### Abstract

The energy-momentum tensor plays an important role in QCD thermodynamics. Its expectation value contains information of the pressure and the energy density as its diagonal part. Further properties like viscosity and specific heat can be extracted from its correlation function. A nonperturbative evaluation of it on the lattice is called. Recently, a new method based on the gradient flow was introduced to calculate the energy-momentum tensor on the lattice and has been successfully applied to quenched QCD. In this paper, we apply the gradient flow method to calculate the energy-momentum tensor in (2+1)-flavor QCD adopting a nonperturbatively O(a)-improved Wilson quark action and the renormalization group-improved Iwasaki gauge action. As the first application of the method with dynamical quarks, we study at a single but fine lattice spacing a≃0.07 fm with heavy u and d quarks (mπ/mρ≃0.63) and approximately physical s quark (mηss/mφ≃0.74). With the fixed-scale approach, temperature is varied by the temporal lattice size Nt at a fixed lattice spacing. Performing simulations on lattices with Nt=16 to 4, the temperature range of T≃174-697 MeV is covered. We find that the results of the pressure and the energy density by the gradient flow method are consistent with the previous results using the T-integration method at T280 MeV (Nt10), while the results show disagreement at T350 MeV (Nt8), presumably due to the small-Nt lattice artifact of O((aT)2)=O(1/Nt2). We also apply the gradient flow method to evaluate the chiral condensate taking advantage of the gradient flow method that renormalized quantities can be directly computed avoiding the difficulty of explicit chiral violation with lattice quarks. We compute the renormalized chiral condensate in the MS- scheme at renormalization scale μ=2 GeV with a high precision to study the temperature dependence of the chiral condensate and its disconnected susceptibility. Even with the Wilson-type quark action which violates the chiral symmetry explicitly, we obtain the chiral condensate and its disconnected susceptibility showing a clear signal of pseudocritical temperature at T∼190 MeV related to the chiral restoration crossover.

Original language | English |
---|---|

Article number | 014509 |

Journal | Physical Review D |

Volume | 96 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jul 1 2017 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D*,

*96*(1), [014509]. https://doi.org/10.1103/PhysRevD.96.014509

**Exploring Nf=2+1 QCD thermodynamics from the gradient flow.** / (WHOT-QCD Collaboration).

Research output: Contribution to journal › Article

*Physical Review D*, vol. 96, no. 1, 014509. https://doi.org/10.1103/PhysRevD.96.014509

}

TY - JOUR

T1 - Exploring Nf=2+1 QCD thermodynamics from the gradient flow

AU - (WHOT-QCD Collaboration)

AU - Taniguchi, Yusuke

AU - Ejiri, Shinji

AU - Iwami, Ryo

AU - Kanaya, Kazuyuki

AU - Kitazawa, Masakiyo

AU - Suzuki, Hiroshi

AU - Umeda, Takashi

AU - Wakabayashi, Naoki

PY - 2017/7/1

Y1 - 2017/7/1

N2 - The energy-momentum tensor plays an important role in QCD thermodynamics. Its expectation value contains information of the pressure and the energy density as its diagonal part. Further properties like viscosity and specific heat can be extracted from its correlation function. A nonperturbative evaluation of it on the lattice is called. Recently, a new method based on the gradient flow was introduced to calculate the energy-momentum tensor on the lattice and has been successfully applied to quenched QCD. In this paper, we apply the gradient flow method to calculate the energy-momentum tensor in (2+1)-flavor QCD adopting a nonperturbatively O(a)-improved Wilson quark action and the renormalization group-improved Iwasaki gauge action. As the first application of the method with dynamical quarks, we study at a single but fine lattice spacing a≃0.07 fm with heavy u and d quarks (mπ/mρ≃0.63) and approximately physical s quark (mηss/mφ≃0.74). With the fixed-scale approach, temperature is varied by the temporal lattice size Nt at a fixed lattice spacing. Performing simulations on lattices with Nt=16 to 4, the temperature range of T≃174-697 MeV is covered. We find that the results of the pressure and the energy density by the gradient flow method are consistent with the previous results using the T-integration method at T280 MeV (Nt10), while the results show disagreement at T350 MeV (Nt8), presumably due to the small-Nt lattice artifact of O((aT)2)=O(1/Nt2). We also apply the gradient flow method to evaluate the chiral condensate taking advantage of the gradient flow method that renormalized quantities can be directly computed avoiding the difficulty of explicit chiral violation with lattice quarks. We compute the renormalized chiral condensate in the MS- scheme at renormalization scale μ=2 GeV with a high precision to study the temperature dependence of the chiral condensate and its disconnected susceptibility. Even with the Wilson-type quark action which violates the chiral symmetry explicitly, we obtain the chiral condensate and its disconnected susceptibility showing a clear signal of pseudocritical temperature at T∼190 MeV related to the chiral restoration crossover.

AB - The energy-momentum tensor plays an important role in QCD thermodynamics. Its expectation value contains information of the pressure and the energy density as its diagonal part. Further properties like viscosity and specific heat can be extracted from its correlation function. A nonperturbative evaluation of it on the lattice is called. Recently, a new method based on the gradient flow was introduced to calculate the energy-momentum tensor on the lattice and has been successfully applied to quenched QCD. In this paper, we apply the gradient flow method to calculate the energy-momentum tensor in (2+1)-flavor QCD adopting a nonperturbatively O(a)-improved Wilson quark action and the renormalization group-improved Iwasaki gauge action. As the first application of the method with dynamical quarks, we study at a single but fine lattice spacing a≃0.07 fm with heavy u and d quarks (mπ/mρ≃0.63) and approximately physical s quark (mηss/mφ≃0.74). With the fixed-scale approach, temperature is varied by the temporal lattice size Nt at a fixed lattice spacing. Performing simulations on lattices with Nt=16 to 4, the temperature range of T≃174-697 MeV is covered. We find that the results of the pressure and the energy density by the gradient flow method are consistent with the previous results using the T-integration method at T280 MeV (Nt10), while the results show disagreement at T350 MeV (Nt8), presumably due to the small-Nt lattice artifact of O((aT)2)=O(1/Nt2). We also apply the gradient flow method to evaluate the chiral condensate taking advantage of the gradient flow method that renormalized quantities can be directly computed avoiding the difficulty of explicit chiral violation with lattice quarks. We compute the renormalized chiral condensate in the MS- scheme at renormalization scale μ=2 GeV with a high precision to study the temperature dependence of the chiral condensate and its disconnected susceptibility. Even with the Wilson-type quark action which violates the chiral symmetry explicitly, we obtain the chiral condensate and its disconnected susceptibility showing a clear signal of pseudocritical temperature at T∼190 MeV related to the chiral restoration crossover.

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U2 - 10.1103/PhysRevD.96.014509

DO - 10.1103/PhysRevD.96.014509

M3 - Article

VL - 96

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 1

M1 - 014509

ER -