Correlation femtoscopy of small systems

The basic principles of the correlation femtoscopy, including its correspondence to the Hanbury Brown and Twiss intensity interferometry, are re-examined. The main subject of the paper is an analysis of the correlation femtoscopy when the source size is as small as the order of the uncertainty limit. It is about 1 fm for the current high energy experiments. Then the standard femtoscopy model of random sources is inapplicable. The uncertainty principle leads to the partial indistinguishability and coherence of closely located emitters that affect the observed femtoscopy scales. In thermal systems the role of corresponding coherent length is taken by the thermal de Broglie wavelength that also defines the size of a single emitter. The formalism of partially coherent phases in the amplitudes of closely located individual emitters is used for the quantitative analysis. The general approach is illustrated analytically for the case of the Gaussian approximation for emitting sources. A reduction of the interferometry radii and a suppression of the Bose-Einstein correlation functions for small sources due to the uncertainty principle are found. There is a positive correlation between the source size and the intercept of the correlation function. The peculiarities of the non-femtoscopic correlations caused by minijets and fluctuations of the initial states of the systems formed in $pp$ and $e^+e^-$ collisions are also analyzed. The factorization property for the contributions of femtoscopic and non-femtoscopic correlations into complete correlation function is observed in numerical calculations in a wide range of the model parameters.Comment: 34 pages, 5 figures. In the version 4 some stylistic improvements were made, some misprints were corrected. The results and conclusions are not change

Particle production at energies available at the CERN Large Hadron Collider within evolutionary model

The particle yields and particle number ratios in Pb+Pb collisions at the LHC energy $\sqrt{s_{NN}}=2.76$ TeV are described within the integrated hydrokinetic model (iHKM) at the two different equations of state (EoS) for the quark-gluon matter and the two corresponding hadronization temperatures, $T=165$ MeV and $T=156$ MeV. The role of particle interactions at the final afterburner stage of the collision in the particle production is investigated by means of comparison of the results of full iHKM simulations with those where the annihilation and other inelastic processes (except for resonance decays) are switched off after hadronization/particlization, similarly as in the thermal models. An analysis supports the picture of continuous chemical freeze-out in the sense that the corrections to the sudden chemical freeze-out results, which arise because of the inelastic reactions at the subsequent evolution times, are noticeable and improve the description of particle and number ratios. An important observation is that although the particle number ratios with switched-off inelastic reactions are quite different at different particlization temperatures which are adopted for different equations of state to reproduce experimental data, the complete iHKM calculations bring very close results in both cases.Comment: 12 pages, 4 figure

Quantum canonical ensemble and correlation femtoscopy at fixed multiplicities

Identical particle correlations at fixed multiplicity are considered by means of quantum canonical ensemble of finite systems. We calculate one-particle momentum spectra and two-particle Bose-Einstein correlation functions in the ideal gas by using a recurrence relation for the partition function. Within such a model we investigate the validity of the thermal Wick's theorem and its applicability for decomposition of the two-particle distribution function. The dependence of the Bose-Einstein correlation parameters on the average momentum of the particle pair is also investigated. Specifically, we present the analytical formulas that allow one to estimate the effect of suppressing the correlation functions in a finite canonical system. The results can be used for the femtoscopy analysis of the A+A and p+p collisions with selected (fixed) multiplicity.Comment: 20 pages, 1 figur

On final conditions in high energy heavy ion collisions

Motivated by the recent experimental observations, we discuss the freeze-out properties of the fireball created in central heavy ion collisions. We find that the freeze-out conditions, like temperature, velocity gradient near center of the fireball, are similar for different colliding systems and beam energies. This means that the transverse flow is stronger in the collisions of heavy nuclei than that of the light ones.Comment: 10 pages, 1 figure, 1 tabl

Sudden freeze-out vs continuous emission: duality in hydro-kinetic approach to A+A collisions

The problem of spectra formation in hydrodynamic approach to A+A collisions is discussed. It is analyzed in terms of the two different objects: distribution and emission functions. We show that though the process of particle liberation, described by the emission function, is, usually, continuous in time, the observable spectra can be also expressed by means of the Landau/Cooper-Frye prescription. We argue that such an approximate duality results from some symmetry properties that systems in A+A collisions reach to the end of hydrodynamic evolution and reduction of the collision rate at post hydrodynamic stageComment: 6 pages, talk presented by S.V. Akkelin during the 3rd Budapest Winter School on Heavy Ion Physics, Dec. 8-11, 2003, Budapest, Hungar