Local and global polarization of $Λ$ hyperons across RHIC-BES energies: the roles of spin hall effect, initial condition and baryon diffusion

Abstract

We perform a systematic study on the local and global spin polarization of Λ and Λ hyperons in relativistic heavy-ion collisions at beam energy scan energies via the (3+1)-dimensional CLVisc hydrodynamics model with AMPT and SMASH initial conditions. Following the quantum kinetic theory, we decompose the polarization vector as the parts induced by thermal vorticity, shear tensor and the spin Hall effect (SHE). We find that the polarization induced by SHE and the total polarization strongly depends on the initial conditions. At 7.7GeV, SHE gives a sizeable contribution and even flips the sign of the local polarization along the beam direction for AMPT initial condition, which is not observed for SMASH initial condition. Meanwhile, the local polarization along the out-of-plane direction induced by SHE with AMPT initial condition does not always increase with decreasing collision energies. Next, we find that the polarization along the beam direction is sensitive to the baryon diffusion coefficient, but the local polarization along the out-of-plane direction is not. Our results for the global polarization of Λ and Λ agree well with the STAR data. Interestingly, the global polarization of Λ is not always larger than that of Λ due to various competing effects. Our findings are helpful for understanding the polarization phenomenon and the detailed structure of quark-gluon plasma in relativistic heavy-ion collisions.

Spin evolution of massive fermion in QED plasma

“…Together the above two parts, the vorticity term will be the C (8) term in (28), with C (8) defined in (30). b. shear After momentum integral, the collision term C shear Aµ (24) will only be function of P , thus can in general be expressed in terms of a series of symmetric and traceless projectors as,…”

“…Since T µαβ C µαβ is at least O(Q), it is enough to expand the distribution functions to O(Q) (A18). After taking the momentum integral according to Appendix.A 1, one will obtain the C (9) term in (28), with C (9) in (30). Using (A27) to complete the contraction, and carrying out the momentum integral according to Appendix.A 1, one will obtain the C (10) and C (11) term in (28), with C (10) and C (11) in (30).…”

“…It is realized later the inclusion of shear tensor in the polarization yields the qualitatively correct sign [23][24][25][26], indicating off-equilibrium effects of spin maybe essential in polarization phenomenon. It is also found that the numerical results could be sensitive to the parameters in numerical analysis [27][28][29][30]. This calls for more thorough investigations of the non-equilibrium effects in the spin polarization.…”

Tensor Polarization and Spectral Properties of Vector Meson in QCD Medium

“…Refs. [9,[22][23][24][25][26][27][28][29][30][31][32][33] and see Refs. [34][35][36][37] for reviews), deepening our understandings on the relativistic spin physics and making spin related observables as new tools to study the properties of the hot and dense matter created in heavy-ion collisions.…”

“…Using the standard parametrization p µ = (m T cosh Y, p T cos φ p , p T sin φ p , m T sinh Y ) , (33) where Y is rapidity and φ p , p T are azimuthal angle and momentum in x − y plane respectively, and where m T = m 2 + p 2 T . The relative velocity in PRF can be read from ( 27) and we have:…”