Relativistic spin hydrodynamics

Pu Shi; Huang Xu-Guang

doi:10.7498/aps.72.20230036

Abstract

In recent years, due to the discoveries of hyperon spin polarization and vector meson spin alignment in relativistic heavy-ion collision experiments, the spin transports in quark-gluon matter has received intensive studies. The relativistic spin hydrodynamics is one of the important theoretical frameworks to describe the spin transports, which encodes the spin degree of freedom into a hydrodynamic theory. The relativistic spin hydrodynamics have the conservation equations for energy-momentum tensor, currents and total angular momentum. In this article, we give an overview of the recent progresses of the relativistic spin hydrodynamics. We focus on the following topics: 1) The derivation of the relativistic spin hydrodynamic equations, including the phenomenological approach, the effective theory method, and the kinetic approach, 2) Some special properties of spin hydrodynamics, especially the asymmetric energy-momentum tensor and the pseudogauge transformation, and 3) The analytical solutions to the relativistic spin hydrodynamics for systems under Bjorken and Gubser expansion.

Keywords:

Authors and contacts

Pu Shi¹,
Huang Xu-Guang²

1.
Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
2.
Shanghai Research Center for Theoretical Nuclear Physics, Key Laboratory of Nuclear Physics and Ion-beam Application, Ministry of Education, Certer for Particle Physics and Field Theory, Physics Department, Fudan University, Shanghai 200433

Corresponding author: Huang Xu-Guang, huangxuguang@fudan.edu.cn

Funds: Project supported by the National Key R&D Program of China (Grant No. 2022YFA1604900), the National Natural Science Foundation of China (Grant Nos. 12225502, 12075061, 12147101, 12075235, 12135011), and the Natural Science Foundation of Shanghai, China (Grant No. 20ZR1404100)

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References

[1]	Deng W T, Huang X G 2016 Phys. Rev. C 93 064907 Google Scholar
[2]	Jiang Y, Lin Z W, Liao J 2016 Phys. Rev. C 94 044910 Google Scholar
[3]	Liang Z T, Wang X N 2005 Phys. Rev. Lett. 94 102301 Google Scholar
[4]	Liang Z T, Wang X N 2005 Phys. Lett. B 629 20 Google Scholar
[5]	Adamczyk L, Adkins J K, Agakishiev G, et al. 2017 Nature 548 62 Google Scholar
[6]	Adam J, Adamczyk L, Adams J R, et al. 2021 Phys. Rev. Lett. 126 162301 Google Scholar
[7]	STAR Collaboration 2023 Nature 614 244 Google Scholar
[8]	ALICE Collaboration 2022 arXiv: 2204.10171
[9]	Ma Y G 2023 Nucl. Sci. Technol. 34 16 Google Scholar
[10]	Wang X N 2023 Nucl. Sci. Technol. 34 15 Google Scholar
[11]	Liu Y C, Huang X G 2020 Nucl. Sci. Technol. 31 56 Google Scholar
[12]	Gao J H, Ma G L, Pu S, Wang Q 2020 Nucl. Sci. Technol. 31 90 Google Scholar
[13]	孙旭, 周晨升, 陈金辉, 陈震宇, 马余刚, 唐爱洪, 徐庆华 2023 72 072401 Sun X, Zhou C S, Chen J H, Chen Z Y, Ma Y G, Tang A H, Xu Q H 2023 Acta Phys. Sin. 72 072401
[14]	高建华, 黄旭光, 梁作堂, 王群, 王新年 2023 72 072501 Google Scholar Gao J H, Huang X G, Liang Z T, Wang Q, Wang X N 2023 Acta Phys. Sin. 72 072501 Google Scholar
[15]	江泽方, 吴祥宇, 余华清, 曹杉杉, 张本威 2023 72 072504 Google Scholar Jiang Z F, Wu X Y, Yu H Q, Cao S S, Zhang B W 2023 Acta Phys. Sin. 72 072504 Google Scholar
[16]	赵新丽, 马国亮, 马余刚 2023 Accepted Zhao X L, Ma G L, Ma Y G 2023 Acta Phys. Sin. Accepted
[17]	盛欣力, 梁作堂, 王群 2023 Accepted Sheng X L, Liang Z T, Wang Q 2023 Acta Phys. Sin. Accepted
[18]	尹伊 2023 Accepted Yin Y 2023 Acta Phys. Sin. Accepted
[19]	Hidaka Y, Pu S, Wang Q, Yang D L 2022 Prog. Part. Nucl. Phys. 127 103989 Google Scholar
[20]	高建华, 盛欣力, 王群, 庄鹏飞 2023 Accepted Gao J H, Sheng X L, Wang Q, Zhuang P F 2023 Acta Phys. Sin. Accepted
[21]	Takahashi R, Matsuo M, Ono M, et al. 2016 Nat. Phys. 12 52 Google Scholar
[22]	Jepsen P N, Amato-Grill J, Dimitrova I, Ho W W, Demler E, Ketterle W 2020 Nature 588 403 Google Scholar
[23]	Hattori K, Hongo M, Huang X G, Matsuo M, Taya H 2019 Phys. Lett. B 795 100 Google Scholar
[24]	Fukushima K, Pu S 2021 Phys. Lett. B 817 136346 Google Scholar
[25]	Israel W, Stewart J M 1979 Ann. Phys. 118 341 Google Scholar
[26]	Becattini F, Bucciantini L, Grossi E, Tinti L 2015 Eur. Phys. J. C 75 191 Google Scholar
[27]	Glorioso P, Liu H 2016 arXiv: 1612.07705
[28]	Glorioso P, Crossley M, Liu H 2017 JHEP 09 096
[29]	Son D T, Surowka P 2009 Phys. Rev. Lett. 103 191601 Google Scholar
[30]	Becattini F, Tinti L 2011 Phys. Rev. D 84 025013 Google Scholar
[31]	Becattini F, Tinti L 2013 Phys. Rev. D 87 025029 Google Scholar
[32]	Becattini F, Florkowski W, Speranza E 2019 Phys. Lett. B 789 419 Google Scholar
[33]	Kovtun P 2012 J. Phys. A 45 473001 Google Scholar
[34]	Fukuda M, Ichikawa K, Senami M, Tachibana A 2016 AIP Adv. 6 025108 Google Scholar
[35]	Crossley M, Glorioso P, Liu H 2017 JHEP 09 095
[36]	Hongo M, Huang X G, Kaminski M, Stephanov M, Yee H U 2021 JHEP 11 150
[37]	Gallegos A D, Gürsoy U, Yarom A 2021 SciPost Phys. 11 41 Google Scholar
[38]	Gallegos A D, Gürsoy U, Yarom A 2022 arXiv: 2203.05044
[39]	Peng H H, Zhang J J, Sheng X L, Wang Q 2021 Chin. Phys. Lett. 38 116701 Google Scholar
[40]	Heinz U W 1983 Phys. Rev. Lett. 51 351 Google Scholar
[41]	Elze H T, Gyulassy M, Vasak D 1986 Nucl. Phys. B 276 706 Google Scholar
[42]	Vasak D, Gyulassy M, Elze H T 1987 Annals Phys. 173 462 Google Scholar
[43]	Sheng X L 2019 arXiv: 1912.01169
[44]	Sheng X L, Wang Q, Huang X G 2020 Phys. Rev. D 102 025019 Google Scholar
[45]	Yang D L, Hattori K, Hidaka Y 2020 JHEP 07 070
[46]	Weickgenannt N, Speranza E, Sheng X L, Wang Q, Rischke D H 2021 Phys. Rev. Lett. 127 052301 Google Scholar
[47]	Sheng X L, Weickgenannt N, Speranza E, Rischke D H, Wa ng Q 2021 Phys. Rev. D 104 016029 Google Scholar
[48]	Wang Z Y, Zhuang P F 2021 arXiv: 2105.00915
[49]	Fang S, Pu S, Yang D L 2022 Phys. Rev. D 106 016002 Google Scholar
[50]	Gao J H, Liang Z T 2019 Phys. Rev. D 100 056021 Google Scholar
[51]	Weickgenannt N, Sheng X L, Speranza E, Wang Q, Rischke D H 2019 Phys. Rev. D 100 056018 Google Scholar
[52]	Hattori K, Hidaka Y, Yang D L 2019 Phys. Rev. D 100 096011 Google Scholar
[53]	Wang Z, Guo X, Shi S, Zhuang P F 2019 Phys. Rev. D 100 014015 Google Scholar
[54]	Liu Y C, Mameda K, Huang X G 2020 Chin. Phys. C 44 094101 Google Scholar
[55]	Becattini F, Chandra V, Del Zanna L, Grossi E 2013 Ann. Phys. 338 32 Google Scholar
[56]	Romatschke P, Romatschke U 2019 Relativistic Fluid Dynamics In and Out of Equilibrium (Cambridge: Cambridge University Press)
[57]	Bhadury S, Florkowski W, Jaiswal A, Kumar A, Ryblewski R 2021 Phys. Rev. D 103 014030 Google Scholar
[58]	Wang D L, Fang S, Pu S 2021 Phys. Rev. D 104 114043 Google Scholar
[59]	Wang D L, Xie X Q, Fang S, Pu S 2022 Phys. Rev. D 105 114050 Google Scholar
[60]	Gubser S S, Yarom A 2011 Nucl. Phys. B 846 469 Google Scholar
[61]	Gubser S S 2010 Phys. Rev. D 82 085027 Google Scholar
[62]	Montenegro D, Torrieri G 2019 Phys. Rev. D 100 056011 Google Scholar
[63]	Montenegro D, Tinti L, Torrieri G 2017 Phys. Rev. D 96 056012A Google Scholar
[64]	Florkowski W, Friman B, Jaiswal A, Speranza E 2018 Phys. Rev. C 97 041901 Google Scholar
[65]	Florkowski W, Kumar A, Ryblewski R 2019 Prog. Part. Nucl. Phys. 108 103709 Google Scholar
[66]	Li S, Yee H U 2019 Phys. Rev. D 100 056022 Google Scholar
[67]	Bhadury S, Florkowski W, Jaiswal A, Kumar A, Ryblewski R 2021 Phys. Lett. B 814 136096 Google Scholar
[68]	Montenegro D, Torrieri G 2020 Phys. Rev. D 102 036007 Google Scholar
[69]	Li S, Stephanov M A, Yee H U 2021 Phys. Rev. Lett. 127 082302 Google Scholar
[70]	Shi S, Gale C, Jeon S 2021 Phys. Rev. C 103 044906 Google Scholar
[71]	She D, Huang A, Hou D F, Liao J F 2022 Sci. Bull. 67 2265 Google Scholar
[72]	Hu J 2021 Phys. Rev. D 103 116015 Google Scholar
[73]	Hu J 2022 Phys. Rev. D 105 076009 Google Scholar
[74]	Hongo M, Huang X G, Kaminski M, Stephanov M, Yee H U 2022 JHEP 08 263
[75]	Singh R, Shokri M, Mehr S M A T 2022 arXiv: 2202.11504
[76]	Daher A, Das A, Florkowski W, Ryblewski R 2022 arXiv: 2202.12609
[77]	Weickgenannt N, Wagner D, Speranza E, Rischke D H 2022 Phys. Rev. D 106 096014 Google Scholar
[78]	Bhadury S, Florkowski W, Jaiswal A, Kumar A, Ryblewski R 2022 Phys. Rev. Lett. 129 192301 Google Scholar
[79]	Cao Z, Hattori K, Hongo M, Huang X G, Taya H 2022 PTEP 2022 071D
[80]	Liu Y C, Huang X G 2022 Sci. China Phys. Mech. Astron. 65 272011 Google Scholar

Cited By

[1]	Deng W T, Huang X G 2016 Phys. Rev. C 93 064907 Google Scholar
[2]	Jiang Y, Lin Z W, Liao J 2016 Phys. Rev. C 94 044910 Google Scholar
[3]	Liang Z T, Wang X N 2005 Phys. Rev. Lett. 94 102301 Google Scholar
[4]	Liang Z T, Wang X N 2005 Phys. Lett. B 629 20 Google Scholar
[5]	Adamczyk L, Adkins J K, Agakishiev G, et al. 2017 Nature 548 62 Google Scholar
[6]	Adam J, Adamczyk L, Adams J R, et al. 2021 Phys. Rev. Lett. 126 162301 Google Scholar
[7]	STAR Collaboration 2023 Nature 614 244 Google Scholar
[8]	ALICE Collaboration 2022 arXiv: 2204.10171
[9]	Ma Y G 2023 Nucl. Sci. Technol. 34 16 Google Scholar
[10]	Wang X N 2023 Nucl. Sci. Technol. 34 15 Google Scholar
[11]	Liu Y C, Huang X G 2020 Nucl. Sci. Technol. 31 56 Google Scholar
[12]	Gao J H, Ma G L, Pu S, Wang Q 2020 Nucl. Sci. Technol. 31 90 Google Scholar
[13]	孙旭, 周晨升, 陈金辉, 陈震宇, 马余刚, 唐爱洪, 徐庆华 2023 72 072401 Sun X, Zhou C S, Chen J H, Chen Z Y, Ma Y G, Tang A H, Xu Q H 2023 Acta Phys. Sin. 72 072401
[14]	高建华, 黄旭光, 梁作堂, 王群, 王新年 2023 72 072501 Google Scholar Gao J H, Huang X G, Liang Z T, Wang Q, Wang X N 2023 Acta Phys. Sin. 72 072501 Google Scholar
[15]	江泽方, 吴祥宇, 余华清, 曹杉杉, 张本威 2023 72 072504 Google Scholar Jiang Z F, Wu X Y, Yu H Q, Cao S S, Zhang B W 2023 Acta Phys. Sin. 72 072504 Google Scholar
[16]	赵新丽, 马国亮, 马余刚 2023 Accepted Zhao X L, Ma G L, Ma Y G 2023 Acta Phys. Sin. Accepted
[17]	盛欣力, 梁作堂, 王群 2023 Accepted Sheng X L, Liang Z T, Wang Q 2023 Acta Phys. Sin. Accepted
[18]	尹伊 2023 Accepted Yin Y 2023 Acta Phys. Sin. Accepted
[19]	Hidaka Y, Pu S, Wang Q, Yang D L 2022 Prog. Part. Nucl. Phys. 127 103989 Google Scholar
[20]	高建华, 盛欣力, 王群, 庄鹏飞 2023 Accepted Gao J H, Sheng X L, Wang Q, Zhuang P F 2023 Acta Phys. Sin. Accepted
[21]	Takahashi R, Matsuo M, Ono M, et al. 2016 Nat. Phys. 12 52 Google Scholar
[22]	Jepsen P N, Amato-Grill J, Dimitrova I, Ho W W, Demler E, Ketterle W 2020 Nature 588 403 Google Scholar
[23]	Hattori K, Hongo M, Huang X G, Matsuo M, Taya H 2019 Phys. Lett. B 795 100 Google Scholar
[24]	Fukushima K, Pu S 2021 Phys. Lett. B 817 136346 Google Scholar
[25]	Israel W, Stewart J M 1979 Ann. Phys. 118 341 Google Scholar
[26]	Becattini F, Bucciantini L, Grossi E, Tinti L 2015 Eur. Phys. J. C 75 191 Google Scholar
[27]	Glorioso P, Liu H 2016 arXiv: 1612.07705
[28]	Glorioso P, Crossley M, Liu H 2017 JHEP 09 096
[29]	Son D T, Surowka P 2009 Phys. Rev. Lett. 103 191601 Google Scholar
[30]	Becattini F, Tinti L 2011 Phys. Rev. D 84 025013 Google Scholar
[31]	Becattini F, Tinti L 2013 Phys. Rev. D 87 025029 Google Scholar
[32]	Becattini F, Florkowski W, Speranza E 2019 Phys. Lett. B 789 419 Google Scholar
[33]	Kovtun P 2012 J. Phys. A 45 473001 Google Scholar
[34]	Fukuda M, Ichikawa K, Senami M, Tachibana A 2016 AIP Adv. 6 025108 Google Scholar
[35]	Crossley M, Glorioso P, Liu H 2017 JHEP 09 095
[36]	Hongo M, Huang X G, Kaminski M, Stephanov M, Yee H U 2021 JHEP 11 150
[37]	Gallegos A D, Gürsoy U, Yarom A 2021 SciPost Phys. 11 41 Google Scholar
[38]	Gallegos A D, Gürsoy U, Yarom A 2022 arXiv: 2203.05044
[39]	Peng H H, Zhang J J, Sheng X L, Wang Q 2021 Chin. Phys. Lett. 38 116701 Google Scholar
[40]	Heinz U W 1983 Phys. Rev. Lett. 51 351 Google Scholar
[41]	Elze H T, Gyulassy M, Vasak D 1986 Nucl. Phys. B 276 706 Google Scholar
[42]	Vasak D, Gyulassy M, Elze H T 1987 Annals Phys. 173 462 Google Scholar
[43]	Sheng X L 2019 arXiv: 1912.01169
[44]	Sheng X L, Wang Q, Huang X G 2020 Phys. Rev. D 102 025019 Google Scholar
[45]	Yang D L, Hattori K, Hidaka Y 2020 JHEP 07 070
[46]	Weickgenannt N, Speranza E, Sheng X L, Wang Q, Rischke D H 2021 Phys. Rev. Lett. 127 052301 Google Scholar
[47]	Sheng X L, Weickgenannt N, Speranza E, Rischke D H, Wa ng Q 2021 Phys. Rev. D 104 016029 Google Scholar
[48]	Wang Z Y, Zhuang P F 2021 arXiv: 2105.00915
[49]	Fang S, Pu S, Yang D L 2022 Phys. Rev. D 106 016002 Google Scholar
[50]	Gao J H, Liang Z T 2019 Phys. Rev. D 100 056021 Google Scholar
[51]	Weickgenannt N, Sheng X L, Speranza E, Wang Q, Rischke D H 2019 Phys. Rev. D 100 056018 Google Scholar
[52]	Hattori K, Hidaka Y, Yang D L 2019 Phys. Rev. D 100 096011 Google Scholar
[53]	Wang Z, Guo X, Shi S, Zhuang P F 2019 Phys. Rev. D 100 014015 Google Scholar
[54]	Liu Y C, Mameda K, Huang X G 2020 Chin. Phys. C 44 094101 Google Scholar
[55]	Becattini F, Chandra V, Del Zanna L, Grossi E 2013 Ann. Phys. 338 32 Google Scholar
[56]	Romatschke P, Romatschke U 2019 Relativistic Fluid Dynamics In and Out of Equilibrium (Cambridge: Cambridge University Press)
[57]	Bhadury S, Florkowski W, Jaiswal A, Kumar A, Ryblewski R 2021 Phys. Rev. D 103 014030 Google Scholar
[58]	Wang D L, Fang S, Pu S 2021 Phys. Rev. D 104 114043 Google Scholar
[59]	Wang D L, Xie X Q, Fang S, Pu S 2022 Phys. Rev. D 105 114050 Google Scholar
[60]	Gubser S S, Yarom A 2011 Nucl. Phys. B 846 469 Google Scholar
[61]	Gubser S S 2010 Phys. Rev. D 82 085027 Google Scholar
[62]	Montenegro D, Torrieri G 2019 Phys. Rev. D 100 056011 Google Scholar
[63]	Montenegro D, Tinti L, Torrieri G 2017 Phys. Rev. D 96 056012A Google Scholar
[64]	Florkowski W, Friman B, Jaiswal A, Speranza E 2018 Phys. Rev. C 97 041901 Google Scholar
[65]	Florkowski W, Kumar A, Ryblewski R 2019 Prog. Part. Nucl. Phys. 108 103709 Google Scholar
[66]	Li S, Yee H U 2019 Phys. Rev. D 100 056022 Google Scholar
[67]	Bhadury S, Florkowski W, Jaiswal A, Kumar A, Ryblewski R 2021 Phys. Lett. B 814 136096 Google Scholar
[68]	Montenegro D, Torrieri G 2020 Phys. Rev. D 102 036007 Google Scholar
[69]	Li S, Stephanov M A, Yee H U 2021 Phys. Rev. Lett. 127 082302 Google Scholar
[70]	Shi S, Gale C, Jeon S 2021 Phys. Rev. C 103 044906 Google Scholar
[71]	She D, Huang A, Hou D F, Liao J F 2022 Sci. Bull. 67 2265 Google Scholar
[72]	Hu J 2021 Phys. Rev. D 103 116015 Google Scholar
[73]	Hu J 2022 Phys. Rev. D 105 076009 Google Scholar
[74]	Hongo M, Huang X G, Kaminski M, Stephanov M, Yee H U 2022 JHEP 08 263
[75]	Singh R, Shokri M, Mehr S M A T 2022 arXiv: 2202.11504
[76]	Daher A, Das A, Florkowski W, Ryblewski R 2022 arXiv: 2202.12609
[77]	Weickgenannt N, Wagner D, Speranza E, Rischke D H 2022 Phys. Rev. D 106 096014 Google Scholar
[78]	Bhadury S, Florkowski W, Jaiswal A, Kumar A, Ryblewski R 2022 Phys. Rev. Lett. 129 192301 Google Scholar
[79]	Cao Z, Hattori K, Hongo M, Huang X G, Taya H 2022 PTEP 2022 071D
[80]	Liu Y C, Huang X G 2022 Sci. China Phys. Mech. Astron. 65 272011 Google Scholar

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