Skip to main content

Spin polarization induced by the hydrodynamic gradients

A preprint version of the article is available at arXiv.

Abstract

We systematically analyze the effects of the derivatives of the hydrodynamic fields on axial Wigner function that describes the spin polarization vector in phase space. We have included all possible first-order derivative contributions that are allowed by symmetry and compute the associated transport functions at one-loop using the linear response theory. In addition to reproducing known effects due to the temperature gradient and vorticity, we have identified a number of potentially significant contributions that are overlooked previously. In particular, we find that the shear strength, the symmetric and traceless part of the flow gradient, will induce a quadrupole for spin polarization in the phase space. Our results, together with hydrodynamic gradients obtained from hydrodynamic simulations, can be employed as a basis for the interpretation of the Λ (anti-Λ) spin polarization measurement in heavy-ion collisions.

References

  1. [1]

    Z.-T. Liang and X.-N. Wang, Globally polarized quark-gluon plasma in non-central A+A collisions, Phys. Rev. Lett. 94 (2005) 102301 [Erratum ibid. 96 (2006) 039901] [nucl-th/0410079] [INSPIRE].

  2. [2]

    F. Becattini, V. Chandra, L. Del Zanna and E. Grossi, Relativistic distribution function for particles with spin at local thermodynamical equilibrium, Annals Phys. 338 (2013) 32 [arXiv:1303.3431] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  3. [3]

    F. Becattini, Polarization in relativistic fluids: a quantum field theoretical derivation, 4, 2020 [arXiv:2004.04050] [INSPIRE].

  4. [4]

    W. Florkowski, B. Friman, A. Jaiswal and E. Speranza, Relativistic fluid dynamics with spin, Phys. Rev. C 97 (2018) 041901 [arXiv:1705.00587] [INSPIRE].

    ADS  Article  Google Scholar 

  5. [5]

    K. Hattori, M. Hongo, X.-G. Huang, M. Matsuo and H. Taya, Fate of spin polarization in a relativistic fluid: An entropy-current analysis, Phys. Lett. B 795 (2019) 100 [arXiv:1901.06615] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  6. [6]

    S.Y.F. Liu, Y. Sun and C.M. Ko, Spin polarizations in a covariant angular-momentum-conserved chiral transport model, Phys. Rev. Lett. 125 (2020) 062301 [arXiv:1910.06774] [INSPIRE].

    ADS  Article  Google Scholar 

  7. [7]

    K. Fukushima and S. Pu, Spin hydrodynamics and symmetric energy-momentum tensors — A current induced by the spin vorticity, Phys. Lett. B 817 (2021) 136346 [arXiv:2010.01608] [INSPIRE].

    MathSciNet  Article  Google Scholar 

  8. [8]

    S. Shi, C. Gale and S. Jeon, From chiral kinetic theory to relativistic viscous spin hydrodynamics, Phys. Rev. C 103 (2021) 044906 [arXiv:2008.08618] [INSPIRE].

    ADS  Article  Google Scholar 

  9. [9]

    S. Li, M.A. Stephanov and H.-U. Yee, Non-dissipative second-order transport, spin, and pseudo-gauge transformations in hydrodynamics, arXiv:2011.12318 [INSPIRE].

  10. [10]

    R. Singh, G. Sophys and R. Ryblewski, Spin polarization dynamics in the Gubser-expanding background, Phys. Rev. D 103 (2021) 074024 [arXiv:2011.14907] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  11. [11]

    STAR collaboration, Global Λ hyperon polarization in nuclear collisions: evidence for the most vortical fluid, Nature 548 (2017) 62 [arXiv:1701.06657] [INSPIRE].

  12. [12]

    STAR collaboration, Global polarization of Λ hyperons in Au+Au collisions at \( \sqrt{s_{NN}} \) = 200 GeV, Phys. Rev. C 98 (2018) 014910 [arXiv:1805.04400] [INSPIRE].

  13. [13]

    STAR collaboration, Global and local polarization of Λ hyperons in Au+Au collisions at 200 GeV from STAR, Nucl. Phys. A 982 (2019) 511 [arXiv:1808.10482] [INSPIRE].

  14. [14]

    STAR collaboration, Polarization of Λ (\( \overline{\Lambda} \)) hyperons along the beam direction in Au+Au collisions at \( \sqrt{s_{NN}} \) = 200 GeV, Phys. Rev. Lett. 123 (2019) 132301 [arXiv:1905.11917] [INSPIRE].

  15. [15]

    F. Becattini and I. Karpenko, Collective longitudinal polarization in relativistic heavy-ion collisions at very high energy, Phys. Rev. Lett. 120 (2018) 012302 [arXiv:1707.07984] [INSPIRE].

    ADS  Article  Google Scholar 

  16. [16]

    X.-L. Xia, H. Li, Z.-B. Tang and Q. Wang, Probing vorticity structure in heavy-ion collisions by local Λ polarization, Phys. Rev. C 98 (2018) 024905 [arXiv:1803.00867] [INSPIRE].

    ADS  Article  Google Scholar 

  17. [17]

    J.-Y. Chen, D.T. Son, M.A. Stephanov, H.-U. Yee and Y. Yin, Lorentz invariance in chiral kinetic theory, Phys. Rev. Lett. 113 (2014) 182302 [arXiv:1404.5963] [INSPIRE].

    ADS  Article  Google Scholar 

  18. [18]

    J.-Y. Chen, D.T. Son and M.A. Stephanov, Collisions in chiral kinetic theory, Phys. Rev. Lett. 115 (2015) 021601 [arXiv:1502.06966] [INSPIRE].

    ADS  Article  Google Scholar 

  19. [19]

    K. Hattori, Y. Hidaka and D.-L. Yang, Axial kinetic theory and spin transport for fermions with arbitrary mass, Phys. Rev. D 100 (2019) 096011 [arXiv:1903.01653] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  20. [20]

    S. A. Crooker and D. L. Smith, Imaging spin flows in semiconductors subject to electric, magnetic, and strain fields, Phys. Rev. Lett. 94 (2005) 236601.

    ADS  Article  Google Scholar 

  21. [21]

    A. G. Mal’Shukov, C.S. Tang, C.S. Chu and K.A. Chao, Strain-induced coupling of spin current to nanomechanical oscillations, Phys. Rev. Lett. 95 (2005) 107203 [cond-mat/0504773].

  22. [22]

    D.E. Kharzeev, M.A. Stephanov and H.-U. Yee, Anatomy of chiral magnetic effect in and out of equilibrium, Phys. Rev. D 95 (2017) 051901 [arXiv:1612.01674] [INSPIRE].

    ADS  Article  Google Scholar 

  23. [23]

    S.Y.F. Liu and Y. Yin, Spin Hall effect in heavy ion collisions, arXiv:2006.12421 [INSPIRE].

  24. [24]

    J.M. Luttinger, Theory of thermal transport coefficients, Phys. Rev. 135 (1964) A1505 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  25. [25]

    Y.-C. Liu, K. Mameda and X.-G. Huang, Covariant spin kinetic theory I: collisionless limit, Chin. Phys. C 44 (2020) 094101 [arXiv:2002.03753] [INSPIRE].

    ADS  Article  Google Scholar 

  26. [26]

    T. Hayata, Y. Hidaka and K. Mameda, Second order chiral kinetic theory under gravity and antiparallel charge-energy flow, JHEP 05 (2021) 023 [arXiv:2012.12494] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  27. [27]

    K. Landsteiner, E. Megias, L. Melgar and F. Pena-Benitez, Holographic gravitational anomaly and chiral vortical effect, JHEP 09 (2011) 121 [arXiv:1107.0368] [INSPIRE].

    ADS  Article  Google Scholar 

  28. [28]

    S. Lin and L. Yang, Mass correction to chiral vortical effect and chiral separation effect, Phys. Rev. D 98 (2018) 114022 [arXiv:1810.02979] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  29. [29]

    R.-h. Fang, L.-g. Pang, Q. Wang and X.-n. Wang, Polarization of massive fermions in a vortical fluid, Phys. Rev. C 94 (2016) 024904 [arXiv:1604.04036] [INSPIRE].

    ADS  Article  Google Scholar 

  30. [30]

    H.-Z. Wu, L.-G. Pang, X.-G. Huang and Q. Wang, Local spin polarization in high energy heavy ion collisions, Phys. Rev. Research. 1 (2019) 033058 [arXiv:1906.09385] [INSPIRE].

    ADS  Article  Google Scholar 

  31. [31]

    W. Florkowski, A. Kumar, R. Ryblewski and A. Mazeliauskas, Longitudinal spin polarization in a thermal model, Phys. Rev. C 100 (2019) 054907 [arXiv:1904.00002] [INSPIRE].

    ADS  Article  Google Scholar 

  32. [32]

    D.T. Son and N. Yamamoto, Berry curvature, triangle anomalies, and the chiral magnetic effect in Fermi liquids, Phys. Rev. Lett. 109 (2012) 181602 [arXiv:1203.2697] [INSPIRE].

    ADS  Article  Google Scholar 

  33. [33]

    M.A. Stephanov and Y. Yin, Chiral kinetic theory, Phys. Rev. Lett. 109 (2012) 162001 [arXiv:1207.0747] [INSPIRE].

    ADS  Article  Google Scholar 

  34. [34]

    N. Mueller and R. Venugopalan, Worldline construction of a covariant chiral kinetic theory, Phys. Rev. D 96 (2017) 016023 [arXiv:1702.01233] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  35. [35]

    N. Mueller and R. Venugopalan, Constructing phase space distributions with internal symmetries, Phys. Rev. D 99 (2019) 056003 [arXiv:1901.10492] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  36. [36]

    N. Weickgenannt, X.-L. Sheng, E. Speranza, Q. Wang and D.H. Rischke, Kinetic theory for massive spin-1/2 particles from the Wigner-function formalism, Phys. Rev. D 100 (2019) 056018 [arXiv:1902.06513] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  37. [37]

    N. Weickgenannt, E. Speranza, X.-l. Sheng, Q. Wang and D.H. Rischke, Generating spin polarization from vorticity through nonlocal collisions, arXiv:2005.01506 [INSPIRE].

  38. [38]

    B. Fu, S.Y.F. Liu, L. Pang, H. Song and Y. Yin, Shear-induced spin polarization in heavy-ion collisions, arXiv:2103.10403 [INSPIRE].

  39. [39]

    D. Hou and S. Lin, Polarization rotation of chiral fermions in vortical fluid, Phys. Lett. B 818 (2021) 136386 [arXiv:2008.03862] [INSPIRE].

    MathSciNet  Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Yi Yin.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

ArXiv ePrint: 2103.09200

Rights and permissions

Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Liu, S.Y.F., Yin, Y. Spin polarization induced by the hydrodynamic gradients. J. High Energ. Phys. 2021, 188 (2021). https://doi.org/10.1007/JHEP07(2021)188

Download citation

Keywords

  • Quark-Gluon Plasma
  • Phase Diagram of QCD