Local and global polarization of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="normal">?</mml:mi></mml:math> hyperons across RHIC-BES energies: The roles of spin hall effect, initial condition, and baryon diffusion

We perform a systematic study on the local and global spin polarization of $\mathrm{\ensuremath{\Lambda}}$ $\overline{\mathrm{\ensuremath{\Lambda}}}$ hyperons in relativistic heavy-ion collisions at beam energy scan energies via ($3+1$)-dimensional CLVisc hydrodynamics model with multiphase transport (AMPT) simulating many accelerated strongly interacting hadron (SMASH) initial conditions. Following quantum kinetic theory, we decompose vector as parts induced by thermal vorticity, shear tensor Hall effect (SHE). find that SHE total depends At $7.7\phantom{\rule{0.28em}{0ex}}\mathrm{GeV}$, gives sizable contribution even flips sign along direction for AMPT condition, which is not observed SMASH condition. Meanwhile, out-of-plane condition does always increase decreasing collision energies. Next, sensitive to baryon diffusion coefficient, but not. Our results agree well data STAR Collaboration. Interestingly, larger than due various competing effects. findings are helpful understanding phenomenon detailed structure quark-gluon plasma collisions.