Vortical Fluid and Λ Spin Correlations in High-Energy Heavy-Ion Collisions

Abstract

Fermions become polarized in a vortical fluid due to spin-vorticity coupling. The spin polarization density is proportional to the local fluid vorticity at the next-to-leading order of a gradient expansion in a quantum kinetic theory. Spin correlations of two Λ-hyperons can therefore reveal the vortical structure of the dense matter in high-energy heavy-ion collisions. We employ a (3+1)D viscous hydrodynamic model with event-by-event fluctuating initial conditions from A MultiPhase Transport (AMPT) model to calculate the vorticity distributions and Λ spin correlations. The azimuthal correlation of the transverse spin is shown to have a cosine form plus an offset due to a circular structure of the transverse vorticity around the beam direction and global spin polarization. The longitudinal spin correlation shows a structure of vortex-pairing in the transverse plane due to the convective flow of hot spots in the radial direction. The dependence on colliding energy, rapidity, centrality and sensitivity to the shear viscosity are also investigated. Introduction. -Low-energy nuclear reactions can create rotating and deformed compound nuclei that carry a large amount of orbital angular momentum of the colliding nuclei [1]. The large orbital angular momentum in non-central high-energy heavy-ion collisions cannot produce a rotating quark-gluon plasma because of the soft equation of state (EoS). It should instead lead to fluid shear and non-vanishing local fluid vorticity [2][3][4][5][6][7][8][9][10][11][12][13][14]. In such a vorticular fluid, the spin-orbital coupling polarizes the spin of fermions (quarks and baryons) [2][3][4][5][6][7][8][9][10][11][12] along the direction of the vorticity.

Collective Longitudinal Polarization in Relativistic Heavy-Ion Collisions at Very High Energy

“…For instance, in ref. [14], a connection between local vortical structures in eventby-event hydrodynamics and correlation of polarizations of two Λ hyperons in transverse and longitudinal (along the beam line) directions has been studied. In this letter, we argue that in non-central heavy ion collisions, a non-zero longitudinal polarization of Λ with different transverse momenta p T is a more generic effect present in a simple non-fluctuating hydrodynamic picture, and propose to measure it in experiment [15].…”

“…In this letter, we argue that in non-central heavy ion collisions, a non-zero longitudinal polarization of Λ with different transverse momenta p T is a more generic effect present in a simple non-fluctuating hydrodynamic picture, and propose to measure it in experiment [15]. As it will be shown, this observable has several attractive features:-unlike the polarization along J, it is sensitive only to the transverse expansion dynamics;-it is found not to decrease rapidly as a function of center-of-mass energy (similar to longitudinal correlations in [14]) and it can be detected even at the LHC energy in the TeV range;-it survives the "minimal vorticity" scenario of Bjorken longitudinal boost invariance;-unlike the polarization component along the angular momentum, it does not require the identification of the orientation 1 of the reaction plane, thus greatly reducing the experimental labor.The effect is dominated by the geometry of collision, therefore we do not include event-by-event fluctuations in this study.Symmetries in relativistic nuclear collisions at very high energyIn principle, (average) collisions of two identical nuclei at a finite impact parameter feature two initial discrete symmetries: rotation by an angle π around the total angular momentum axis and reflection in the transverse plane with respect to the reaction plane (see fig. 1).…”

Covariant chiral kinetic equation in the Wigner function approach

“…This is a piece of evidence for the local polarization effect from vorticity in collisions at lower energy and was first predicted in Ref. [28] and later extensively studied [30][31][32][45][46][47][48][49][50].…”

Phenomenology of anomalous chiral transports in heavy-ion collisions

“…(3) Although the total angular momentum J 0 increases with √ s, the event-averaged vorticity at mid rapidity decreases with increasing √ s. This counterintuitive behavior is mainly because that the quark-gluon medium at mid rapidity behaves closer to the Bjorken boost invariant picture at higher √ s and thus supports lower vorticity. The vorticity can be measured through measuring the spin polarization of hadrons, e.g., the Λ hyperon [23][24][25][26]. The underlying mechanism is the spin-orbit coupling.…”