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Pattern of global spin alignment of ϕ and K*0 mesons in heavy-ion collisions

Nature volume 614, pages 244–248 (2023)Cite this article

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Abstract

Notwithstanding decades of progress since Yukawa first developed a description of the force between nucleons in terms of meson exchange1, a full understanding of the strong interaction remains a considerable challenge in modern science. One remaining difficulty arises from the non-perturbative nature of the strong force, which leads to the phenomenon of quark confinement at distances on the order of the size of the proton. Here we show that, in relativistic heavy-ion collisions, in which quarks and gluons are set free over an extended volume, two species of produced vector (spin-1) mesons, namely ϕ and K*0, emerge with a surprising pattern of global spin alignment. In particular, the global spin alignment for ϕ is unexpectedly large, whereas that for K*0 is consistent with zero. The observed spin-alignment pattern and magnitude for ϕ cannot be explained by conventional mechanisms, whereas a model with a connection to strong force fields2,3,4,5,6, that is, an effective proxy description within the standard model and quantum chromodynamics, accommodates the current data. This connection, if fully established, will open a potential new avenue for studying the behaviour of strong force fields.

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Fig. 1: A schematic view of the coordinate setup for measuring global spin alignment in heavy-ion collisions.
Fig. 2: Schematic display of a single Au+Au collision at \(\sqrt{{{\boldsymbol{s}}}_{{\bf{NN}}}}{\boldsymbol{=}}{\bf{27}}\,{\bf{GeV}}\) in the STAR detector.
Fig. 3: Global spin alignment of ϕ and K*0 vector mesons in heavy-ion collisions.

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Data availability

All raw data for this study were collected using the STAR detector at Brookhaven National Laboratory and are not available to the public. Derived data supporting the findings of this study are publicly available in the HEPData repository (https://www.hepdata.net/record/129067) or from the corresponding author on request.

Code availability

Codes to process raw data collected by the STAR detector and codes to analyse the produced data are not available to the public.

References

  1. Yukawa, H. On the interaction of elementary particles. I. Proc. Phys. Math. Soc. Jpn. 17, 48–57 (1935).

    MATH  Google Scholar 

  2. Sheng, X.-L., Oliva, L. & Wang, Q. What can we learn from the global spin alignment of ϕ mesons in heavy-ion collisions? Phys. Rev. D 101, 096005 (2020).

    Article  ADS  CAS  Google Scholar 

  3. Sheng, X.-L., Oliva, L. & Wang, Q. Erratum: What can we learn from the global spin alignment of ϕ mesons in heavy-ion collisions? Phys. Rev. D 105, 099903 (2022).

    Article  ADS  Google Scholar 

  4. Sheng, X.-L., Wang, Q. & Wang, X.-N. Improved quark coalescence model for spin alignment and polarization of hadrons. Phys. Rev. D 102, 056013 (2020).

    Article  ADS  CAS  Google Scholar 

  5. Sheng, X.-L., Oliva, L., Liang, Z.-T., Wang, Q. & Wang, X.-N. Spin alignment of vector mesons in heavy-ion collisions. Preprint at https://arxiv.org/abs/2205.15689 (2022).

  6. Sheng, X.-L., Oliva, L., Liang, Z.-T., Wang, Q. & Wang, X.-N. Relativistic spin dynamics for vector mesons. Preprint at https://arxiv.org/abs/2206.05868 (2022).

  7. Arsene, I. et al. Quark–gluon plasma and color glass condensate at RHIC? The perspective from the BRAHMS experiment. Nucl. Phys. A 757, 1–27 (2005).

    Article  ADS  Google Scholar 

  8. Back, B. B. et al. The PHOBOS perspective on discoveries at RHIC. Nucl. Phys. A 757, 28–101 (2005).

    Article  ADS  Google Scholar 

  9. Adams, J. et al. Experimental and theoretical challenges in the search for the quark–gluon plasma: the STAR Collaboration’s critical assessment of the evidence from RHIC collisions. Nucl. Phys. A 757, 102–183 (2005).

    Article  ADS  Google Scholar 

  10. Adcox, K. et al. Formation of dense partonic matter in relativistic nucleus–nucleus collisions at RHIC: experimental evaluation by the PHENIX Collaboration. Nucl. Phys. A 757, 184–283 (2005).

    Article  ADS  Google Scholar 

  11. Liang, Z.-T. & Wang, X.-N. Globally polarized quark-gluon plasma in noncentral A + A collisions. Phys. Rev. Lett. 94, 102301 (2005); erratum: 96, 039901(2006).

    Article  ADS  Google Scholar 

  12. Liang, Z.-T. & Wang, X.-N. Spin alignment of vector mesons in non-central A + A collisions. Phys. Lett. B 629, 20–26 (2005).

    Article  ADS  CAS  Google Scholar 

  13. Voloshin, S. A. Polarized secondary particles in unpolarized high energy hadron-hadron collisions? Preprint at https://arxiv.org/abs/nucl-th/0410089 (2004).

  14. Betz, B., Gyulassy, M. & Torrieri, G. Polarization probes of vorticity in heavy ion collisions. Phys. Rev. C 76, 044901 (2007).

    Article  ADS  Google Scholar 

  15. Becattini, F., Piccinini, F. & Rizzo, J. Angular momentum conservation in heavy ion collisions at very high energy. Phys. Rev. C 77, 024906 (2008).

    Article  ADS  Google Scholar 

  16. Gao, J.-H. et al. Global quark polarization in noncentral A + A collisions. Phys. Rev. C 77, 044902 (2008).

    Article  ADS  Google Scholar 

  17. Close, F. E. An Introduction to Quarks and Partons (Academic, 1979).

  18. Adamczyk, L. et al. Global Λ hyperon polarization in nuclear collisions: evidence for the most vortical fluid. Nature 548, 62–65 (2017).

    Article  ADS  CAS  Google Scholar 

  19. Adam, J. et al. Global polarization of Λ hyperons in Au + Au collisions at \(\sqrt{{s}_{NN}}\) = 200 GeV. Phys. Rev. C 98, 014910 (2018).

    Article  ADS  CAS  Google Scholar 

  20. Abdallah, M. S. et al. Global Λ-hyperon polarization in Au + Au collisions at \(\sqrt{{s}_{NN}}\) = 3 GeV. Phys. Rev. C 104, L061901 (2021).

    Article  ADS  CAS  Google Scholar 

  21. Acharya, S. et al. Global polarization of Λ and \(\bar{\Lambda }\) hyperons in Pb-Pb collisions at \(\sqrt{{s}_{NN}}\) = 2.76 and 5.02 TeV. Phys. Rev. C 101, 044611 (2020).

    Article  ADS  CAS  Google Scholar 

  22. Kornas, F. J. Systematics in the global polarization measurements of Λ hyperons with HADES at SIS18. EPJ Web Conf. 259, 11016 (2022).

    Article  CAS  Google Scholar 

  23. Schilling, K., Seyboth, P. & Wolf, G. E. On the analysis of vector-meson production by polarized photons. Nucl. Phys. B 15, 397–412 (1970); erratum 18, 332 (1970).

    Article  ADS  CAS  Google Scholar 

  24. Poskanzer, A. M. & Voloshin, S. A. Methods for analyzing anisotropic flow in relativistic nuclear collisions. Phys. Rev. C 58, 1671–1678 (1998).

    Article  ADS  CAS  Google Scholar 

  25. Yang, Y.-G., Fang, R.-H., Wang, Q. & Wang, X.-N. Quark coalescence model for polarized vector mesons and baryons. Phys. Rev. C 97, 034917 (2018).

    Article  ADS  CAS  Google Scholar 

  26. Xia, X.-L., Li, H., Huang, X.-G. & Zhong Huang, H. Local spin alignment of vector mesons in relativistic heavy-ion collisions. Phys. Lett. B 817, 136325 (2021).

    Article  MathSciNet  CAS  MATH  Google Scholar 

  27. Gao, J.-H. Helicity polarization in relativistic heavy ion collisions. Phys. Rev. D 104, 076016 (2021).

    Article  ADS  CAS  Google Scholar 

  28. Becattini, F., Csernai, L. & Wang, D. J. Λ polarization in peripheral heavy ion collisions. Phys. Rev. C 88, 034905 (2013); erratum 93, 069901 (2016).

    Article  ADS  Google Scholar 

  29. Müller, B. & Yang, D.-L. Anomalous spin polarization from turbulent color fields. Phys. Rev. D 105, L011901 (2022).

    Article  ADS  Google Scholar 

  30. Abelev, B. I. et al. Spin alignment measurements of the K*0(892) and ϕ(1020) vector mesons in heavy ion collisions at \(\sqrt{{s}_{NN}}\) = 200 GeV. Phys. Rev. C 77, 061902 (2008).

    Article  ADS  Google Scholar 

  31. Anderson, M. et al. The STAR time projection chamber: a unique tool for studying high multiplicity events at RHIC. Nucl. Instrum. Methods Phys. Res. A 499, 659–678 (2003).

    Article  ADS  CAS  Google Scholar 

  32. Llope, W. J. Multigap RPCs in the STAR experiment at RHIC. Nucl. Instrum. Methods Phys. Res. A 661, S110–S113 (2012).

    Article  CAS  Google Scholar 

  33. Acharya, S. et al. Evidence of spin-orbital angular momentum interactions in relativistic heavy-ion collisions. Phys. Rev. Lett. 125, 012301 (2020).

    Article  ADS  CAS  Google Scholar 

  34. Serot, B. D. & Walecka, J. D. The relativistic nuclear many body problem. Adv. Nucl. Phys. 16, 1–327 (1986).

    Google Scholar 

  35. Gasser, J. & Leutwyler, H. Chiral perturbation theory to one loop. Ann. Phys. 158, 142–210 (1984).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  36. Shifman, M. A., Vainshtein, A. I. & Zakharov, V. I. Remarks on Higgs-boson interactions with nucleons. Phys. Lett. B 78, 443–446 (1978).

    Article  ADS  Google Scholar 

  37. Csernai, L. P., Kapusta, J. I. & Welle, T. Λ and \(\bar{\Lambda }\) spin interaction with meson fields generated by the baryon current in high energy nuclear collisions. Phys. Rev. C 99, 021901 (2019).

    Article  ADS  CAS  Google Scholar 

  38. Karpenko, I. & Becattini, F. Study of Λ polarization in relativistic nuclear collisions at \(\sqrt{{s}_{{\rm{NN}}}}\) 7.7–200 GeV. Eur. Phys. J. C 77, 213 (2017).

    Article  ADS  Google Scholar 

  39. Bryan, R. & Scott, B. L. Nucleon-nucleon scattering from one-boson-exchange potentials. III. S waves included. Phys. Rev. 177, 1435–1442 (1969).

    Article  ADS  CAS  Google Scholar 

  40. Nagels, M. M., Rijken, T. A. & de Swart, J. J. Low-energy nucleon-nucleon potential from Regge-pole theory. Phys. Rev. D 17, 768 (1978).

    Article  ADS  CAS  Google Scholar 

  41. Walecka, J. D. A theory of highly condensed matter. Ann. Phys. 83, 491–529 (1974).

    Article  ADS  CAS  Google Scholar 

  42. Mayer, M. G. On closed shells in nuclei. II. Phys. Rev. 75, 1969–1970 (1949).

    Article  ADS  Google Scholar 

  43. Haxel, O., Jensen, J. H. D. & Suess, H. E. On the “magic numbers” in nuclear structure. Phys. Rev. 75, 1766 (1949).

    Article  ADS  CAS  Google Scholar 

  44. Adler, C. et al. The RHIC zero degree calorimeters. Nucl. Instrum. Methods Phys. Res. A 470, 488–499 (2001).

    Article  ADS  CAS  Google Scholar 

  45. Whitten, C. A. The beam-beam counter: a local polarimeter at STAR. AIP Conf. Proc. 980, 390–396 (2008).

    Article  ADS  CAS  Google Scholar 

  46. Allgower, C. E. et al. The STAR endcap electromagnetic calorimeter. Nucl. Instrum. Methods Phys. Res. A 499, 740–750 (2003).

    Article  ADS  CAS  Google Scholar 

  47. Tang, A. H., Tu, B. & Zhou, C. S. Practical considerations for measuring global spin alignment of vector mesons in relativistic heavy ion collisions. Phys. Rev. C 98, 044907 (2018).

    Article  ADS  CAS  Google Scholar 

  48. Abelev, B. et al. Identified particle production, azimuthal anisotropy, and interferometry measurements in Au + Au collisions at \(\sqrt{{s}_{NN}}\) = 9.2 GeV. Phys. Rev. C 81, 024911 (2010).

    Article  ADS  Google Scholar 

  49. Adams, J. et al. K(892)* resonance production in Au+Au and p+p collisions at \(\sqrt{{s}_{NN}}\) = 200 GeV. Phys. Rev. C 71, 064902 (2005).

    Article  ADS  Google Scholar 

  50. Aggarwal, M. M. et al. K*0 production in Cu + Cu and Au + Au collisions at \(\sqrt{{s}_{NN}}\) = 62.4 GeV and 200 GeV. Phys. Rev. C 84, 034909 (2011).

    Article  ADS  Google Scholar 

  51. Lan, S., Lin, Z.-W., Shi, S. & Sun, X. Effects of finite coverage on global polarization observables in heavy ion collisions. Phys. Lett. B 780, 319–324 (2018).

    Article  ADS  CAS  Google Scholar 

  52. Fine, V. & Nevski, P. in Proc. 11th International Conference on Computing in High-Energy and Nuclear Physics 143–146 (2000).

  53. Chen, K.-B., Liang, Z.-T., Song, Y.-K. & Wei, S.-Y. Spin alignment of vector mesons in high energy pp collisions. Phys. Rev. D 102, 034001 (2020).

    Article  ADS  CAS  Google Scholar 

  54. Florkowski, W. & Ryblewski, R. Interpretation of Λ spin polarization measurements. Phys. Rev. C 106, 024905 (2022).

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

We thank the RHIC Operations Group and RCF at BNL, the NERSC Center at LBNL and the Open Science Grid Consortium for providing resources and support. This work was supported in part by the Office of Nuclear Physics within the U.S. DOE Office of Science, the U.S. National Science Foundation, National Natural Science Foundation of China, Chinese Academy of Sciences, the Ministry of Science and Technology of China and the Chinese Ministry of Education, the Higher Education Sprout Project by Ministry of Education at NCKU, the National Research Foundation of Korea, the Czech Science Foundation and Ministry of Education, Youth and Sports of the Czech Republic, the Hungarian National Research, Development and Innovation Office, New National Excellency Programme of the Hungarian Ministry of Human Capacities, Department of Atomic Energy and Department of Science and Technology of the Government of India, the National Science Centre of Poland, the Ministry of Science, Education and Sports of the Republic of Croatia, German Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie (BMBF), Helmholtz Association, Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS).

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Author notes

  1. Deceased: J. Sandweiss

  2. Deceased: H. M. Spinka

Authors and Affiliations

  1. The American University in Cairo, New Cairo, Egypt

    M. S. Abdallah, F. M. Fawzi & A. Hamed

  2. Texas A&M University, College Station, TX, USA

    B. E. Aboona, D. M. Anderson, C. A. Gagliardi, Y. Liu, S. Mioduszewski, J. Pan & R. E. Tribble

  3. Brookhaven National Laboratory, Upton, NY, USA

    J. Adam, E. C. Aschenauer, J. D. Brandenburg, Z. Chang, W. Christie, X. Chu, L. Didenko, J. C. Dunlop, O. Eyser, Y. Fisyak, W. Guryn, A. Jentsch, J. Jia, D. Kalinkin, K. Kauder, H. W. Ke, A. Kiselev, J. M. Landgraf, J. Lauret, A. Lebedev, J. H. Lee, N. Lewis, T. Ljubicic, R. S. Longacre, R. Ma, A. S. Nunes, A. Ogawa, B. S. Page, R. Pak, L. Ruan, W. B. Schmidke, P. V. Shanmuganathan, A. H. Tang, P. Tribedy, Z. Tu, T. Ullrich, G. Van Buren, F. Videbæk, J. C. Webb, Z. Xu, K. Yip, Z. Zhang & M. Zhao

  4. Faculty of Physics and Applied Computer Science (FPACS), AGH University of Science and Technology, Kraków, Poland

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    I. Chakaberia, X. Dong, Y. Ji, H. S. Ko, Y. H. Leung, H. S. Matis, G. Odyniec, S. Oh, J. Porter, H. G. Ritter, E. P. Sichtermann, J. H. Thomas, H. Wieman, G. Xie & N. Xu

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    A. Gibson, D. Grosnick, T. D. S. Stanislaus & D. G. Underwood

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    B. Pawlik

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    J. Seger & D. Tlusty

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    N. Shah

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    M. J. Skoby

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  62. Universidade de São Paulo, São Paulo, Brazil

    A. A. P. Suaide

  63. Huzhou University, Huzhou, China

    Y. Sun, J. S. Wang & H. Xu

  64. Michigan State University, East Lansing, MI, USA

    T. Tarnowsky & G. D. Westfall

  65. United States Naval Academy, Annapolis, MD, USA

    R. Witt

  66. South China Normal University, Guangzhou, China

    S. Yang

Consortia

STAR Collaboration

  • M. S. Abdallah
  • , B. E. Aboona
  • , J. Adam
  • , L. Adamczyk
  • , J. R. Adams
  • , J. K. Adkins
  • , G. Agakishiev
  • , I. Aggarwal
  • , M. M. Aggarwal
  • , Z. Ahammed
  • , A. Aitbaev
  • , I. Alekseev
  • , D. M. Anderson
  • , A. Aparin
  • , E. C. Aschenauer
  • , M. U. Ashraf
  • , F. G. Atetalla
  • , G. S. Averichev
  • , V. Bairathi
  • , W. Baker
  • , J. G. Ball Cap
  • , K. Barish
  • , A. Behera
  • , R. Bellwied
  • , P. Bhagat
  • , A. Bhasin
  • , J. Bielcik
  • , J. Bielcikova
  • , I. G. Bordyuzhin
  • , J. D. Brandenburg
  • , A. V. Brandin
  • , X. Z. Cai
  • , H. Caines
  • , M. Calderón de la Barca Sánchez
  • , D. Cebra
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  • , B. K. Chan
  • , F.-H. Chang
  • , Z. Chang
  • , A. Chatterjee
  • , S. Chattopadhyay
  • , D. Chen
  • , J. Chen
  • , J. H. Chen
  • , X. Chen
  • , Z. Chen
  • , J. Cheng
  • , S. Choudhury
  • , W. Christie
  • , X. Chu
  • , H. J. Crawford
  • , M. Csanád
  • , M. Daugherity
  • , T. G. Dedovich
  • , I. M. Deppner
  • , A. A. Derevschikov
  • , A. Dhamija
  • , L. Di Carlo
  • , L. Didenko
  • , P. Dixit
  • , X. Dong
  • , J. L. Drachenberg
  • , E. Duckworth
  • , J. C. Dunlop
  • , J. Engelage
  • , G. Eppley
  • , S. Esumi
  • , O. Evdokimov
  • , A. Ewigleben
  • , O. Eyser
  • , R. Fatemi
  • , F. M. Fawzi
  • , S. Fazio
  • , C. J. Feng
  • , Y. Feng
  • , E. Finch
  • , Y. Fisyak
  • , A. Francisco
  • , C. Fu
  • , C. A. Gagliardi
  • , T. Galatyuk
  • , F. Geurts
  • , N. Ghimire
  • , A. Gibson
  • , K. Gopal
  • , X. Gou
  • , D. Grosnick
  • , A. Gupta
  • , W. Guryn
  • , A. Hamed
  • , Y. Han
  • , S. Harabasz
  • , M. D. Harasty
  • , J. W. Harris
  • , H. Harrison
  • , S. He
  • , W. He
  • , X. H. He
  • , Y. He
  • , S. Heppelmann
  • , N. Herrmann
  • , E. Hoffman
  • , L. Holub
  • , C. Hu
  • , Q. Hu
  • , Y. Hu
  • , H. Huang
  • , H. Z. Huang
  • , S. L. Huang
  • , T. Huang
  • , X. Huang
  • , Y. Huang
  • , T. J. Humanic
  • , D. Isenhower
  • , M. Isshiki
  • , W. W. Jacobs
  • , C. Jena
  • , A. Jentsch
  • , Y. Ji
  • , J. Jia
  • , K. Jiang
  • , 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
  • , D. P. Kikoła
  • , B. Kimelman
  • , D. Kincses
  • , I. Kisel
  • , A. Kiselev
  • , A. G. Knospe
  • , H. S. Ko
  • , L. Kochenda
  • , A. Korobitsin
  • , L. K. Kosarzewski
  • , L. Kramarik
  • , P. Kravtsov
  • , L. Kumar
  • , S. Kumar
  • , R. Eunnawalkam Elayavalli
  • , J. H. Kwasizur
  • , R. Lacey
  • , S. Lan
  • , J. M. Landgraf
  • , J. Lauret
  • , A. Lebedev
  • , R. Lednicky
  • , J. H. Lee
  • , Y. H. Leung
  • , N. Lewis
  • , C. Li
  • , C. Li
  • , W. Li
  • , X. Li
  • , Y. Li
  • , X. Liang
  • , Y. Liang
  • , R. Licenik
  • , T. Lin
  • , Y. Lin
  • , M. A. Lisa
  • , F. Liu
  • , H. Liu
  • , H. Liu
  • , P. Liu
  • , T. Liu
  • , X. Liu
  • , Y. Liu
  • , Z. Liu
  • , T. Ljubicic
  • , W. J. Llope
  • , R. S. Longacre
  • , E. Loyd
  • , T. Lu
  • , N. S. Lukow
  • , X. F. Luo
  • , L. Ma
  • , R. Ma
  • , Y. G. Ma
  • , N. Magdy
  • , D. Mallick
  • , S. L. Manukhov
  • , S. Margetis
  • , C. Markert
  • , H. S. Matis
  • , J. A. Mazer
  • , N. G. Minaev
  • , S. Mioduszewski
  • , B. Mohanty
  • , M. M. Mondal
  • , I. Mooney
  • , D. A. Morozov
  • , A. Mukherjee
  • , M. Nagy
  • , J. D. Nam
  • , Md. Nasim
  • , K. Nayak
  • , D. Neff
  • , J. M. Nelson
  • , D. B. Nemes
  • , M. Nie
  • , G. Nigmatkulov
  • , T. Niida
  • , R. Nishitani
  • , L. V. Nogach
  • , T. Nonaka
  • , A. S. Nunes
  • , G. Odyniec
  • , A. Ogawa
  • , S. Oh
  • , V. A. Okorokov
  • , K. Okubo
  • , B. S. Page
  • , R. Pak
  • , J. Pan
  • , A. Pandav
  • , A. K. Pandey
  • , Y. Panebratsev
  • , P. Parfenov
  • , A. Paul
  • , B. Pawlik
  • , D. Pawlowska
  • , C. Perkins
  • , J. Pluta
  • , B. R. Pokhrel
  • , J. Porter
  • , M. Posik
  • , V. Prozorova
  • , N. K. Pruthi
  • , M. Przybycien
  • , J. Putschke
  • , H. Qiu
  • , A. Quintero
  • , C. Racz
  • , S. K. Radhakrishnan
  • , N. Raha
  • , R. L. Ray
  • , R. Reed
  • , H. G. Ritter
  • , M. Robotkova
  • , J. L. Romero
  • , D. Roy
  • , L. Ruan
  • , A. K. Sahoo
  • , N. R. Sahoo
  • , H. Sako
  • , S. Salur
  • , E. Samigullin
  • , J. Sandweiss
  • , S. Sato
  • , W. B. Schmidke
  • , N. Schmitz
  • , B. R. Schweid
  • , F. Seck
  • , J. Seger
  • , R. Seto
  • , P. Seyboth
  • , N. Shah
  • , E. Shahaliev
  • , P. V. Shanmuganathan
  • , M. Shao
  • , T. Shao
  • , R. Sharma
  • , A. I. Sheikh
  • , D. Y. Shen
  • , S. S. Shi
  • , Y. Shi
  • , Q. Y. Shou
  • , E. P. Sichtermann
  • , R. Sikora
  • , J. Singh
  • , S. Singha
  • , P. Sinha
  • , M. J. Skoby
  • , N. Smirnov
  • , Y. Söhngen
  • , W. Solyst
  • , Y. Song
  • , H. M. Spinka
  • , B. Srivastava
  • , T. D. S. Stanislaus
  • , M. Stefaniak
  • , D. J. Stewart
  • , M. Strikhanov
  • , B. Stringfellow
  • , A. A. P. Suaide
  • , M. Sumbera
  • , X. M. Sun
  • , X. Sun
  • , Y. Sun
  • , Y. Sun
  • , B. Surrow
  • , D. N. Svirida
  • , Z. W. Sweger
  • , P. Szymanski
  • , A. H. Tang
  • , Z. Tang
  • , A. Taranenko
  • , T. Tarnowsky
  • , J. H. Thomas
  • , A. R. Timmins
  • , D. Tlusty
  • , T. Todoroki
  • , M. Tokarev
  • , C. A. Tomkiel
  • , S. Trentalange
  • , R. E. Tribble
  • , P. Tribedy
  • , S. K. Tripathy
  • , T. Truhlar
  • , B. A. Trzeciak
  • , O. D. Tsai
  • , Z. Tu
  • , T. Ullrich
  • , D. G. Underwood
  • , I. Upsal
  • , G. Van Buren
  • , J. Vanek
  • , A. N. Vasiliev
  • , I. Vassiliev
  • , V. Verkest
  • , F. Videbæk
  • , S. Vokal
  • , S. A. Voloshin
  • , F. Wang
  • , G. Wang
  • , J. S. Wang
  • , P. Wang
  • , X. Wang
  • , Y. Wang
  • , Y. Wang
  • , Z. Wang
  • , J. C. Webb
  • , P. C. Weidenkaff
  • , G. D. Westfall
  • , H. Wieman
  • , S. W. Wissink
  • , R. Witt
  • , J. Wu
  • , J. Wu
  • , Y. Wu
  • , B. Xi
  • , Z. G. Xiao
  • , G. Xie
  • , W. Xie
  • , H. Xu
  • , N. Xu
  • , Q. H. Xu
  • , Y. Xu
  • , Z. Xu
  • , Z. Xu
  • , G. Yan
  • , C. Yang
  • , Q. Yang
  • , S. Yang
  • , Y. Yang
  • , Z. Ye
  • , Z. Ye
  • , L. Yi
  • , K. Yip
  • , Y. Yu
  • , H. Zbroszczyk
  • , W. Zha
  • , C. Zhang
  • , D. Zhang
  • , J. Zhang
  • , S. Zhang
  • , S. Zhang
  • , Y. Zhang
  • , Y. Zhang
  • , Y. Zhang
  • , Z. J. Zhang
  • , Z. Zhang
  • , Z. Zhang
  • , F. Zhao
  • , J. Zhao
  • , M. Zhao
  • , C. Zhou
  • , Y. Zhou
  • , X. Zhu
  • , M. Zurek
  •  & M. Zyzak

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All authors contributed extensively.

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Additional information

Extended data

is available for this paper at https://doi.org/10.1038/s41586-022-05557-5.

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Extended data figures and tables

Extended Data Fig. 1 Example of combinatorial-background-subtracted invariant-mass distributions and the extracted yields as a function of cosθ* for ϕ and K*0 mesons.

a, Example of ϕ → K+ + K− invariant-mass distributions, with combinatorial background subtracted, integrated over cosθ*. b, Example of \({{\rm{K}}}^{* 0}\,(\bar{{{\rm{K}}}^{* 0}})\to {{\rm{K}}}^{-}{{\rm{\pi }}}^{+}\,({{\rm{K}}}^{+}{{\rm{\pi }}}^{-})\) invariant-mass distributions, with combinatorial background subtracted, integrated over cosθ*. c, Extracted yields of ϕ as a function of cosθ*. d, Extracted yields of K*0 as a function of cosθ*.

Extended Data Fig. 2 Efficiency-corrected ϕ-meson yields as a function of cosθ* and corresponding fits with equation (2) in Methods.

The red stars are efficiency-corrected yields for ϕ mesons with |y| < 1.0 and 1.2 < pT < 1.8 GeV c−1, for 20–60% centrality at \(\sqrt{{s}_{{\rm{NN}}}}=27\,{\rm{GeV}}\).

Extended Data Fig. 3 Efficiency-corrected and acceptance-corrected K*0-meson yields as a function of cosθ* and corresponding fits with equation (5) in Methods.

The blue circles are efficiency-corrected and acceptance-corrected yields for K*0 mesons with |y| < 1.0 and 2.0 < pT < 2.5 GeV c−1, for 20–60% centrality at \(\sqrt{{s}_{{\rm{NN}}}}=54.4\,{\rm{GeV}}\).

Extended Data Fig. 4 ϕ-meson ρ00 obtained from first-order and second-order event planes.

The red stars (grey squares) show the ϕ-meson ρ00 as a function of beam energy, obtained with the second-order (first-order) event plane.

Extended Data Fig. 5 ϕ-meson ρ00 with respect to different quantization axes.

ϕ-meson ρ00 as a function of beam energy, for the out-of-plane direction (stars) and the in-plane direction (diamonds). Curves are fits based on theoretical calculations with a ϕ-meson field2. The corresponding Gs values obtained from the fits are shown in the legend.

Extended Data Fig. 6 ρ00 as a function of transverse momentum for ϕ for different collision energies.

The grey squares and red stars are results obtained with the first-order and second-order event planes, respectively.

Extended Data Fig. 7 ρ00 as a function of transverse momentum for K*0 for different collision energies.

The solid circles are results obtained with the second-order event plane.

Extended Data Fig. 8 ρ00 as a function of centrality for ϕ (upper panels) and K*0 (lower panels).

The solid squares and stars are results for the ϕ meson, obtained with the first-order and second-order event planes, respectively. The solid circles are results for the K*0 meson, obtained with the second-order event plane.

Extended Data Fig. 9 Global spin alignment measurement of ϕ and K*0 vector mesons in Au+Au collisions at 0–20% centrality.

The solid squares and stars are results for the ϕ meson, obtained with the first-order and second-order event planes, respectively. The solid circles are results for the K*0 meson, obtained with the second-order event plane.

Extended Data Table 1 Sources of systematic error in ϕ
Full size table
Extended Data Table 2 Sources of systematic error in K*0
Full size table

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STAR Collaboration. Pattern of global spin alignment of ϕ and K*0 mesons in heavy-ion collisions. Nature 614, 244–248 (2023). https://doi.org/10.1038/s41586-022-05557-5

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