Systematics in the global polarization measurements of Λ hyperons with HADES at SIS18

The global polarization of Λ hyperons has been measured in Au+Au and Ag+Ag collisions at √SNN = 2.4 and 2.55 GeV recorded with HADES. An increase of the polarization is observed following the trend measured by the STAR Collaboration. The high statistics Ag+Ag data allowed for differential measurements of the polarization. The study of acceptance effects is very important in the fixed target setup, as the phase-space coverage is not symmetric. These studies are reported together with the evaluation procedure of the systematic uncertainties.

Introduction. In non-central heavy-ion collisions, large orbital angular momenta are created [1] which might manifest itself in a global spin polarization of the produced particles [2,3]. Such a global polarization can be accessed using weak decays of strange hyperons, where the spin direction is transferred to the momentum direction of the decay products. The most abundantly produced hyperons in heavy-ion collisions are Λs. Measurements performed during the beam energy scan phase I by the STAR Collaboration show an increasing trend of the global polarization in Au+Au collisions down to √ s NN = 7.7 GeV [4]. Further measurements by the ALICE and STAR Collaboration confirm the decreasing trend towards higher collision energies [5,6]. The HADES experiment at SIS-18 collected high statistics data samples for the reactions Au+Au at √ s NN = 2.42 and Ag+Ag at 2.55 GeV. A measurement of the global polarization of the Λ hyperons at these lower collision energies provides new insights into the evolution of the angular momentum and the collective behavior of the matter created. Theoretical predictions are not conclusive in this energy range [7][8][9][10]. Measurement technique. The measurement of the global polarization is performed using the decay channel Λ → p + π − in which the proton is preferentially emitted in the spin direction of the Λ hyperon. Hence, the polarization P Λ is connected to the momentum direction p * p of the proton in the rest frame of the Λ by P Λ = (3/α Λ ) p * p [11]. Here α Λ = 0.732±0.014 [12] is the decay parameter quantifying the emission probability of the proton along the spin direction of the Λ hyperon and . denotes the average over all Λ decays. The direction of the orbital angular momentum is perpendicular to the reaction plane, spanned by the impact parameter of the colliding nuclei and the beam direction. It can be defined by a single azimuthal angle Ψ RP in the laboratory frame which is estimated from a Q-vector analysis using the spectator distributions [13,14]. The result of this procedure is the so-called event plane angle Ψ EP . This can be used to express the polarization in terms of azimuthal angles by integrating over the polar angle and assuming perfect detector acceptance [11]: Due to the finite resolution of the event plane reconstruction, the associated reduction of the measured correlation has to be taken into account by introducing the event plane resolution correction R EP [14]. The event plane and its resolution are determined for the HADES detector [15] as described in [16]. The reconstruction of the Λ hyperons in HADES is done by identifying their its decay topology in a multi-variate analysis. The polarization signal is extracted with the invariant mass method. More details can be found in [17].
Efficiency correction. The efficiency map for the reconstruction of Λ hyperons in HADES in transverse momentum and rapidity space is shown in the left panel of Fig. 1(bottom). As only relative changes are important for the averaged polarization observable, for application the efficiencies are rescaled to the weighted mean efficiency. The Λ hyperons reconstructed in the experimental data as displayed in the left panel of Fig. 1(top) are used as weights. To minimize effects related to the finite binning, a Savitzky-Golay filter is used in addition [18].
Radial distance asymmetry (RDA) correction. A strong dependence of the extracted polarization signal has been observed on the proton radial distance R p . The R p is a signed value, calculated as the minimum distance of the proton track to a straight line parallel to the beam axis through the event vertex of the collision. The sign is determined by the cross product between the minimum distance vector and the track direction. The same dependence could be reproduced using Monte-Carlo simulations with polarized Λ hyperons and a multidifferential flow pattern. However, the signal distribution as a function of R p is not symmetric around zero in the experiment in contrast to the simulations. A data driven approach has been developed to correct for this asymmetry. Therefore, the distribution is divided into a finite amount of bins which are weighted in order to restore the symmetry of the distribution. The application of the same weights to the polarization observable results in a slight increase of the extracted signal value by ∼ 8 % consistently for both, Au+Au and Ag+Ag. Variations of the correction procedure, in an extreme scenario by flattening the distribution of R p , give consistent results within statistical uncertainties.
Acceptance effects. The phase-space coverage in fixed target experiments is usually not symmetric as displayed in the left panel of Fig. 1. To study the acceptance effects in more detail, Monte-Carlo simulations with polarized Λ hyperons are used. The flow pattern for the directed and elliptic flow has been implemented in addition according to the experimentally measured values. Different input values have been tested for the Λ polarization. For the different samples the input value could be reconstructed within statistical uncertainties as summarized in the right panel of Fig. 1. A non-zero background polarization is extracted which qualitatively matches the observations in the experimental data. It could be traced back to a mis-matching of π − from polarized Λ hyperons with primary protons. However, the effect on the polarization extraction is negligible.
In summary, the global polarization of Λ hyperons has been measured in Au+Au and Ag+Ag collisions at √ s NN = 2.4 and 2.55 GeV with the fixed-target experiment HADES. Acceptance effects have been studied using experimental data but also Monte-Carlo simulations. An effect related to the direction of the proton tracks has been studied and an experimental approach has been developed to correct for it. The appearance of a background correlation in the experimental data could be qualitatively reproduced in the simulations and is found to be insignificant for the signal extraction. A detailed study of the systematic uncertainties has been performed using the Barlow criterion to identify relevant contributions beyond statistical fluctuations. For the Ag+Ag data, the global polarization has been extracted differentially as a function of centrality, rapidity and transverse momentum. Overall, the increasing trend towards lower collision energies observed by STAR is found to continue down to √ s NN