Spin polarization induced by the hydrodynamic gradients

Abstract

We systematically analyze the effects of the derivatives of the hydrodynamic fields on axial Wigner function that describes the spin polarization vector in phase space. We have included all possible first-order derivative contributions that are allowed by symmetry and compute the associated transport functions at one-loop using the linear response theory. In addition to reproducing known effects due to the temperature gradient and vorticity, we have identified a number of potentially significant contributions that are overlooked previously. In particular, we find that the shear strength, the symmetric and traceless part of the flow gradient, will induce a quadrupole for spin polarization in the phase space. Our results, together with hydrodynamic gradients obtained from hydrodynamic simulations, can be employed as a basis for the interpretation of the Λ (anti-Λ) spin polarization measurement in heavy-ion collisions.

Signatures of the spin Hall effect in hot and dense QCD matter

“…[16][17][18][19][20][21][22] for examples of studies on differential spin polarization at BES energies. Newly-discovered shear-induced polarization (SIP) [23][24][25] is found to be crucial for solving this "polarization sign puzzle" [24,26]. Despite of those developments, the possible signature of the SHE has not been fully explored until now (see Refs.…”

“…Specifically, we shall consider the SHE induced by baryon chemical potential gradient ∇µ B which becomes sizable in the fireballs created at colliding energy of O (10) GeV. This phenomena as well as spin polarized by electric field has been predicted and quantitatively described within the framework of relativistic quantum kinetic equations [23,[29][30][31][32][33] and linear response theory [23,27]. Just as charge current will be induced by both chemical potential gradient and electric field, the spin Hall current can be generated by ∇µ B which plays an analogous role of the electric field [34].…”

Lorentz-covariant kinetic theory for massive spin-1/2 particles

“…Given explicit expressions for the Dirac spinors, we can derive the matrix D in Eq. (17). Then, we substitute D into Eq.…”

“…Various efforts [10][11][12][13][14][15][16] have been made to resolve this so-called "sign problem of the longitudinal polarization", but a fully convincing explanation does not yet exist. It was recently proposed [17][18][19] that previous calculations had missed a shear-induced contribution to the polarization at freeze-out, which has the potential to solve this problem, but so far results including this term appear to be sensitive to the equation of state and other parameters of the calculation [20].…”

Spin relaxation rate for heavy quarks in weakly coupled QCD plasma

“…The recent experimental observation of the spin polarization of hadrons in the rotating QCD plasma produced in off-central relativistic heavy-ion collisions at RHIC and LHC [1][2][3][4] has motivated much theoretical and phenomenological study of the dynamical evolution of spin polarization in a finite temperature plasma. A large amount of theoretical effort has been invested into the development of a description of spin in kinetic theory [5][6][7][8][9][10][11][12][13][14][15][16][17] and spin in hydrodynamics [18][19][20][21][22][23][24][25][26][27][28][29]. As the spin angular momentum is not conserved and is transferable to orbital angular momentum, the spin density, in general, shows a relaxation behavior toward its local equilibrium value in hydrodynamics [20,28].…”