Sum rule of the correlation function

We discuss a sum rule satisfied by the correlation function of two particles with small relative momenta. The sum rule, which results from the completeness condition of the quantum states of the two particles, is first derived and then we check how it works in practice. The sum rule is shown to be trivially satisfied by free particle pair, and then there are considered three different systems of interacting particles. We discuss a pair of neutron and proton in the s-wave approximation and the case of the so-called hard spheres with the phase shifts taken into account up to l=4. Finally, the Coulomb system of two charged particles is analyzed.Comment: 18 pages, 18 figures, revised, to appear in Phys. Rev.

Femtoscopy of Pb-Pb and pp collisions at the LHC with the ALICE experiment

We report on the results of femtoscopic analysis of Pb-Pb collisions at sqrt(s_NN)=2.76 TeV and pp collisions at sqrt(s)=0.9, 2.76 and 7 TeV with identical pions and kaons. Detailed femtoscopy studies in heavy-ion collisions at SPS and RHIC have shown that emission region sizes ("HBT radii") decrease with increasing pair transverse momentum k_T, which is understood as a manifestation of the collective behavior of matter. The trend was predicted to persist at the LHC. The data from Pb-Pb collisions confirm the existence of a flowing medium and provide strict constraints on the dynamical models. Similar analysis is carried out for pp collisions for pions and kaons and qualitative similarities to heavy-ion data are seen, especially in collisions producing large number of particles. The observed trends give insight into the soft particle production mechanism in pp collisions. 3D radii were also found to universally scale with event multiplicity in heavy-ion collisions. We extend the range of multiplicities both upwards with the Pb-Pb data and downwards with the pp data to test the scaling in new areas. In particular the high multiplicity pp collisions reach particle densities comparable to the ones measured in peripheral Cu-Cu and Au-Au collisions at RHIC. This allows for the first time to directly compare freeze-out sizes for systems with very different initial states.Comment: 8 pages, 5 figures, Proceedings of the Quark Matter 2011 plenary tal

Study of ππ\pi\pi correlations at LHC and RHIC energies in pppp collisions within the quark-gluon string model

The Quark Gluon String Model (QGSM) reproduces well the global characteristics of the $pp$ collisions at RHIC and LHC, e.g., the pseudorapidity and transverse momenta distributions at different centralities. The main goal of this work is to employ the Monte Carlo QGSM for description of femtoscopic characteristics in $pp$ collisions at RHIC and LHC. The study is concentrated on the low multiplicity and multiplicity averaged events, where no collective effects are expected. The different procedures for fitting the one-dimensional correlation functions of pions are studied and compared with the space-time distributions extracted directly from the model. Particularly, it is shown that the double Gaussian fit reveals the contributions coming separately from resonances and from directly produced particles. The comparison of model results with the experimental data favors decrease of particle formation time with rising collision energy.Comment: 9 pages, 14 figures, 2 table

Sum rule of the correlation function

We derive a sum rule satisfied by the correlation function of two particles with small relative momenta, which results from the completeness condition of the quantum states.Comment: 6 pages, no macro

Deciphering nonfemtoscopic two-pion correlations in p+pp+p collisions with simple analytical models

A simple model of nonfemtoscopic particle correlations in proton-proton collisions is proposed. The model takes into account correlations induced by the conservation laws as well as correlations induced by minijets. It reproduces well the two-pion nonfemtoscopic correlations of like-sign and unlike-sign pions in proton-proton collision events at $\sqrt{s} = 900$ GeV analyzed by the ALICE Collaboration. We also argue that similar nonfemtoscopic correlations can appear in the hydrodynamic picture with event-by-event fluctuating nonsymmetric initial conditions that are typically associated with nonzero higher-order flow harmonics.Comment: 21 pages, 10 figures, misprints correcte

(Strange) Meson Interferometry at RHIC

We make predictions for the kaon interferometry measurements in Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC). A first order phase transition from a thermalized Quark-Gluon-Plasma (QGP) to a gas of hadrons is assumed for the transport calculations. The fraction of kaons that are directly emitted from the phase boundary is considerably enhanced at large transverse momenta K_T ~ 1 GeV/c. In this kinematic region, the sensitivity of the R_out/R_side ratio to the QGP-properties is enlarged. Here, the results of the 1-dimensional correlation analysis are presented. The extracted interferometry radii, depending on $K_T$, are not unusually large and are strongly affected by momentum resolution effects.Comment: 8 pages, 6 figure

Relative space-time asymmetries in pion and nucleon production in non-central nucleus-nucleus collisions at high energies

We propose to use the ratio of the pion-proton correlation functions evaluated under different conditions to study the relative space-time asymmetries in pion and proton emission (pion and nucleon source relative shifts) in high energy heavy ion collision. We address the question of the non-central collisions, where the sources can be shifted spatially both in the longitudinal and in the transverse directions in the reaction plane. We use the RQMD event generator to illustrate the effect and the technique.Comment: RevTex, 4 pages, 3 figures included as eps file

A Fast Hadron Freeze-out Generator

We have developed a fast Monte Carlo procedure of hadron generation allowing one to study and analyze various observables for stable hadrons and hadron resonances produced in ultra-relativistic heavy ion collisions. Particle multiplicities are determined based on the concept of chemical freeze-out. Particles can be generated on the chemical or thermal freeze-out hypersurface represented by a parameterization or a numerical solution of relativistic hydrodynamics with given initial conditions and equation of state. Besides standard space-like sectors associated with the volume decay, the hypersurface may also include non-space-like sectors related to the emission from the surface of expanding system. For comparison with other models and experimental data we demonstrate the results based on the standard parameterizations of the hadron freeze-out hypersurface and flow velocity profile under the assumption of a common chemical and thermal freeze-out. The C++ generator code is written under the ROOT framework and is available for public use at http://uhkm.jinr.ru/.Comment: 28 pages,7 figure

HBT search for new states of matter in A+A collisions

A method allowing studies of the hadronic matter at the early evolution stage in A+A collisions is developed. It is based on an interferometry analysis of approximately conserved values such as the averaged phase-space density (APSD) and the specific entropy of thermal pions. The plateau found in the APSD behavior vs collision energy at SPS is associated, apparently, with the deconfinement phase transition at low SPS energies; a saturation of this quantity at the RHIC energies indicates the limiting Hagedorn temperature for hadronic matter. It is shown that if the cubic power of effective temperature of pion transverse spectra grows with energy similarly to the rapidity density (that is roughly consistent with experimental data), then the interferometry volume is inverse proportional to the pion APSD that is about a constant because of limiting Hagedorn temperature. This sheds light on the HBT puzzle.Comment: 23 pages, 8 figures, minor correction

Analysis of nucleus-nucleus collisions at high energies and Random Matrix Theory

We propose a novel statistical approach to the analysis of experimental data obtained in nucleus-nucleus collisions at high energies which borrows from methods developed within the context of Random Matrix Theory. It is applied to the detection of correlations in momentum distributions of emitted particles. We find good agreement between the results obtained in this way and a standard analysis based on the method of effective mass spectra and two-pair correlation function often used in high energy physics. The method introduced here is free from unwanted background contributions.Comment: 11 pages, 10 figure