In non-central collisions between ultra-relativistic heavy ions, the freeze-out distribution is anisotropic, and its major longitudinal axis may be tilted away from the beam direction. The shape and orientation of this distribution are particularly interesting, as they provide a snapshot of the evolving source and reflect the space-time aspect of anisotropic flow. Experimentally, this information is extracted by measuring pion HBT radii as a function of angle with respect to the reaction plane. Existing formulae relating the oscillations of the radii and the freezeout anisotropy are in principle only valid for Gaussian sources with no collective flow. With a realistic transport model of the collision, which generates flow and non-Gaussian sources, we find that these formulae approximately reflect the anisotropy of the freezeout distribution.
Hanbury-Brown--Twiss interferometry is a technique which yields effective widths (i.e., "HBT radii") of homogeneity regions in the fireballs produced in heavy ion collisions. Because the initial conditions of these collisions are stochastically fluctuating, the measured HBT radii also exhibit variation on an event-by-event basis. However, HBT measurements have, to date, been performed only on an ensemble-averaged basis, due to inherent limitations of finite particle statistics. In this paper, we show that experimental measurements to date are best characterized theoretically as weighted averag…
I compute the first viscous correction to the thermal distribution function. With this correction, I calculate the effect of viscosity on spectra, elliptic flow, and HBT radii. Indicating the breakdown of hydrodynamics, viscous corrections become of order one for $p_{T}\sim 1.5$ GeV. Viscous corrections to HBT radii are particularly large and reduce the outward and longitudinal radii. This reduction is a direct consequence of the reduction in longitudinal pressure.
We calculate two-pion correlation functions at finite rapidities based on a hydrodynamical model which does not assume explicit boost invariance along the collision axis. Extracting the HBT radii through $χ^2$ fits in both Cartesian and Yano-Koonin-Podgoretski\uı parametrizations, we compare them with the experimental results obtained by the PHOBOS. Based on the results, we discuss longitudinal expansion dynamics.
We explore the effects of event-by-event fluctuations of Hanbury Brown-Twiss (HBT) radii and show how they can be observed experimentally. The relation of measured HBT radii extracted from ensemble-averaged correlation functions to the mean of their event-by-event probability distribution is clarified. We propose a method to experimentally determine the mean and variance of this distribution and test it on an ensemble of fluctuating events generated with the viscous hydrodynamic code VISH2+1. Using the same code, the sensitivity of the mean and variance of the HBT radii to the specific QGP she…
We investigate the effect of early chemical freeze-out on hydrodynamic flow and HBT radii at the RHIC energy with a genuinely three dimensional hydrodynamic model. It is found that the property of early chemical freeze out reduces radial flow, elliptic flow, R_out and R_long.
We investigate HBT radii based on the numerical solutions of the hydrodynamical model which are so tuned as to reproduce the recent experimental data at the CERN SPS. Comparing the sizes of freeze-out hypersurface with HBT radii, we discuss dynamical effect of the systematic flow on the apparent HBT radii. Finally we compare HBT radii of the QGP phase transition model with those of the hadron gas model without phase transition.
The expansion of the fireball created in relativistic heavy ion collisions is described using the 3+1D hydrodynamical model. Experimentally observed transverse momentum spectra at different rapdities, elliptic flow and HBT correlations of produced particles can be reproduced. We give estimates of shear viscosity corrections at freeze-out, which we find important only for the elliptic flow coefficient.
Results from the data obtained in the first physics run of the Relativistic Heavy Ion Collider (RHIC) have shown suprisingly large elliptic flow and suprisingly small HBT radii. Attempts to explain both results in a consistant picture have so far been unsuccessful. The present work shows that a thermal model + hadronic rescattering calculation can explain both elliptic flow and HBT results from RHIC. The calculation requires a very early hadronization time of about 1 fm/c after the initial collision of the nuclei.
The Wigner function formalism which relates source size parameters to experimental ``HBT radii'' extracted from two-particle Bose-Einstein correlations is generalized to azimuthally deformed and longitudinally tilted sources. It is explained how this can be used to complement anisotropic flow measurements with relevant space-time information on the source.
The inability of otherwise successful dynamical models to reproduce the ``HBT radii'' extracted from two-particle correlations measured at the Relativistic Heavy Ion Collider (RHIC) is known as the ``RHIC HBT Puzzle.'' Most comparisons between models and experiment exploit the fact that for Gaussian sources the HBT radii agree with certain combinations of the space-time widths of the source which can be directly computed from the emission function, without having to evaluate, at significant expense, the two-particle correlation function. We here study the validity of this approach for realisti…
In this paper we summarize the ellipsoidally symmetric Buda-Lund model's results on HBT radii. We calculate the Bose-Einstein correlation function from the model and derive formulas for the transverse momentum dependence of the correlation radii in the Bertsch-Pratt system of out, side and longitudinal directions. We show a comparison to $\sqrt{s_{\rm NN}}=200 GeV$ RHIC PHENIX two-pion correlation data and make prediction on the same observable for different particles.
We present hydrodynamic predictions for the charged pion HBT radii for a range of initial conditions covering those presumably reached in Pb+Pb collisions at the LHC. We study central (b=0) and semi-central (b=7fm) collisions and show the expected increase of the HBT radii and their azimuthal oscillations. The predicted trends in the oscillation amplitudes reflect a change of the final source shape from out-of-plane to in-plane deformation as the initial entropy density is increased.
We continue the analysis of the preceding talk with a discussion of the elliptic flow and the HBT pion correlation radii. It is shown that the thermal model can be extended to describe these phenomena. The description of the elliptic flow involves an appropriate deformation of the freeze-out hypersurface and flow velocity. The obtained results agree reasonably with the data for soft (< 2 GeV) transverse momenta. For the pionic HBT correlation radii the experimental feature that R_out/R_side ~ 1 is naturally obtained. The reproduction of individual R_side and R_out can be achieved with the incl…
We study the temperature profile, pion spectra and HBT radii in central symmetric and boost-invariant nuclear collisions using a super hybrid model for heavy-ion collisions (SONIC) combining pre-equilibrium flow with viscous hydrodynamics and late-stage hadronic rescatterings. In particular, we simulate Pb+Pb collisions at Sqrt(s)=2.76 TeV, Au+Au, Cu+Cu, Al+Al, and C+C collisions at Sqrt(s)=200 GeV and Au+Au, Cu+Cu collisions at Sqrt(s)=62.4 GeV. We find that SONIC provides a good match to the pion spectra and HBT radii for all collision systems and energies, confirming earlier work that a com…
We describe RHIC pion data in central A+A collisions and make predictions for LHC based on hydro-kinetic model, describing continuous 4D particle emission, and initial conditions taken from Color Glass Condensate (CGC) model.
Identified particle spectra of pions, kaons and (anti)protons, and elliptic flow and azimuthal dependence of Bose-Einstein or HBT correlations of identified pions in sqrt(s_NN) = 200 GeV Au+Au collisions is analyzed simultaneously using an ellipsoidally symmetric generalization of the Buda-Lund hydrodynamical model. The transverse flow is found to be faster in the reaction plane than out of plane, which results in a reaction zone that gets slightly more elongated in-plane than out of plane.
Using several source models, we analyze the transverse momentum dependence of HBT radii in the relativistic heavy-ion collisions. The results indicate that the single-particle space-momentum angle distribution plays an important role in the transverse momentum dependence of HBT radii. In a cylinder source, we use several formulas to describe the transverse momentum dependence of HBT radii and the single-particle space-momentum angle distribution. We also make a numerical connection between them in the transverse plane.
We present a calculation of the elliptic flow and azimuthal dependence of the correlation radii in the ellipsoidally symmetric generalization of the Buda-Lund model. The elliptic flow is shown to depend only on the flow anisotropy while in case of correlation radii both flow and space anisotropy play an important role in determining their azimuthal oscillation. We also outline a simple procedure for determining the parameters of the model from data.
Single particle transverse mass spectra and HBT radii of identical pion and identical kaon are analyzed with a blast-wave parametrization under the assumptions local thermal equilibrium and transverse expansion. Under the assumptions, temperature parameter $T$ and transverse expansion rapidity $ρ$ are sensitive to the shapes of transverse mass $m_\text T$ spectrum and HBT radius $R_\text{s}(K_\text T)$. Negative and positive correlations between $T$ and $ρ$ are observed by fitting $m_\text{T}$ spectrum and HBT radius $R_\text s (K_\text T)$, respectively. For a Monte Carlo simulation using the…
Recent observations of QGP-like phenomena in small collision systems like p+p and p+A collisions have questioned our understanding of the basic paradigms of high energy heavy-ion physics. A brief discussion of these new aspects in small systems which in turn influence our understanding of hard probes like heavy quarks has been provided. Furthermore, a closer observation of the two-particle Hanbury-Brown Twiss (HBT) interferometry measurements provide new insights in our understanding of medium-like phenomena in small systems. An outlook of future goals and measurements is also made.
We analyze the pion femtoscopy correlations in noncentral Au-Au and Pb-Pb collisions. The azimuthally sensitive Hanbury Brown-Twiss (HBT) method is used to extract the interferometry radii depending on the azimuthal angle with respect to the second and third-order event plane. The results are in semiquantitative agreement with the STAR collaboration data on the HBT radii with respect to the second-order reaction plane, with the preliminary PHENIX collaboration data on the HBT radii with respect to the third-order reaction plane in Au-Au collisions at 200GeV, and with the preliminary ALICE coll…
We study the intensity interferometry with lepton pairs for nuclear collisions at RHIC and LHC energies. It is argued that the invariant mass dependence of HBT radii extracted from the correlation functions of dilepton pairs can be used as an efficient tool to scale the size and life time of the quark gluon plasma expected to be formed in nuclear collisions at RHIC and LHC. Quantitatively different magnitudes of HBT radii are obtained at RHIC and LHC indicating stronger radial flow at LHC.
Hydrodynamical models have generally failed to describe interferometry radii measured at RHIC. In order to investigate this ``HBT puzzle'', we carry out a systematic study of HBT radii in ultrarelativistic heavy-ion collisions within a two-dimensional transport model. We compute the transverse radii $R_o$ and $R_s$ as functions of $p_t$ for various values of the Knudsen number, which measures the degree of thermalization in the system. For realistic values of the Knudsen number estimated from $v_2$ data, we obtain $R_o/R_s \simeq 1.2$, much closer to data than standard hydrodynamical results. …
The pseudo-rapidity dependence of the elliptic flow at various excitation energies measured by the PHOBOS Collaboration in Au+Au collisions at RHIC is one of the surprising results that has not been explained before in terms of hydrodynamical models. Here we show that these data are in agreement with theoretical predictions and satisfy the universal scaling relation predicted by the Buda-Lund hydrodynamical model, based on exact solutions of perfect fluid hydrodynamics. We also show a theoretical prediction on the rapidity and transverse momentum scaling of the HBT radii measured in heavy ion …
The effect of initial state momentum-space anisotropy on invariant mass dependence of HBT radii extracted from the leptonpair interferometry is presented here. We have studied the Bose-Einstein Correlation Function (BECF) for two identical virtual photons decaying to leptonpairs at most central collision of LHC energy having fixed transverse momentum of one of the virtual photons ($k_{1T}$= 2 GeV). The {\em free streaming interpolating} model with fixed initial condition has been used for the evolution in anisotropic Quark Gluon Plasma (aQGP) and the relativistic (1+2)d hydrodynamics model wit…
Hanbury Brown--Twiss interferometry (HBT) provides crucial insights into both the space-time structure and the momentum-space evolution of ultrarelativistic nuclear collisions at freeze-out. In particular, the dependence of the HBT radii on the transverse pair momentum $K_T$ and the system charged multiplicity $dN_{\mathrm{ch}}/dη$ may reflect the mechanisms driving collective behavior in small systems. This paper argues that certain features observed in the multiplicity dependence of the HBT radii can be naturally understood if small systems evolve hydrodynamically at high-multiplicity. This …
We present calculations of elliptic flow and azimuthal dependence of correlation radii in the ellipsoidally symmetric generalization of the Buda-Lund hydrodynamic model of hadron production in high-energy nuclear collisions. We compare them to data from RHIC by simultaneous fits to azimuthally integrated invariant spectra of pions, kaons and protons-antiprotons measured by PHENIX in Au+Au reactions at center of mass energy of 200 AGeV. STAR data were used for azimuthally sensitive two-particle correlation function radii and for the transverse momentum dependence of the elliptic flow parameter …
Causal viscous hydrodynamic fits to experimental data for pion and kaon transverse momentum spectra from central Au+Au collisions at \sqrt{s_{NN}}=200 GeV are presented. Starting the hydrodynamic evolution at 1 fm/c and using small values for the relaxation time, reasonable fits up to moderate ratios η/s\simeq 0.4 can be obtained. It is found that a percentage of roughly 50 η/s to 75 η/s of the final meson multiplicity is due to viscous entropy production. Finally, it is shown that with increasing viscosity, the ratio of HBT radii R_{out}/R_{side} approaches and eventually matches the experime…
A systematic study of HBT radii of pions, produced in heavy ion collisions in the intermediate energy regime (SPS), from an integrated (3+1)d Boltzmann+hydrodynamics approach is presented. The calculations in this hybrid approach, incorporating an hydrodynamic stage into the Ultra-relativistic Quantum Molecular Dynamics transport model, allow for a comparison of different equations of state retaining the same initial conditions and final freeze-out. The results are also compared to the pure cascade transport model calculations in the context of the available data. Furthermore, the effect of di…
Through $^{12}$C + $^{197}$Au collisions at $\sqrt{s_{NN}} =$ 200 GeV using a multiphase transport (AMPT) model, the azimuthal angle dependences of the Hanbury Brown-Twiss (HBT) radii relative to the second- and third-order participant plane from $π$-$π$ correlations are discussed. Three initial geometric configurations of $^{12}$C, namely three-$α$-cluster triangle, three-$α$-cluster chain and Woods-Saxon distribution of nucleons, are taken into account, and their effects on the correlations are investigated. The ratio of the third- to the second-order HBT radii $R_{o(s),3}^2/R_{o(s),2}^2$ is…
The transverse momentum spectra, elliptic flow and interferometry radii for Pb-Pb collisions at the LHC are calculated in relativistic viscous hydrodynamics. For Glauber model initial conditions, we find that the data can be described using a small value of shear viscosity eta/s=0.08. The viscosities and the equation of state are the same as used for RHIC energies.
I calculate the first correction to the thermal distribution function of an expanding gas due to shear viscosity. With this modified distribution function I estimate viscous corrections to spectra, elliptic flow, and HBT radii in hydrodynamic simulations of heavy ion collisions using the blast wave model. For reasonable values of the shear viscosity, viscous corrections become of order one when the transverse momentum of the particle is larger than 1.7 GeV. This places a bound on the $p_{T}$ range accessible to hydrodynamics for this observable. Shear corrections to elliptic flow cause $v_{2}(…
The beam energy dependence of correlation lengths (the Hanbury-Brown-Twiss radii) is calculated by using a blast-wave model and the results are comparable with those from RHIC-STAR beam energy scan data as well as the LHC-ALICE measurements. A set of parameter for the blast-wave model as a function of beam energy under study are obtained by fit to the HBT radii at each energy point. The transverse momentum dependence of HBT radii is presented with the extracted parameters for Au + Au collision at $\sqrt{s_{NN}} = $ 200 GeV and for Pb+Pb collisions at 2.76 TeV. From our study one can learn that…
We solve analytically the ellipsoidally expanding fireball hydrodynamics with source terms in the momentum and the energy equations, using the non-relativistic approximation. We find that energy transport from high pt jets of gluons to the medium leads to a transient, exponential inflation of the fireballs created in high energy heavy ion collisions. In this transient, inflatory period, the slopes of the single particle spectra increase, while the HBT radius parameters decrease exponentially with time. This effect is shown to be similar to the development of the homogeneity of our Universe due…
The PHENIX Collaboration has reported third-order harmonic oscillations of the source radius parameters when measuring the Hanbury Brown-Twiss correlation function for charged hadrons relative to the triangular flow angle. We explore possible origins of such third-order oscillations with a simple Gaussian source featuring both a triangular geometric deformation and triangular flow. Third-order oscillations of the HBT radii can arise from a purely geometric triangular deformation superimposed on an azimuthally symmetric radial flow, or from a radially symmetry spatial distribution which expands…
We study the effect of resonance decays on intensity interferometry for heavy ion collisions. Collective expansion of the source leads to a dependence of the two-particle correlation function on the pair momentum K. This opens the possibility to reconstruct the dynamics of the source from the K-dependence of the measured HBT radii. Here we address the question to what extent resonance decays can fake such a flow signal. Within a simple parametrization for the emission function we present a comprehensive analysis of the interplay of flow and resonance decays on the one- and two-particle spectra…
This study is devoted to a detailed numerical testing of the analytical results obtained recently for the $M_t$-scaling of the parameters of the Bose-Einstein correlation functions. Numerical testing of analytical results for the spectrum is also performed, since the geometrical sizes are folded into the momentum distribution in the scaling limiting case. The analytical results are shown to be valid in a wider rapidity-range than thought before.
We study the geometrical features of non-central heavy ion collisions throughout their dynamical evolution from equilibration to thermal freeze-out within a hydrodynamic picture. We discuss resulting observables, in particular the emission angle dependence of the HBT radii and the relation of these oscillations to the geometry at the final stage.
Elliptic flow and HBT are studied for non-central relativistic nuclear collisions. Azimuthal asymmetries show up in both elliptic flow and HBT radii and are calculated in both collisionless and hydrodynamic limits relevant for peripheral and central collisions respectively. Determining the reaction plane and measuring the HBT radii as function of the angle between the reaction plane and the particle momenta can determine the physical quantities as source sizes, deformations, emission times, duration of emission and opacities. Comparison to SPS data and predictions for RHIC and LHC energies are…
Currently, the only known way to obtain experimental information about the space-time structure of a heavy-ion collision is through 2-particle momentum correlations. Azimuthally sensitive HBT interferometry (Hanbury Brown-Twiss intensity interferometry) can complement elliptic flow measurements by constraining the spatial deformation of the source and its time evolution. Performing these measurements on photons allows us to access the fireball evolution at earlier times than with hadrons. Using ideal hydrodynamics to model the space-time evolution of the collision fireball, we explore theoreti…
In this paper, we continue our phenomenological studies of heavy-ion collisions using 3+1d anisotropic hydrodynamics (aHydro). In previous works, we compared quasiparticle aHydro (aHydroQP) with ALICE 2.76 TeV Pb-Pb and RHIC 200 GeV Au-Au collision results. At both energies, the agreement was quite good between aHydroQP and the experimental data for many observables. In this work, we present comparisons of the Hanbury Brown--Twiss (HBT) radii and their ratios determined using pi+ pi+ pairs produced in 200 GeV Au-Au collisions. We first present comparisons with STAR results for the HBT radii an…
The space-time dynamics and pion-HBT radii in central heavy ion-collisions at CERN-SPS and BNL-RHIC are investigated within a hydrodynamic simulation. The dependence of the dynamics and the HBT-parameters on the EoS is studied with different parametrisations of a chiral SU(3) sigma-omega model. The selfconsistent collective expansion includes the effects of effective hadron masses, generated by the nonstrange and strange scalar condensates. Different chiral EoS show different types of phase transitions and even a crossover. The influence of the order of the phase transition and of the differen…
$\textbf{HoTCoffeeh}$ ($\textbf{H}$anbury Br$\textbf{o}$wn-$\textbf{T}$wiss $\textbf{Co}$rrelation $\textbf{f}$unctions and radii $\textbf{f}$rom $\textbf{e}$vent-by-$\textbf{e}$vent $\textbf{h}$ydrodynamics) is a new computational tool which determines Hanbury Brown-Twiss (HBT) charged pion ($π^+$) correlation functions and radii for event-by-event (EBE) hydrodynamics with fluctuating initial conditions in terms of Cooper-Frye integrals, including resonance decay contributions. In this paper, we review the basic formalism for computing the HBT correlation functions and radii with resonance de…
We investigate the transverse momentum dependence of pion HBT radii on the basis of a hydrodynamical model. Recent experimental data show that $R_{\text{out}}/R_{\text{side}} < 1$, which suggests a strong opaqueness of the source. In addition to the opaqueness naturally caused by transverse flow, we introduce an extrinsic opacity by imposing restrictions on the pion emission angle. Comparing the HBT radii obtained from the normal Cooper-Frye prescription and the opaque emission prescription, we find that $R_{\text{out}}/R_{\text{side}}$ is less than unity only for small values of the transvers…
Azimuthally-sensitive femtoscopy for heavy-ion collisions at RHIC and LHC is explored within the approach consisting of the hydrodynamics of perfect fluid followed by statistical hadronization. It is found that for the RHIC initial conditions the very same framework that reproduces the standard soft observables (including the transverse-momentum spectra, the elliptic flow, and the azimuthally-averaged HBT radii) leads to a proper description of the azimuthally-sensitive femtoscopic observables - we find that the azimuthal variation of the side and out HBT radii is very well reproduced for all …
In the light of the recent LHC data on proton-proton and lead-lead collisions we examine the question of the multiplicity scaling of HBT radii in relativistic nuclei and particle interactions. Within the UrQMD transport approach we study a large variety of system sizes at different beam energies and extract the HBT radii. In the calculation, we find a good scaling of the radii as a function of charged particle multiplicity, if the change in the multiplicity is caused by a change of centrality at the same energy. However, the scaling is only approximate when the energy, $\sqrt{s}$, is changed a…
Results from the data obtained in the first physics run of the Relativistic Heavy Ion Collider (RHIC) have shown suprisingly large elliptic flow and suprisingly small HBT radii. Attempts to explain both results in a consistant picture have so far been unsuccessful. The present work shows that a simple thermal-like initial state model coupled to a hadronic rescattering calculation can explain reasonably well both elliptic flow and HBT results from RHIC. The calculation suggests a very early hadronization time of about 1 fm/c after the initial collision of the nuclei.
We investigate the two-pion interferometry in ultrarelativistic heavy ion collisions in the granular source model of quark-gluon plasma droplets. The pion transverse momentum spectra and HBT radii of the granular sources agree well with the experimental data of the $\sqrt{s_{NN}}=200$ GeV Au-Au and $\sqrt{s_{NN}}=2.76$ TeV Pb-Pb most central collisions. In the granular source model the larger initial system breakup time may lead to the larger HBT radii $R_{\rm out}$, $R_{\rm side}$, and $R_{\rm long}$. However, the large droplet transverse expansion and limited average relative emitting time o…
The Hanbury-Brown-Twiss (HBT) radii have been calculated from the two particle correlation functions with virtual photons produced in the collisions of two nuclei at ultra-relativistic energies. We show that the variation of the HBT radii with the invariant mass of the virtual photon can be used to characterize and distinguish the hadronic as well as the partonic phase that might have produced initially in the collisions. It has been illustrated that the non-monotonic variation of the HBT radii with invariant mass provides an access to the development of collective flow in the system.
We calculate the HBT radius Rs for π+ particles with the Coulomb interaction by using the string melting version of a multiphase transport(AMPT) model. We study the relationship between the single-particle space-momentum angle and the particle sources and discuss HBT radii without single-particle space-momentum correlation. Additionally, we study the Coulomb interaction effect on the numerical connection between the single-particle space-momentum angle distribution and the transverse momentum dependence of Rs.
We show that a consistent hydrodynamic description of soft-hadronic one- and two-particle observables (the HBT radii) studied in the relativistic heavy-ion collisions at RHIC may be obtained if one uses the Gaussian energy density profile as the initial condition. The transverse-momentum spectra, the elliptic flow coefficient $v_2$, and the pionic azimuthally sensitive HBT radii are successfully reproduced, which hints that the long standing HBT puzzle has been solved.
HBT correlations of $π^--π^-$ pairs at FAIR/AGS energies are investigated by using the UrQMD transport model and the CRAB analyzing program. Three different possible sources (treatment of resonance lifetimes, a soft equation of state and non-Gaussian effects) to understand the HBT $R_O/R_S$ puzzle are investigated. Firstly, we find that different treatments of the resonance decay time can not resolve the HBT time-related puzzle, however it can modify the HBT radii at low transverse momenta to some extent to explain the data slightly. Secondly, with a soft equation of state with momentum depend…
The transverse momentum dependence of Hanbury-Brown/Twiss (HBT) interferometry radii for 2-body correlation functions provides experimental access to the collective dynamics in heavy-ion collisions. We present an analytical approximation scheme for these HBT radii which combines the recently derived model-independent expressions with an approximate determination of the saddle point of the emission function. The method is illustrated for a longitudinally boost-invariant hydrodynamical model of a heavy ion collision with freeze-out on a sharp hypersurface. The analytical approximation converges …
We used an Isospin dependent Quantum Molecular Dynamics (IQMD) model to simulate Au + Au collisions at beam energy $E_{beam}$ = 1.23$A$ GeV, which corresponds to center of mass energy $\sqrt{s_{NN}} = 2.4$ GeV. Firstly, we obtained reasonable rapidity and transverse mass spectra of $π^-$ and $π^+$ as well as "apparent" temperature parameters in comparison with the HADES data. Then by calculating three-dimensional Hanbury Brown and Twiss (HBT) radius of same charged pion-pairs, we obtained the square difference of outward radius and sideward radius, i.e. $R_{out}^{2}-R_{side}^{2}$, as well as t…
We investigate the two-pion interferometry in ultrarelativistic heavy ion collisions in the granular source model of quark-gluon plasma droplets. The pion transverse momentum spectra and HBT radii of the granular sources agree well with the experimental data of the most central Au-Au collisions at $\sqrt{s_{NN}}=200$ GeV at RHIC and Pb-Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV at LHC. In the granular source model the larger initial system breakup time for the LHC collisions as compared to the RHIC collisions may lead to the larger HBT radii $R_{\rm out}$, $R_{\rm side}$, and $R_{\rm long}$. Ho…
We address the problem if the early thermalization and HBT puzzles in relativistic heavy-ion collisions may be solved by the assumption that the early dynamics of the produced matter is locally anisotropic. The hybrid model describing the purely transverse hydrodynamic evolution followed by the perfect-fluid hydrodynamic stage is constructed. The transition from the transverse to perfect-fluid hydrodynamics is described by the Landau matching conditions applied at a fixed proper time. The global fit to the RHIC data reproduces the soft hadronic observables (the pion, kaon, and the proton spect…
