Correlation femtoscopy study at energies available at the JINR Nuclotron-based Ion Collider fAcility and the BNL Relativistic Heavy Ion Collider within a viscous hydrodynamic plus cascade model

Correlation femtoscopy allows one to measure the space-time characteristics of particle production in relativistic heavy-ion collisions due to the effects of quantum statistics (QS) and final state interactions (FSIs). The main features of the femtoscopy measurements at top RHIC and LHC energies are considered as a manifestation of strong collective flow and are well interpreted within hydrodynamic models employing equation of state (EoS) with a crossover type transition between quark-gluon plasma (QGP) and hadron gas phases. The femtoscopy at lower energies was intensively studied at AGS and SPS accelerators and is being studied now in the Beam Energy Scan program (BES) at the BNL Relativistic Heavy Ion Collider in the context of exploration of the QCD phase diagram. In this article we present femtoscopic observables calculated for Au-Au collisions at $\sqrt{s_{NN}}=7.7–62.4$ GeV in a viscous hydro + cascade model vHLLE+UrQMD and their dependence on the EoS of thermalized matter.

Figure 1

Thermodynamic pressure as a function of energy density, evaluated at zero baryon density from the equations of state used in the hydrodynamic stage: chiral model EoS with crossover transition (XPT) and bag model EoS with first order phase transition (1PT).

Figure 2

Pion emission times at the particlization surface (a) and the last interactions (b) in the center-of-mass system of colliding gold nuclei at different values of $\sqrt{s_{NN}}$.

Figure 3

One-dimensional projections of three-dimensional correlation function [see Eq. (7)] of noninteracting identical pion pairs onto out (a), side (b), and long (c) directions. While projecting onto a direction, other two directions are required to be within the range of $(-0.03,0.03)$ GeV/$c$. A fit with the Gaussian function is presented by dashed and solid lines for the 1PT and XPT scenarios, respectively.

Figure 4

Ratios of one-dimensional projections of three-dimensional correlation functions for the two EoSs. For each direction the corresponding ratio is calculated as follows: $C\left(q_i\right)\left(XPT\right)/C\left(q_i\right)\left(1PT\right)$, where $i$ denotes out (a), side (b), and long (c) directions, $1PT$ and $XPT$ denote a type of the used EoS.

Figure 5

Comparison of the model three-dimensional LCMS femtoscopy radii fitted according to Eq. (7) with those measured by the STAR collaboration at $\sqrt{s_{NN}}=7.7$ (a)–(d), 11.5 (e)–(h), 19.6 (i)–(l), 27 (m)–(p), 39 (q)–(t), 62.4 (u)–(x) GeV. Open squares represent the STAR data. Triangles correspond to different types of EoSs like they do in Fig. 3.

Figure 6

Ratio of the out and side radii (a) and difference of the radii squared (b) as a function of $\sqrt{s_{NN}}$ derived from the STAR data ($0.15<k_T<0.25$ GeV/$c$, 0–5% centrality) and compared with the model calculations using the two EoSs.

Figure 7

One-dimensional projections of source emission functions of pions from the model (full simulation with cascade) obtained at $\sqrt{s_{NN}}=7.7\mathrm{GeV}$ for pion pairs satisfying the cut on transverse momentum: $0.2<k_T<0.4\mathrm{GeV}/c$.

Figure 8

$\sqrt{s_{NN}}$ dependence of radii extracted from the double Gaussian fit (a)–(c) and relative contribution of them ($\lambda$) to out, side, and long directions (d)–(f). Pion pairs satisfying $0.2<k_T<0.8\mathrm{GeV}/c$ are taken into account.