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Register a new userConstraining nuclear quadrupole deformation from correlation of elliptic flow and transverse momentum in nuclear collisions
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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).
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We propose observables $v_0$ and $v_0(p_T)$ which quantify the relative fluctuations in the total transverse momentum at fixed multiplicity. We first study the factorization of the fixed multiplicity momentum dependent two particle correlation function into a product of $v_0(p_T^a)$ and $v_0(p_T^b)$ within realistic hydrodynamic simulations. Then we present computations of $v_0(p_T)$ for different particle types. We determine the relation between the integrated $v_0$ and previously measured observables, and compare results from a hybrid hydrodynamics based model to experimental data. The effects of bulk viscosity and an initial pre-equilibrium stage on the results are quantified. We find that $v_0$ is strongly correlated with the initial state entropy per elliptic area, $S/A$. Using this result, we explain how the observed correlations between the elliptic flow and the transverse momentum (both in simulations and experiment) reflect the initial state correlations between $1/A$ and ellipticity $varepsilon_2$ at fixed multiplicity. We argue that the systematic experimental study of $v_0$, with the same sophistication as used for the other $v_n$, can contribute significantly to our understanding of quark gluon plasma properties.
Preliminary data by the STAR collaboration at the BNL Relativistic Heavy Ion Collider shows that the elliptic flow, $v_2$, and the average transverse momentum, $langle p_t rangle$, of final-state hadrons produced in high-multiplicity $^{238}$U+$^{238}$U collisions are negatively correlated. This observation brings experimental evidence of a significant prolate deformation, $betaapprox 0.3$, in the colliding $^{238}$U nuclei. I show that a quantitative description of this new phenomenon can be achieved within the hydrodynamic framework of heavy-ion collisions, and that thus such kind of data in the context of high-energy nuclear experiments can help constrain the quadrupole deformation of the colliding species.
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.
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).
In the continuation of our previous work, the transverse momentum ($p_T$) spectra and nuclear modification factor ($R_{AA}$) are derived using relaxation time approximation of Boltzmann Transport Equation (BTE). The initial $p_T$-distribution used to describe $p+p$ collisions has been studied with the pQCD inspired power-law distribution, the Hagedorns empirical formula and with the Tsallis non-extensive statistical distribution. The non-extensive Tsallis distribution is observed to describe the complete range of the transverse momentum spectra. The Boltzmann-Gibbs Blast Wave (BGBW) distribution is used as the equilibrium distribution in the present formalism, to describe the $p_T$-distribution and nuclear modification factor in nucleus-nucleus collisions. The experimental data for Pb+Pb collisions at $sqrt{s_{NN}}$ = 2.76 TeV at the Large Hadron Collider at CERN have been analyzed for pions, kaons, protons, $K^{*0}$ and $phi$. It is observed that the present formalism while explaining the transverse momentum spectra upto 5 GeV/c, explains the nuclear modification factor very well upto 8 GeV/c in $p_T$ for all these particles except for protons. $R_{AA}$ is found to be independent of the degree of non-extensivity, $q_{pp}$ after $p_T sim$ 8 GeV/c.
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