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Register a new userGlobal Polarization Effect in the Extremely Rapidly Rotating QGP in HIC
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This is prepared for a featured article in Nuclear Physics News. Recently, the global polarization of Lambda and bar{Lambda} hyperons in heavy-ion collisions (HIC) has been observed by the STAR Collaboration at the Relativistic Heavy Ion Collider in Brookhaven National Laboratory. The discovery confirms the theoretical prediction made more than ten years ago and indicates that the quark gluon plasma (QGP) produced in HIC possesses a vorticity as high as 10^21s^-1, much higher than any other fluid observed in nature. This opens a new window to study properties of QGP and a new direction in high energy heavy ion physics. This featured article is aimed to report the basic idea, current status and outlook.
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We investigate the possible occurrence of the highly-elongated shapes near the yrast line in $^{40}$Ca and $^{41}$Ca at high spins on the basis of the nuclear energy-density functional method. Not only the superdeformed (SD) yrast configuration but the yrare configurations on top of the SD band are described by solving the cranked Skyme-Kohn-Sham equation in the three-dimensional coordinate-space representation. It is suggested that some of the excited SD bands undergo band crossings and develop to the hyperdeformation (HD) beyond $J simeq 25 hbar$ in $^{40}$Ca. We find that the change of triaxiality in response to rotation plays a decisive role for the shape evolution towards HD, and that this is governed by the signature quantum number of the last occupied orbital at low spins. This mechanism can be verified in an experimental observation of the positive-parity SD yrast signature-partner bands in $^{41}$Ca, one of which ($alpha=+1/2$) undergoes crossings with the HD band while the other ($alpha=-1/2$) shows the smooth evolution from the collective rotation at low spins to the non-collective rotation with oblate shape at the termination.
In non-central relativistic heavy ion collisions, the created matter possesses a large initial orbital angular momentum. Particles produced in the collisions could be polarized globally in the direction of the orbital angular momentum due to spin-orbit coupling. Recently, the STAR experiment has presented polarization signals for $Lambda$ hyperons and possible spin alignment signals for $phi$ mesons. Here we discuss the effects of finite coverage on these observables. The results from a multi-phase transport and a toy model both indicate that a pseudorapidity coverage narrower than $|eta|< sim 1$ will generate a larger value for the extracted $phi$-meson $rho_{00}$ parameter; thus a finite coverage can lead to an artificial deviation of $rho_{00}$ from 1/3. We also show that a finite $eta$ and $p_T$ coverage affect the extracted $p_H$ parameter for $Lambda$ hyperons when the real $p_H$ value is non-zero. Therefore proper corrections are necessary to reliably quantify the global polarization with experimental observables.
In non-central high energy heavy ion collisions the colliding system posses a huge orbital angular momentum in the direction opposite to the normal of the reaction plane. Due to the spin-orbit coupling in strong interaction, such huge orbital angular momentum leads to the polarization of quarks and anti-quarks in the same direction. This effect, known as the global polarization effect, has been recently observed by STAR Collaboration at RHIC that confirms the theoretical prediction made more than ten years ago. The discovery has attracted much attention on the study of spin effects in heavy ion collision. It opens a new window to study properties of QGP and a new direction in high energy heavy ion physics -- Spin Physics in Heavy Ion Collisions. In this chapter, we review the original ideas and calculations that lead to the predictions. We emphasize the role played by spin-orbit coupling in high energy spin physics and discuss the new opportunities and challenges in this connection.
Global polarization of $Lambda$ and $bar{Lambda}$ is calculated based on the axial vortical effect (AVE). Simulations are performed within the model of the three-fluid dynamics. Equations of state with the deconfinement transition result in a good agreement with STAR data for both $Lambda$ and $bar{Lambda}$ polarization, in particular, with the $Lambda$-$bar{Lambda}$ splitting. Suppression of the gravitational-anomaly contribution required for the data reproduction is in agreement with predictions of the QCD lattice simulations. Predictions for the global polarization in forthcoming experiments at lower collision energies are made. These forthcoming data will provide a critical test for the AVE and thermodynamic mechanisms of the polarization.
A rotating system, such as a star, liquid drop, or atomic nucleus, may rotate as an oblate spheroid about its symmetry axis or, if the angular velocity is greater than a critical value, as a triaxial ellipsoid about a principal axis. The oblate and triaxial equilibrium configurations minimize the total energy, a sum of the rotational kinetic energy plus the potential energy. For a star or galaxy the potential is the self-gravitating potential, for a liquid drop, the surface tension energy, and for a nucleus, the potential is the sum of the repulsive Coulomb energy plus the attractive surface energy. A simple, but accurate, Pad{e} approximation to the potential function is used for the energy minimization problem that permits closed analytic expressions to be derived. In particular, the critical deformation and angular velocity for bifurcation from MacLaurin spheroids to Jacobi ellipsoids is determined analytically in the approximation.
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