to the MDPI journal Univers

First Results of a Detailed Analysis of p+p Elastic Scattering Data from ISR to LHC Energies in the Quark-Diquark Model

First results of a detailed analysis of p+p elastic scattering data are presented from ISR to LHC energies utilizing the quark-diquark model of protons in a form proposed by Bialas and Bzdak. The differential cross-section of elastic proton-proton collisions is analyzed in detailed and systematic manner at small momentum transfers, starting from the energy range of CERN ISR at $\sqrt{s}= 23.5$ GeV, including also recent TOTEM data at the present LHC energies at $\sqrt{s} = 7$ TeV. These studies confirm the picture that the size of protons increases systematically with increasing energies, while the size of the constituent quarks and diquarks remains approximately independent of (or only increases only slightly with) the colliding energy. The detailed analysis indicates correlations between model parameters and also indicates an increasing role of shadowing at LHC energies.Comment: Proceeding from conference material, which was presented by F. Nemes at the Wilhelm and Else Heraeus SummerSchool on Diffractive and Electromagnetic Processes at High Energies, Heidelberg, Germany, September 5-9, 201

Bose-Einstein correlations for Levy stable source distributions

The peak of the two-particle Bose-Einstein correlation functions has a very interesting structure. It is often believed to have a multivariate Gaussian form. We show here that for the class of stable distributions, characterized by the index of stability $0 < \alpha \le 2$, the peak has a stretched exponential shape. The Gaussian form corresponds then to the special case of $\alpha = 2$. We give examples for the Bose-Einstein correlation functions for univariate as well as multivariate stable distributions, and check the model against two-particle correlation data.Comment: 30 pages, 1 figure, an important misprint in former eqs. (37-38) and other minor misprints are corrected, citations update

A 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.Comment: Dedicated to T. Kodama on the occasion of his 70th birthday. 15 pages, no figures. Accepted for publication at Phys. Rev. C. Minor rewritings from previous versio

Simple solutions of fireball hydrodynamics for rotating and expanding triaxial ellipsoids and final state observables

We present a class of analytic solutions of non-relativistic fireball hydrodynamics for a fairly general class of equation of state. The presented solution describes the expansion of a triaxial ellipsoid that rotates around one of the principal axes. We calculate the hadronic final state observables such as single-particle spectra, directed, elliptic and third flows, as well as HBT correlations and corresponding radius parameters, utilizing simple analytic formulas. We call attention to the fact that the final tilt angle of the fireball, an important observable quantity, is not independent on the exact definition of it: one gets different angles from the single-particle spectra and from HBT measurements. Taken together, it is pointed out that these observables may be sufficient for the determination of the magnitude of the rotation of the fireball. We argue that observing this rotation and its dependence on collision energy would reveal the softness of the equation of state. Thus determining the rotation may be a powerful tool for the experimental search for the critical point in the phase diagram of strongly interacting matter.Comment: 17 pages, 12 figure panel