Global polarization of Ξ and Ω hyperons in Au+Au collisions at \sqrt{s_{_{NN}}} = 200 GeV
STAR Collaboration, J. Adam, L. Adamczyk, J. R. Adams, J. K. Adkins, G. Agakishiev, M. M. Aggarwal, Z. Ahammed, I. Alekseev, D. M. Anderson, A. Aparin, E. C. Aschenauer, M. U. Ashraf, F. G. Atetalla, A. Attri, G. S. Averichev, V. Bairathi, K. Barish, A. Behera, R. Bellwied, A. Bhasin, J. Bielcik, J. Bielcikova, L. C. Bland, I. G. Bordyuzhin, J. D. Brandenburg, A. V. Brandin, J. Butterworth, H. Caines, M. Calderón de la Barca Sánchez, D. Cebra, I. Chakaberia, P. Chaloupka, B. K. Chan, F-H. Chang, Z. Chang, N. Chankova-Bunzarova, A. Chatterjee, D. Chen, J. Chen, J. H. Chen, X. Chen, Z. Chen, J. Cheng, M. Cherney, M. Chevalier, S. Choudhury, W. Christie, X. Chu, H. J. Crawford, M. Csanád, M. Daugherity, T. G. Dedovich, I. M. Deppner, A. A. Derevschikov, L. Didenko, X. Dong, J. L. Drachenberg, J. C. Dunlop, T. Edmonds, N. Elsey, J. Engelage, G. Eppley, S. Esumi, O. Evdokimov, A. Ewigleben, O. Eyser, R. Fatemi, S. Fazio, P. Federic, J. Fedorisin, C. J. Feng, Y. Feng, P. Filip, E. Finch, Y. Fisyak, A. Francisco, L. Fulek, C. A. Gagliardi, T. Galatyuk, F. Geurts, N. Ghimire, A. Gibson, K. Gopal, X. Gou, D. Grosnick, W. Guryn, A. I. Hamad, A. Hamed, S. Harabasz, J. W. Harris, S. He, W. He, X. H. He, Y. He, S. Heppelmann, S. Heppelmann, N. Herrmann, E. Hoffman, L. Holub, et al. (271 additional authors not shown)
GGlobal polarization of Ξ and Ω hyperons in Au+Au collisions at √ s NN = 200 GeV J. Adam, L. Adamczyk, J. R. Adams, J. K. Adkins, G. Agakishiev, M. M. Aggarwal, Z. Ahammed, I. Alekseev,
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D. M. Anderson, A. Aparin, E. C. Aschenauer, M. U. Ashraf, F. G. Atetalla, A. Attri, G. S. Averichev, V. Bairathi, K. Barish, A. Behera, R. Bellwied, A. Bhasin, J. Bielcik, J. Bielcikova, L. C. Bland, I. G. Bordyuzhin, J. D. Brandenburg, A. V. Brandin, J. Butterworth, H. Caines, M. Calder´on de la Barca S´anchez, D. Cebra, I. Chakaberia,
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P. Chaloupka, B. K. Chan, F-H. Chang, Z. Chang, N. Chankova-Bunzarova, A. Chatterjee, D. Chen, J. Chen, J. H. Chen, X. Chen, Z. Chen, J. Cheng, M. Cherney, M. Chevalier, S. Choudhury, W. Christie, X. Chu, H. J. Crawford, M. Csan´ad, M. Daugherity, T. G. Dedovich, I. M. Deppner, A. A. Derevschikov, L. Didenko, X. Dong, J. L. Drachenberg, J. C. Dunlop, T. Edmonds, N. Elsey, J. Engelage, G. Eppley, S. Esumi, O. Evdokimov, A. Ewigleben, O. Eyser, R. Fatemi, S. Fazio, P. Federic, J. Fedorisin, C. J. Feng, Y. Feng, P. Filip, E. Finch, Y. Fisyak, A. Francisco, L. Fulek, C. A. Gagliardi, T. Galatyuk, F. Geurts, N. Ghimire, A. Gibson, K. Gopal, X. Gou, D. Grosnick, W. Guryn, A. I. Hamad, A. Hamed, S. Harabasz, J. W. Harris, S. He, W. He, X. H. He, Y. He, S. Heppelmann, S. Heppelmann, N. Herrmann, E. Hoffman, L. Holub, Y. Hong, S. Horvat, Y. Hu, H. Z. Huang, S. L. Huang, T. Huang, X. Huang, T. J. Humanic, P. Huo, G. Igo, D. Isenhower, W. W. Jacobs, C. Jena, A. Jentsch, Y. Ji, J. Jia,
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K. Jiang, S. Jowzaee, X. Ju, E. G. Judd, S. Kabana, M. L. Kabir, S. Kagamaster, D. Kalinkin, K. Kang, D. Kapukchyan, K. Kauder, H. W. Ke, D. Keane, A. Kechechyan, M. Kelsey, Y. V. Khyzhniak, D. P. Kiko(cid:32)la, C. Kim, B. Kimelman, D. Kincses, T. A. Kinghorn, I. Kisel, A. Kiselev, M. Kocan, L. Kochenda, L. K. Kosarzewski, L. Kramarik, P. Kravtsov, K. Krueger, N. Kulathunga Mudiyanselage, L. Kumar, S. Kumar, R. Kunnawalkam Elayavalli, J. H. Kwasizur, R. Lacey, S. Lan, J. M. Landgraf, J. Lauret, A. Lebedev, R. Lednicky, J. H. Lee, Y. H. Leung, C. Li, C. Li, W. Li, W. Li, X. Li, Y. Li, Y. Liang, R. Licenik, T. Lin, Y. Lin, M. A. Lisa, F. Liu, H. Liu, P. Liu, P. Liu, T. Liu, X. Liu, Y. Liu, Z. Liu, T. Ljubicic, W. J. Llope, R. S. Longacre, N. S. Lukow, S. Luo, X. Luo, G. L. Ma, L. Ma, R. Ma, Y. G. Ma, N. Magdy, R. Majka, D. Mallick, S. Margetis, C. Markert, H. S. Matis, J. A. Mazer, N. G. Minaev, S. Mioduszewski, B. Mohanty, I. Mooney, Z. Moravcova, D. A. Morozov, M. Nagy, J. D. Nam, Md. Nasim, K. Nayak, D. Neff, J. M. Nelson, D. B. Nemes, M. Nie, G. Nigmatkulov, T. Niida, L. V. Nogach, T. Nonaka, A. S. Nunes, G. Odyniec, A. Ogawa, S. Oh, V. A. Okorokov, B. S. Page, R. Pak, A. Pandav, Y. Panebratsev, B. Pawlik, D. Pawlowska, H. Pei, C. Perkins, L. Pinsky, R. L. Pint´er, J. Pluta, B. R. Pokhrel, J. Porter, M. Posik, N. K. Pruthi, M. Przybycien, J. Putschke, H. Qiu, A. Quintero, S. K. Radhakrishnan, S. Ramachandran, R. L. Ray, R. Reed, H. G. Ritter, O. V. Rogachevskiy, J. L. Romero, L. Ruan, J. Rusnak, N. R. Sahoo, H. Sako, S. Salur, J. Sandweiss, S. Sato, W. B. Schmidke, N. Schmitz, B. R. Schweid, F. Seck, J. Seger, M. Sergeeva, R. Seto, P. Seyboth, N. Shah, E. Shahaliev, P. V. Shanmuganathan, M. Shao, A. I. Sheikh, W. Q. Shen, S. S. Shi, Y. Shi, Q. Y. Shou, E. P. Sichtermann, R. Sikora, M. Simko, J. Singh, S. Singha, N. Smirnov, W. Solyst, P. Sorensen, H. M. Spinka, B. Srivastava, T. D. S. Stanislaus, M. Stefaniak, D. J. Stewart, M. Strikhanov, B. Stringfellow, A. A. P. Suaide, M. Sumbera, B. Summa, X. M. Sun, X. Sun, Y. Sun, Y. Sun, B. Surrow, D. N. Svirida, P. Szymanski, A. H. Tang, Z. Tang, A. Taranenko, T. Tarnowsky, J. H. Thomas, A. R. Timmins, D. Tlusty, M. Tokarev, C. A. Tomkiel, S. Trentalange, R. E. Tribble, P. Tribedy, S. K. Tripathy, O. D. Tsai, Z. Tu, T. Ullrich, D. G. Underwood, I. Upsal,
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G. Van Buren, J. Vanek, A. N. Vasiliev, I. Vassiliev, F. Videbæk, S. Vokal, S. A. Voloshin, F. Wang, G. Wang, J. S. Wang, P. Wang, Y. Wang, Y. Wang, Z. Wang, J. C. Webb, P. C. Weidenkaff, L. Wen, G. D. Westfall, H. Wieman, S. W. Wissink, R. Witt, Y. Wu, Z. G. Xiao, G. Xie, W. Xie, H. Xu, N. Xu, Q. H. Xu, Y. F. Xu, Y. Xu, Z. Xu, Z. Xu, C. Yang, Q. Yang, S. Yang, Y. Yang, Z. Yang, Z. Ye, Z. Ye, L. Yi, K. Yip, Y. Yu, H. Zbroszczyk, W. Zha, C. Zhang, D. Zhang, S. Zhang, S. Zhang, X. P. Zhang, Y. Zhang, Y. Zhang, Z. J. Zhang, Z. Zhang, Z. Zhang, J. Zhao, C. Zhong, C. Zhou, X. Zhu, Z. Zhu, M. Zurek, and M. Zyzak (STAR Collaboration) a r X i v : . [ nu c l - e x ] D ec Abilene Christian University, Abilene, Texas 79699 AGH University of Science and Technology, FPACS, Cracow 30-059, Poland Alikhanov Institute for Theoretical and Experimental Physics NRC ”Kurchatov Institute”, Moscow 117218, Russia Argonne National Laboratory, Argonne, Illinois 60439 American University of Cairo, New Cairo 11835, New Cairo, Egypt Brookhaven National Laboratory, Upton, New York 11973 University of California, Berkeley, California 94720 University of California, Davis, California 95616 University of California, Los Angeles, California 90095 University of California, Riverside, California 92521 Central China Normal University, Wuhan, Hubei 430079 University of Illinois at Chicago, Chicago, Illinois 60607 Creighton University, Omaha, Nebraska 68178 Czech Technical University in Prague, FNSPE, Prague 115 19, Czech Republic Technische Universit¨at Darmstadt, Darmstadt 64289, Germany ELTE E¨otv¨os Lor´and University, Budapest, Hungary H-1117 Frankfurt Institute for Advanced Studies FIAS, Frankfurt 60438, Germany Fudan University, Shanghai, 200433 University of Heidelberg, Heidelberg 69120, Germany University of Houston, Houston, Texas 77204 Huzhou University, Huzhou, Zhejiang 313000 Indian Institute of Science Education and Research (IISER), Berhampur 760010 , India Indian Institute of Science Education and Research (IISER) Tirupati, Tirupati 517507, India Indian Institute Technology, Patna, Bihar 801106, India Indiana University, Bloomington, Indiana 47408 Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, Gansu 730000 University of Jammu, Jammu 180001, India Joint Institute for Nuclear Research, Dubna 141 980, Russia Kent State University, Kent, Ohio 44242 University of Kentucky, Lexington, Kentucky 40506-0055 Lawrence Berkeley National Laboratory, Berkeley, California 94720 Lehigh University, Bethlehem, Pennsylvania 18015 Max-Planck-Institut f¨ur Physik, Munich 80805, Germany Michigan State University, East Lansing, Michigan 48824 National Research Nuclear University MEPhI, Moscow 115409, Russia National Institute of Science Education and Research, HBNI, Jatni 752050, India National Cheng Kung University, Tainan 70101 Nuclear Physics Institute of the CAS, Rez 250 68, Czech Republic Ohio State University, Columbus, Ohio 43210 Institute of Nuclear Physics PAN, Cracow 31-342, Poland Panjab University, Chandigarh 160014, India Pennsylvania State University, University Park, Pennsylvania 16802 NRC ”Kurchatov Institute”, Institute of High Energy Physics, Protvino 142281, Russia Purdue University, West Lafayette, Indiana 47907 Rice University, Houston, Texas 77251 Rutgers University, Piscataway, New Jersey 08854 Universidade de S˜ao Paulo, S˜ao Paulo, Brazil 05314-970 University of Science and Technology of China, Hefei, Anhui 230026 Shandong University, Qingdao, Shandong 266237 Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800 Southern Connecticut State University, New Haven, Connecticut 06515 State University of New York, Stony Brook, New York 11794 Instituto de Alta Investigaci´on, Universidad de Tarapac´a, Arica 1000000, Chile Temple University, Philadelphia, Pennsylvania 19122 Texas A&M University, College Station, Texas 77843 University of Texas, Austin, Texas 78712 Tsinghua University, Beijing 100084 University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan United States Naval Academy, Annapolis, Maryland 21402 Valparaiso University, Valparaiso, Indiana 46383 Variable Energy Cyclotron Centre, Kolkata 700064, India Warsaw University of Technology, Warsaw 00-661, Poland Wayne State University, Detroit, Michigan 48201 Yale University, New Haven, Connecticut 06520 (Dated: December 29, 2020)Global polarization of Ξ and Ω hyperons has been measured for the first time in Au+Au collisionsat √ s NN = 200 GeV. The measurements of the Ξ − and ¯Ξ + hyperon polarization have been performedby two independent methods, via analysis of the angular distribution of the daughter particlesin the parity violating weak decay Ξ → Λ + π , as well as by measuring the polarization of thedaughter Λ-hyperon, polarized via polarization transfer from its parent. The polarization, obtainedby combining the results from the two methods and averaged over Ξ − and Ξ + , is measured to be (cid:104) P Ξ (cid:105) = 0 . ± .
10 (stat . ) ± .
23 (syst . ) % for the collision centrality 20%-80%. The (cid:104) P Ξ (cid:105) is found tobe slightly larger than the inclusive Λ polarization and in reasonable agreement with a multi-phasetransport model (AMPT). The (cid:104) P Ξ (cid:105) is found to follow the centrality dependence of the vorticitypredicted in the model, increasing toward more peripheral collisions. The global polarization of Ω, (cid:104) P Ω (cid:105) = 1 . ± .
87 (stat . ) ± .
97 (syst . ) % was obtained by measuring the polarization of daughterΛ in the decay Ω → Λ + K , assuming the polarization transfer factor C ΩΛ = 1. PACS numbers: 25.75.-q, 25.75.Ld, 24.70.+s
The phenomenon of global polarization in heavy-ioncollisions arises from the partial conversion of the orbitalangular momentum of colliding nuclei into the spin an-gular momentum of the particles produced in the colli-sion [1–4]. As a result, these particles become globallypolarized along the direction of the initial orbital mo-mentum of the nuclei. Global polarization was first ob-served by the STAR Collaboration in the beam energyscan Au+Au collisions [5] and was later confirmed, tobetter precision, in the analysis of the 200 GeV data withhigh statistics [6]. Assuming local thermal equilibrium,the polarization of the produced particles is determinedby the local thermal vorticity of the fluid [3]. In the non-relativistic limit (for hyperons m H (cid:29) T , where T is thetemperature), the polarization of the particles is givenby [7]: P = (cid:104) s (cid:105) s ≈ ( s + 1)3 ω T , (1)where s is the spin of the particle, (cid:104) s (cid:105) is the mean spinvector, and ω = ∇ × v is the local vorticity of the fluidvelocity field. Averaged over the entire system volume,the vorticity direction should coincide with the directionof the system orbital momentum.Following from Eq. 1, all particles, as well as antipar-ticles of the same spin should have the same polariza-tion. A difference could arise from effects of the initialmagnetic field [7], from the fact that different particlesare produced at different times or regions as the systemfreezes out [8], or through meson-baryon interactions [9].Therefore, to establish the global nature of the polar-ization, it is important to measure the polarization fordifferent particles, and if possible, particles of differentspins. In order to study the possible contribution fromthe initial magnetic field, the polarization measurementwith particles of different magnetic moment would pro-vide additional information. Thus far, only Λ and ¯Λ po-larizations have been measured [5, 6, 10], and they differby a couple of standard deviations at most, with availablestatistics.In this paper we present the first measurements of the global polarization of spin s = 1 / − and ¯Ξ + hyperons,as well as spin s = 3 / √ s NN =200 GeV.Hyperon weak decays present the most straightforwardpossibility for measuring the polarization of the producedparticles [11]. In parity-violating weak decays the daugh-ter particle distribution in the rest frame of the hyperondirectly depends on the hyperon polarization: dNd Ω ∗ = 14 π (1 + α H P ∗ H · ˆ p ∗ B ) , (2)where α H is the hyperon decay parameter, P ∗ H is thehyperon polarization, and ˆ p ∗ B is the unit vector in thedirection of the daughter baryon momentum, both in theparent rest frame denoted by an asterisk.Ξ − (¯Ξ + ) hyperon decay happens in two steps: Ξ − → Λ + π − with subsequent decay Λ → p + π − . If Ξ − ispolarized, its polarization is partially transferred to thedaughter Λ. Both steps in such a cascade decay are par-ity violating and thus can be used for an independentmeasurement of the polarization of Ξ − (¯Ξ + ).The polarization of the daughter baryon in a weak de-cay of a spin 1/2 hyperon is described by the Lee-Yangformula [12–14] in terms of the three parameters α (parityviolating part), β (violation of the time reversal symme-try), and γ (satisfying α + β + γ = 1). For a particularcase of Ξ → Λ + π decay it reads: P ∗ Λ = ( α Ξ + P ∗ Ξ · ˆ p ∗ Λ ) ˆ p ∗ Λ + β Ξ P ∗ Ξ × ˆ p ∗ Λ + γ Ξ ˆ p ∗ Λ × ( P ∗ Ξ × ˆ p ∗ Λ )1 + α Ξ P ∗ Ξ · ˆ p ∗ Λ , (3)where ˆ p ∗ Λ is the unit vector of the Λ momentum in theΞ rest frame. Averaging over the angular distribution ofthe Λ in the rest frame of the Ξ given by Eq. 2 yields P ∗ Λ = C Ξ − Λ P ∗ Ξ = (1 + 2 γ Ξ ) P ∗ Ξ . (4)Using the measured value for the γ Ξ parameter [14, 15],the polarization transfer coefficient for Ξ − to Λ decay is: C Ξ − Λ = (1 + 2 × . . . (5)The polarization of the daughter baryon in a two par-ticle decay of spin 3 / → Λ + K , is alsodescribed by three parameters α Ω , β Ω , and γ Ω [16]. Thedecay parameter α Ω , determines the angular distributionof Λ in the Ω rest frame and is measured to be small [15]: α Ω = 0 . ± . γ Ω parameter via [16–18]: P ∗ Λ = C Ω − Λ P ∗ Ω = (1 + 4 γ Ω ) P ∗ Ω . (6)The time-reversal violation parameter β Ω is expected tobe small. This combined with the constraint that α + β + γ = 1 limits the unmeasured parameter to γ Ω ≈ ± C Ω − Λ ≈ C Ω − Λ ≈− . √ s NN = 200 GeV collected in 2010, 2011, 2014, and2016 by the STAR detector. Charged-particle tracks weremeasured in the time projection chamber (TPC) [19],which covers the full azimuth and a pseudorapidity rangeof | η | <
1. The collision vertices were reconstructed usingthe measured charged-particle tracks and were requiredto be within 30 cm relative to the TPC center in thebeam direction for the 2010 and 2011 datasets to ensurea good acceptance of reconstructed tracks. The narrowervertex selection to be within 6 cm was applied in the 2014and 2016 data due to online trigger requirement for theHeavy Flavor Tracker installed prior to 2014 data tak-ing. The vertex in the radial direction relative to thebeam center was also required to be within 2 cm to re-ject background from collisions with beam pipe. Ad-ditionally, the difference in the vertex positions alongthe beam direction from the vertex position detectors(VPD) [20] located at forward and backward pseudo-rapidities (4 . < | η | < .
1) was required to be lessthan 3 cm to suppress pileup events in which more thanone heavy-ion collision occurred. These selection crite-ria yielded about 180 (350) million minimum bias (MB)events for the 2010 (2011) dataset, 1 billion MB eventsfor the 2014 dataset, and 1.5 billion MB events for the2016 dataset. The MB trigger requires hits of both VPDsand the zero-degree calorimeters (ZDCs) [21], which de-tect spectator neutrons in | η | > .
3. The collision cen-trality was determined from the measured multiplicityof charged particles within | η | < . as an exper-imental estimate of the impact parameter direction wasdetermined by measuring the neutron spectator deflec-tion [24] in the ZDCs equipped with Shower MaximumDetectors (SMD) [25–27]. The event plane resolution [28]is largest ( ∼ ] [GeV/c πΛ M × = 200 GeV NN sSTAR Au+Au 20%-80%year2014 - Ξ + Ξσ ] [GeV/c K Λ M - Ω + Ω |y|<1>0.5 GeV/c T p FIG. 1. (Color online) Invariant mass distributions of Ξ − (¯Ξ + ) and Ω − ( ¯Ω + ) for 20%-80% centrality in Au+Au colli-sions at √ s NN = 200 GeV taken in 2014. Vertical dashedlines indicate three standard deviations (3 σ ) from the peakpositions, assuming a normal distribution. The parent Ξ − (¯Ξ + ), Ω − ( ¯Ω + ), and their daughterΛ (¯Λ) were reconstructed utilizing the decay channelsof Ξ − → Λ π − (99.887%), Ω − → Λ K − (67.8%), andΛ → pπ − (63.9%), where the numbers in parenthesisindicate the corresponding branching ratio of the de-cays [15]. Charged pions (kaons) and protons of thedaughter particles were identified based on the ioniza-tion energy loss in the TPC gas, and the timing infor-mation measured by the Time-Of-Flight detector [29].Reconstruction of Ξ − (¯Ξ + ), Ω − ( ¯Ω + ), and Λ (¯Λ) wasperformed using the KF Particle Finder package basedon the Kalman Filter method initially developed for theCBM and ALICE experiments [30–32], which utilizes thequality of the track fit as well as the decay topology.Figure 1 shows the invariant mass distributions for re-constructed Ξ − (¯Ξ + ) and Ω − ( ¯Ω + ) for 20%-80% central-ity. The purities for this centrality bin are higher than90% for both species. The significance with the KalmanFilter method is found to be increased by ∼
30% for Ξcompared to the traditional method for reconstruction ofshort-lived particles (e.g. see Refs. [6, 33]). The hyperoncandidates were also ensured not to share their decayproducts with other particles of interest.The polarization along the initial angular momentumdirection can be defined as [34]: P H = 8 πα H (cid:104) sin(Ψ obs1 − φ ∗ B ) (cid:105) Res(Ψ ) , (7)where α H is the hyperon decay parameter and φ ∗ B is theazimuthal angle of the daughter baryon in the parent hy-peron rest frame. The azimuthal angle of the first-orderevent plane is Ψ obs1 , and Res(Ψ ) is the resolution [28]with which it estimates the reaction plane.The extraction of (cid:104) sin(Ψ obs1 − φ ∗ ) (cid:105) was performed inthe same way as in our previous studies [5, 6]. The decayparameters of Λ, Ξ − , and Ω − have been recently updatedby the Particle Data Group [15] and the latest values areused in this analysis; α Λ = 0 . ± . α Ξ = − . ± . α Ω = 0 . ± . α old /α new . In case of the Ξ andΩ hyperon polarization measurements via measurementsof the daughter Λ polarization, the polarization transferfactors C ΞΛ(ΩΛ) from Eqs. 4 and 6 are used to obtain theparent polarization.The largest systematic uncertainty (37%) was at-tributed to the variation of the results obtained withdatasets taken in different years. Weighted average overdifferent datasets was used as the final result, and allother systematic uncertainties were assessed based onthe weighted average: by comparing different polariza-tion signal extractions [6] (11%), by varying the masswindow for particles of interest from 3 σ to 2 σ (15%), byvarying the decay lengths of both parent and daughterhyperons (4%), and by considering uncertainties on thedecay parameter α H (2%), where the numbers in paren-theses represent the uncertainty for the Ξ polarizationvia the daughter Λ polarization measurement. A correc-tion for non-uniform acceptance effects [34] was appliedfor the appropriate detector configuration for the givendataset. This correction, depending on particle species,was less than 2%. Due to a weak p T dependence on theglobal polarization [6], effects from the p T dependent ef-ficiency of the hyperon reconstruction were found to benegligible.Figure 2 shows the collision energy dependence of the Λhyperon global polarization measured earlier [5, 6, 10, 34]together with the new results on Ξ and Ω global polar-izations at √ s NN = 200 GeV. (Note that the statisti-cal and systematic uncertainties for the Λ are smallerthan the symbol size.) For both Ξ and Ω polariza-tions, the particle and antiparticle results are averagedto reduce the statistical uncertainty. Also to maxi-mize the significance of the polarization signal, the re-sults were integrated over the centrality range 20%-80%, transverse momentum p T > . c , and ra-pidity | y | <
1. Global polarization of Ξ − and ¯Ξ + measurements via daughter Λ polarization show posi-tive values, with no significant difference between Ξ − and ¯Ξ + ( P Ξ (%) = 0 . ± .
16 (stat . ) ± .
49 (syst . )and P ¯Ξ (%) = 0 . ± .
16 (stat . ) ± .
20 (syst . )). Theaverage polarization value obtained by this method is (cid:104) P Ξ (cid:105) (%) = 0 . ± .
11 (stat . ) ± .
26 (syst . ). The Ξ + ¯Ξpolarization was also measured via analysis of the an-gular distribution of daughter Λ in Ξ rest frame. Thisresult, (cid:104) P Ξ (cid:105) (%) = − . ± .
19 (stat . ) ± .
50 (syst . ), haslarger uncertainty in part due to a smaller value of α Ξ compared to α Λ , which leads to smaller sensitivity of themeasurement. The weighted average of the two measure-ments is (cid:104) P Ξ (cid:105) (%) = 0 . ± .
10 (stat . ) ± .
23 (syst . ),which is larger than the polarization of inclusive Λ +¯Λmeasured at the same energy for 20%-80% centrality, (cid:104) P Λ (cid:105) (%) = 0 . ± . ± .
03 [6], although the difference [GeV] NN s - [ % ] H P STAR Au+Au 20%-50% – (7.7)=7.34 L P Nature548.62 (2017) L L PRC76.024915 (2007) L L PRC98.014910 (2018) L L ) H P L (via daughter + X + - X + X + - X STAR Au+Au 20%-80% ) H P L (via daughter + W + - W PRC101.044611 (2020) L L ALICE Pb+Pb 15-50%AMPT PRC99, 014905 (2019) L + L X - W – = 0.732 L a – = -0.758 L a – = -0.401 + X a = - - X a = 1 W g FIG. 2. (Color online) The energy dependence of the hy-peron global polarization measurements. The points corre-sponding to Λ and ¯Λ polarizations, as well as Ξ and Ω pointsin Au+Au collisions at √ s NN = 200 GeV are slightly shiftedfor clarity. Previous results from the STAR [5, 6, 34] andALICE [10] experiments compared here are rescaled by newdecay parameter indicated inside the figure. The data pointfor ¯Λ at 7.7 GeV is out of the axis range and indicated byan arrow with the value. The results of the AMPT modelcalculations [35] for 20-50% centrality are shown by shadedbands where the band width corresponds to the uncertaintyof the calculations. is still not significant considering the statistical and sys-tematic uncertainties of both measurements. Note thatthe above quoted values for the inclusive Λ have beenrescaled by the new decay parameter as mentioned ear-lier.Calculations [35] carried out with a multi-phase trans-port model (AMPT) can describe the particle species de-pendence in data at 200 GeV as well as the energy depen-dence for Λ. These calculations indicate that the lighterparticles with higher spin could be more polarized by thevorticity [35]. The multi-strange particles might freezeout at earlier times, which may lead to larger polariza-tion for Ξ and Ω compared to Λ [8]. The feed-down effectcan also lead to a 15 ∼
20% reduction of the primary Λpolarization [7, 36–38], while the Ξ has less contributionfrom the feed-down. All these effects can contribute tosmall differences in the measured polarizations betweeninclusive Λ and Ξ hyperons.Global polarization of Ω − was also measured and ispresented in Fig. 2 under the assumption of γ Ω = +1and therefore C ΩΛ = 1, as discussed with respect toEq. 6. The result has large uncertainty, (cid:104) P Ω (cid:105) (%) =1 . ± .
87 (stat . ) ± .
97 (syst . ) for 20%-80% centrality.Assumption of γ Ω = − C ΩΛ = − .
6) resultsin (cid:104) P Ω (cid:105) (%) = − . ± .
52 (stat . ) ± .
18 (syst . ). Assum-ing the validity of the global polarization picture, the Centrality [%] [ % ] H P STAR = 200 GeV NN sAu+Au >0.5 Ξ T |<1, p Ξ |y (PRC98.014910) Λ Inclusive ) H P Λ (via daughter + Ξ + - Ξ syst. uncert. ± = 0.732 Λ α ± = -0.758 Λ α = 0.944 ΛΞ C FIG. 3. (Color online) The global polarization of Ξ hyperonsobtained via measurements of the polarization of daughter Λhyperons as a function of the collision centrality in Au+Aucollisions at √ s NN = 200 GeV. Open boxes show the sys-tematic uncertainties. Results for the inclusive Λ measure-ments [6] are shown for comparison. result favors γ Ω ≈ +1 instead of γ Ω ≈ −
1, but the un-certainties are large and more precise measurements areneeded to make a definitive statement.The centrality dependence of Ξ + ¯Ξ polarization viathe measurement of daughter Λ polarization is shown inFig. 3, where the inclusive Λ polarization [6] is plottedfor comparison. The hyperon polarization increases inmore peripheral collisions as expected from the central-ity dependence of the fluid vorticity [39, 40]. The Ξ po-larization looks larger than that of the inclusive Λ inperipheral collisions as already discussed in relation toFig. 2, although the uncertainties preclude a more defi-nite conclusion.In summary, we have presented the first measure-ments of the global polarization for Ξ − (¯Ξ + ) hyperonsin Au+Au collisions at √ s NN = 200 GeV. Our results ofΞ hyperon polarization, along with the previous measure-ments of Λ polarization, confirm the global polarizationpicture based on the system fluid vorticity. The averagepolarization of Ξ + ¯Ξ seems to be larger than that of theinclusive Λ, which is qualitatively captured by the AMPTmodel. The measured polarization seems to exhibit acentrality dependence as expected from the impact pa-rameter dependence of the vorticity. Global polarizationof Ω − hyperons was, also for the first time, extractedvia measurements of the polarization of the daughter Λand presented with the assumption that γ Ω = +1. Fu- ture measurements with higher precision will shed lighton the uncertainty of the decay parameter γ Ω , as well asexperimental results on the global polarization of spin-3/2 particles, providing critical information about spindynamics in heavy-ion collisions.We thank the RHIC Operations Group and RCF atBNL, the NERSC Center at LBNL, and the Open Sci-ence Grid consortium for providing resources and sup-port. This work was supported in part by the Officeof Nuclear Physics within the U.S. DOE Office of Sci-ence, the U.S. National Science Foundation, the Min-istry of Education and Science of the Russian Federa-tion, National Natural Science Foundation of China, Chi-nese Academy of Science, the Ministry of Science andTechnology of China and the Chinese Ministry of Educa-tion, the Higher Education Sprout Project by Ministryof Education at NCKU, the National Research Founda-tion of Korea, Czech Science Foundation and Ministryof Education, Youth and Sports of the Czech Republic,Hungarian National Research, Development and Innova-tion Office, New National Excellency Programme of theHungarian Ministry of Human Capacities, Departmentof Atomic Energy and Department of Science and Tech-nology of the Government of India, the National ScienceCentre of Poland, the Ministry of Science, Education andSports of the Republic of Croatia, RosAtom of Russia andGerman Bundesministerium fur Bildung, Wissenschaft,Forschung and Technologie (BMBF), Helmholtz Associ-ation, Ministry of Education, Culture, Sports, Science,and Technology (MEXT) and Japan Society for the Pro-motion of Science (JSPS). 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