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  • Open Access

Polarization dependence of the ϕ meson from finite-temperature QCD sum rules

Hidefumi Matsuda*

Philipp Gubler†

Koichi Hattori‡

  • Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, Hangzhou, 310027, China

  • *Contact author: da.matsu.00.bbb.kobe@gmail.com
  • †Contact author: gubler.philipp@jaea.go.jp, philipp.gubler1@gmail.com
  • ‡Contact author: koichi.hattori@zju.edu.cn
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Phys. Rev. D 114, 054058 – Published 30 September, 2026

DOI: https://doi.org/10.1103/9zpc-f1hy

Abstract

We study the ϕ meson at finite temperature and finite momentum using QCD sum rules. The presence of medium breaks the Lorentz invariance, and induces distinct in-medium modifications of the transverse and longitudinal modes at finite momentum. We find that, with increasing momentum, the masses of both modes increase and a clear transverse-longitudinal splitting develops. The splitting is found to grow with temperature and to be mainly generated by the dimension-four spin-dependent thermal condensates.

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Phys. Rev. D 114, 054058– Published 30 September, 2026
  • Received 4 June 2026
  • Accepted 8 September 2026
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