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  • Open Access

Analytic structure of stress-energy response functions and new Kubo formulas

Sangyong Jeon*

Alina Czajka†

Juhee Hong‡

  • Department of Physics, McGill University, 3600 Rue University, Montreal, Quebec H3A2T8, Canada

  • Department of Physics and Institute of Physics and Applied Physics, Yonsei University, Seoul 03722, Korea

  • *Contact author: sangyong.jeon@mcgill.ca
  • †Contact author: alina.czajka@ncbj.gov.pl
  • ‡Contact author: juhehong@gmail.com
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Phys. Rev. C 112, 064905 – Published 8 December, 2025

DOI: https://doi.org/10.1103/7rrg-2nq3

Abstract

Determining the transport properties of quark-gluon plasma is one of the most important aspects of relativistic heavy ion collision studies. Field-theoretical calculations of transport coefficients such as the shear and bulk viscosities require Kubo formulas, which in turn require real-time correlation functions of stress-energy tensors. Consequently, knowing the analytic structure of these correlation functions is essential in any such studies. Using the energy-conservation laws and the results from gravity-hydrodynamics analysis, we determine the low-frequency and low-wavenumber analytic structures of all stress-energy correlation functions in the rest frame of the medium. By comparing with the diffusion and sound spectra from the second-order and third-order relativistic hydrodynamics, various new Kubo formulas are derived in the limit where the zero-frequency limit is taken first. We also show that the meaning of the Kubo formulas for relaxation times can change when higher-order terms are added to the hydrodynamics. A subtle issue of taking the zero frequency and zero wave0number limits when using skeleton diagrams is addressed as well.

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Phys. Rev. C 112, 064905– Published 8 December, 2025
  • Received 22 August 2025
  • Accepted 31 October 2025
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