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Register a new userPhenomenological study on correlation between flow harmonics and mean transverse momentum in nuclear collisions
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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).
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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.
In heavy ion collisions, elliptic flow $v_2$ and radial flow, characterized by event-wise average transverse momentum $[p_{mathrm{T}}]$, are related to the shape and size of the overlap region, which are sensitive to the shape of colliding atomic nuclei. The Pearson correlation coefficient between $v_2$ and $[p_{mathrm{T}}]$, $rho_2$, was found to be particularly sensitive to the quadrupole deformation parameter $beta$ that is traditionally measured in low energy experiments. Built on earlier insight that the prolate deformation $beta>0$ reduces the $rho_2$ in ultra-central collisions (UCC), we show that the prolate deformation $beta<0$ enhances the value of $rho_2$. As $beta>0$ and $beta<0$ are the two extremes of triaxiality, the strength and sign of $v_2^2-[p_{mathrm{T}}]$ correlation can be used to provide valuable information on the triaxiality of the nucleus. Our study provide further arguments for using the hydrodynamic flow as a precision tool to directly image the deformation of the atomic nuclei at extremely short time scale ($<10^{-24}$s).
We propose the skewness of mean transverse momentum, $langle p_t rangle$, fluctuations as a fine probe of hydrodynamic behavior in relativistic nuclear collisions. We describe how the skewness of the $langle p_t rangle$ distribution can be analyzed experimentally, and we use hydrodynamic simulations to predict its value. We predict in particular that $langle p_t rangle$ fluctuations have positive skew, which is significantly larger than if particles were emitted independently. We elucidate the origin of this result by deriving generic formulas relating the fluctuations of $langle p_t rangle$ to the fluctuations of the early-time thermodynamic quantities. We postulate that the large positive skewness of $langle p_t rangle$ fluctuations is a generic prediction of hydrodynamic models.
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.
Flow harmonics ($v_n$) in the Fourier expansion of the azimuthal distribution of particles are widely used to quantify the anisotropy in particle emission in high-energy heavy-ion collisions. The symmetric cumulants, $SC(m,n)$, are used to measure the correlations between different orders of flow harmonics. These correlations are used to constrain the initial conditions and the transport properties of the medium in theoretical models. In this Letter, we present the first measurements of the four-particle symmetric cumulants in Au+Au collisions at $sqrt{s_{NN}}$ = 39 and 200 GeV from data collected by the STAR experiment at RHIC. We observe that $v_{2}$ and $v_{3}$ are anti-correlated in all centrality intervals with similar correlation strengths from 39 GeV Au+Au to 2.76 TeV Pb+Pb (measured by the ALICE experiment). The $v_{2}$-$v_{4}$ correlation seems to be stronger at 39 GeV than at higher collision energies. The initial-stage anti-correlations between second and third order eccentricities are sufficient to describe the measured correlations between $v_{2}$ and $v_{3}$. The best description of $v_{2}$-$v_{4}$ correlations at $sqrt{s_{NN}}$ = 200 GeV is obtained with inclusion of the systems nonlinear response to initial eccentricities accompanied by the viscous effect with $eta/s$ $>$ 0.08. Theoretical calculations using different initial conditions, equations of state and viscous coefficients need to be further explored to extract $eta/s$ of the medium created at RHIC.
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