No Arabic abstract
The correlation between the mean transverse momentum of outgoing particles, $langle p_t rangle$, and the magnitude of anisotropic flow, $v_n$, has recently been measured in Pb+Pb collisions at the CERN Large Hadron Collider, as a function of the collision centrality. We confirm the previous observation that event-by-event hydrodynamics predicts a correlation between $v_n$ and $langle p_t rangle$ that is similar to that measured in data. We show that the magnitude of this correlation can be directly predicted from the initial condition of the hydrodynamic calculation, for $n=2,3$, if one replaces $v_n$ by the corresponding initial-state anisotropy, $varepsilon_n$, and $langle p_trangle$ by the total energy per unit rapidity of the fluid at the beginning of the hydrodynamic expansion.
Possible correlations of the global polarization of $Lambda$ hyperons with the angular momentum and transverse flow in the central region of colliding nuclei are studied based on refined estimate of the global polarization. Simulations of Au+Au collisions at collision energies $sqrt{s_{NN}}=$ 6-40 GeV are performed within the model of the three-fluid dynamics. Within the crossover and first-order-phase-transition scenarios this refined estimate quite satisfactorily reproduces the experimental STAR data. Hadronic scenario fails at high collision energies, $sqrt{s_{NN}}>$ 10 GeV, and even predicts opposite sign of the global polarization. It is found that the global polarization correlates with neither the angular momentum accumulated in the central region nor with directed and elliptic flow. At the same time we observed correlation between the angular momentum and directed flow in both their time and collision-energy dependence. These results suggest that, although initially the angular momentum is the driving force for the vortex generation, later the angular momentum and vortex motion become decorrelated in the midrapidity region. Then the midrapidity angular momentum is determined by the pattern of the directed flow and even becomes negative when the antiflow occurs. At the freeze-out stage, the dominant part of the participant angular momentum is accumulated in the fragmentation regions.
We predict that the mean transverse momentum of charged hadrons $langle p_trangle$ rises as a function of the charged-particle multiplicity in ultracentral nucleus-nucleus collisions. We explain that this phenomenon has a simple physical origin and represents an unambiguous prediction of the hydrodynamic framework of heavy-ion collisions. We argue that the relative increase of $langle p_t rangle$ is proportional to the speed of sound squared $c_s^2$ of the quark-gluon plasma. Based on the value of $c_s^2$ from lattice QCD, we expect $langle p_trangle$ to increase by approximately $18$ MeV between 1% and 0.001% centrality in Pb+Pb collisions at $sqrt{s_{rm NN}}=5.02$ TeV.
The correlation between the harmonic flow and the transverse flow in relativistic heavy ion collisions is calculated in the hydrodynamic model. The partial correlation coefficient, corrected for fluctuations of multiplicity, is compared to experimental data. Estimators of the final transverse and harmonic flow are used to predict the value of the correlation coefficient from the moments of the initial distribution. A good description of the hydrodynamic simulation results is obtained if the estimator for the final transverse flow, besides the most important transverse size and entropy, includes also the eccentricities.
Higher-order anisotropic flows in heavy-ion collisions are affected by nonlinear mode coupling effects. It has been suggested that the associated nonlinear hydrodynamic response coefficients probe the transport properties and are largely insensitive to the spectrum of initial density fluctuations of the medium created in these collisions. To test this suggestion, we explore nonlinear mode coupling effects in event-by-event viscous fluid dynamics, using two different models for the fluctuating initial density profiles, and compare the nonlinear coupling coefficients between the initial eccentricity vectors before hydrodynamic expansion and the final flow vectors after the expansion. For several mode coupling coefficients we find significant sensitivity to the initial fluctuation spectrum. They all exhibit strong sensitivity to the specific shear viscosity at freeze-out, but only weak dependence on the shear viscosity during hydrodynamic evolution.
To assess the properties of the quark-gluon plasma formed in nuclear collisions, the Pearson correlation coefficient between flow harmonics and mean transverse momentum, $rholeft(v_{n}^{2},left[p_{mathrm{T}}right]right)$, reflecting the overlapped geometry of colliding atomic nuclei, is measured. $rholeft(v_{2}^{2},left[p_{mathrm{T}}right]right)$ was found to be particularly sensitive to the quadrupole deformation of the nuclei. We study the influence of the nuclear quadrupole deformation on $rholeft(v_{n}^{2},left[p_{mathrm{T}}right]right)$ in $rm{Au+Au}$ and $rm{U+U}$ collisions at RHIC energy using $rm{AMPT}$ transport model, and show that the $rholeft(v_{2}^{2},left[p_{mathrm{T}}right]right)$ is reduced by the prolate deformation $beta_2$ and turns to change sign in ultra-central collisions (UCC).