Transport and Response Coefficients in Second-Order Dissipative Relativistic Hydrodynamics with Quantum Corrections: Probing the Quark–Gluon Plasma

A functional measure encompasses quantum corrections and is explored in the fluid/gravity correspondence. Corrections to the response and transport coefficients in the second-order dissipative relativistic hydrodynamics are proposed, including those to the pressure, relaxation time, and shear relaxation time. Their dependence on the quark-gluon plasma (QGP) temperature sets a temperature dependence on the running parameter encoding the one-loop quantum gravity correction, driven by a functional measure. The experimental range of the bulk-viscosity-to-entropy-density ratio of the QGP, obtained by five different analyses (JETSCAPE Bayesian model, Duke, Jyväskylä-Helsinki-Munich, MIT-Utrecht-Genève, and Shanghai) corroborates the existence of the functional measure. Our results suggest that high-temperature plasmas could be used to experimentally test quantum gravity.