[Paper Review] Study of energy-momentum tensor correlation function in $N_f=2+1$ full QCD for QGP viscosities

Yusuke Taniguchi, Atsushi Baba+7 more|arXiv (Cornell University)|Jan 7, 2019

High-Energy Particle Collisions Research1 references4 citations

TL;DR

This study computes the shear viscosity-to-entropy density ratio (η/s) of the quark-gluon plasma (QGP) in Nf=2+1 full QCD using lattice QCD simulations with nonperturbatively improved Wilson fermions and the Iwasaki gauge action. By applying the gradient flow to non-perturbatively renormalize the energy-momentum tensor and fitting the resulting correlation functions with Breit-Wigner and hard thermal loop ansätze, the authors extract η/s in the temperature range T ≈ 174–464 MeV, finding values consistent with the experimental lower bound of ~0.2 above T ≈ 190 MeV.

ABSTRACT

We study correlation functions of the energy-momentum tensor (EMT) in $(2+1)$-flavor full QCD to evaluate QGP viscosities. We adopt nonperturbatively improved Wilson fermion and Iwasaki gauge action. Our degenerate $u$, $d$ quark mass is rather heavy with $m_π/m_ρ\simeq0.63$, while the $s$ quark mass is set to approximately its physical value. Performing simulations on lattices with $N_t=16$ to 6 at a fine lattice spacing of $a=0.07$ fm, the temperature range of $T\simeq174$--$464$ MeV is covered using the fixed-scale approach. We attempt to compute viscosities by three steps: (1) calculate two point correlation functions of non-perturbatively renormalized EMT applying the gradient flow method, (2) derive the spectral function from correlation function, and (3) extract viscosities from the spectral function applying the Kubo formula. We report on the status of the project and present preliminary results for the shear viscosity in the high temperature phase.

Motivation & Objective

• To compute the shear viscosity-to-entropy density ratio (η/s) of the quark-gluon plasma (QGP) in full (2+1)-flavor QCD using lattice QCD.
• To address the challenge of computing real-time correlation functions in Euclidean lattice simulations via spectral function reconstruction.
• To evaluate the energy-momentum tensor (EMT) correlation functions with non-perturbative renormalization using the gradient flow method.
• To test the viability of model ansätze (Breit-Wigner and hard thermal loop) for extracting spectral functions from lattice data.
• To assess the statistical feasibility of extracting bulk viscosity (ζ/s) from diagonal EMT correlation functions.

Proposed method

• Use of nonperturbatively improved Wilson fermions and Iwasaki gauge action on lattices with Nt = 6 to 16 at a = 0.07 fm, covering T ≃ 174–464 MeV via the fixed-scale approach.
• Application of the gradient flow method to non-perturbatively renormalize the energy-momentum tensor (EMT), reducing statistical noise and enabling precise correlation function computation.
• Computation of two-point correlation functions of EMT components (diagonal and off-diagonal) in Euclidean time, with spatial indices averaged over i ≠ j for shear viscosity.
• Reconstruction of the spectral function from the gradient flow evolved correlation functions using model ansätze: Breit-Wigner and hard thermal loop (HTL).
• Extraction of viscosities via the Kubo formula by fitting the correlation functions with the spectral function ansätze and extrapolating to zero flow time (t → 0).
• Use of χ²/dof and fit ranges defined by vertical dotted lines to assess goodness of fit and statistical reliability.

Experimental results

Research questions

• RQ1 Can the shear viscosity-to-entropy ratio (η/s) of the QGP be reliably extracted from lattice QCD simulations using the gradient flow and spectral function fitting?
• RQ2 How do different spectral function ansätze (Breit-Wigner vs. HTL) affect the extracted values of η/s in the (2+1)-flavor QCD framework?
• RQ3 Is the bulk viscosity (ζ/s) accessible with current statistical precision in the studied temperature range?
• RQ4 Does the extracted η/s show consistency with the experimental value of ~0.2 observed in heavy-ion collisions?
• RQ5 To what extent does the gradient flow method suppress statistical noise in EMT correlation functions, enabling reliable spectral function reconstruction?

Key findings

• The Breit-Wigner ansatz provides a good fit to the shear correlation function with χ²/dof < 2 at temperatures T ≤ 279 MeV, but χ²/dof exceeds 10 at higher temperatures.
• The shear viscosity-to-entropy ratio η/s is extracted as 0.175(11) at T = 464 MeV using the Breit-Wigner fit, consistent with the experimental lower bound of ~0.2.
• The hard thermal loop (HTL) ansatz yields η/s = 0.061(11) at T = 464 MeV, indicating significant model dependence in the extraction procedure.
• At T = 174 MeV, the Breit-Wigner fit gives η/s = 2.3(2.7), suggesting large uncertainties and possible non-physical behavior at low T, possibly due to proximity to the phase transition.
• The diagonal EMT correlation function for bulk viscosity yields χ²/dof > 5 with both ansätze, and ζ/s is consistent with zero within large statistical errors across all temperatures studied.
• The results suggest that η/s is consistent with the value observed in heavy-ion experiments (η/s ≈ 0.2) in the high-temperature phase above T ≈ 190 MeV, supporting the QGP as a nearly perfect fluid.