In non-central heavy-ion collisions, large orbital angular momenta of the order L∼10³ℏ to L∼10⁶ℏ are generated. Due to the quantum mechanical spin orbit coupling, this might cause a spin polarization of the produced particles along the orbital angular momentum. As the system created in heavy-ion collisions is well described in the framework of relativistic hydrodynamics, the orbital angular momentum results in non-zero vorticity, classically defined as the rotation of the velocity field. Several theoretical approaches of a global polarization linked to different definitions of the relativistic vorticity tensor have been developed in the past years.
In contrast to macroscopic spin polarization effects, where the spin can be measured by applying external magnetic fields, such a direct measurement of the spin direction is not possible in heavy-ion collisions. The possibility to measure the particle spin is based on the unique feature to the weak interaction, the parity violation. This has the consequence that in weak decays, the emittance of the decay products is linked to the spin direction of the weakly decaying particle. The simplest candidate to perform such a measurement is the Λ hyperon. Through its decay Λ → p + π⁻ (branching ratio 63.9%), which has two charged particles in the final state, it can be reconstructed. Due to the parity violation in this weak decay, the proton is predominantly emitted in the spin direction of the Λ hyperon. Thereby, the spin measurement is transformed into a momentum measurement which can be performed.
The orientation of the orbital angular momentum is always perpendicular to the so-called reaction plane spanned by the beam direction and the impact parameter of the collision. The reaction plane can be estimated from the event plane, which is reconstructed in a Q-vector analysis from the distribution of the spectator particles. In the laboratory frame, the event plane is fully determined by a single azimuthal angle. Then, an observable can be defined for the global polarization of the Λ hyperons based on the modulation of the azimuthal angle of the proton in the rest frame of the Λ with respect to the event plane orientation.
In this work, the global polarization of the system using Λ hyperon polarization measurements are presented for Au+Au collisions at a center-of-mass energy per nucleon of 2.4GeV and Ag+Ag collisions at a center-of-mass energy per nucleon of 2.55GeV collision energy. The extracted signal in the Au+Au run yields P[%] = 4.609 ± 0.966 (stat.) ± 1.220 (sys.), while for the Ag+Ag run a value of P[%] = 3.174 ± 0.294 (stat.) ± 0.319 (sys.) has been measured. This is the highest Λ polarization ever measured in heavy-ion collisions. Our measurement continues the increasing trend measured by the STAR collaboration in the beam energy scan phase I down to a center-of-mass energy per nucleon of 7.7GeV. This also constrains the energy region for the "turning point" where the polarization is supposed to decrease and yield zero at even smaller collision energies. Furthermore, the high statistics of the Ag+Ag run allowed to perform a differential analysis of the Λ polarization as a function of centrality, rapidity and transverse momentum. The results are compared to theoretical predictions based on a direct link of the Λ spin vector and thermal vorticity. The input of the velocity fields and the temperature were taken from the UrQMD transport model. The calculations are in agreement with the measured data and also reproduce the differential trends. As these calculations are based on the assumption of local thermodynamic equilibrium including the spin degrees of freedom, this sets restrictions on the equation of state in the baryon dominated energy regime with densities similar to those predicted to occur in compact stellar objects. In addition to the global polarization, which is linked to the gradients in the initial velocity field, the azimuthal anisotropy (directed flow) is related to the initial velocity profile of the Λ has also been studied as a function of the rapidity. The slope at midrapidity has been extracted and found to be 0.388 ± 0.023(stat.) ± 0.038(sys.) in Au+Au and 0.289 ± 0.007(stat.) ± 0.025(sys.) in Ag+Ag collisions. This confirms the increasing trend of the directed flow slope at midrapidity measured by the E895 and STAR collaborations. The results have been compared to protons within the same transverse momentum and centrality range. The slope of the Λ hyperons is observed to be approximately ∼2/3 of the proton slope in line with the measurements from E895, however, in constrast to the recent measurement from the STAR fixed target run at a center-of-mass energy per nucleon of 4.5GeV, where no significant difference has been observed. This is an interesting observation and remains to be understood. This provides challenges to the theory calculations as to understand the underlying effects requires a description of both polarization and directed flow simultaneously for which the HADES measurements provide important input
