TY - JOUR

T1 - Nf=2+1 QCD thermodynamics with gradient flow using two-loop matching coefficients

AU - Taniguchi, Yusuke

AU - Ejiri, Shinji

AU - Kanaya, Kazuyuki

AU - Kitazawa, Masakiyo

AU - Suzuki, Hiroshi

AU - Umeda, Takashi

N1 - Funding Information:
We are grateful to Prof. R. V. Harlander for valuable discussions. This work was in part supported by JSPS KAKENHI Grants No. JP20H01903, No. JP19H05146, No. JP19H05598, No. JP19K03819, No. JP18K03607, No. JP17K05442 and No. JP16H03982. This research used computational resources of COMA, Oakforest-PACS, and Cygnus provided by the Interdisciplinary Computational Science Program of Center for Computational Sciences, University of Tsukuba, K and other computers of Joint Usage/Research Center for Interdisciplinary Large-scale Information Infrastructures (JHPCN) through the High Performance Computing Infrastructure System Research Projects (Project ID: hp17208, hp190028, hp190036) and JHPCN projects (jh190003, jh190063), OCTOPUS at Cybermedia Center, Osaka University, ITO at Research Institute for Information Technology, Kyushu University, and Grand Chariot at Information Initiative Center, Hokkaido University. The simulations were in part based on the lattice QCD code set .

PY - 2020/7/1

Y1 - 2020/7/1

N2 - We study thermodynamic properties of Nf=2+1 QCD on the lattice adopting a nonperturbatively O(a)-improved Wilson quark action and the renormalization group-improved Iwasaki gauge action. To cope with the problems due to explicit violation of the Poincaré and chiral symmetries, we apply the small flow-time expansion (SFtX) method based on the gradient flow, which is a general method to correctly calculate any renormalized observables on the lattice. In this method, the matching coefficients in front of operators in the small flow-time expansion are calculated by perturbation theory thanks to the asymptotic freedom around the small flow-time limit. In a previous study using one-loop matching coefficients, we found that the SFtX method works well for the equation of state extracted from diagonal components of the energy-momentum tensor and for the chiral condensates and susceptibilities. In this paper, we study the effect of two-loop matching coefficients which have been calculated by Harlander et al. recently. We also test the influence of the renormalization scale in the SFtX method. We find that, by adopting the μ0 renormalization scale of Harlander et al. instead of the conventional μd=1/8t scale, the linear behavior at large flow-times is improved so that we can perform the t→0 extrapolation of the SFtX method more confidently. In the calculation of the two-loop matching coefficients by Harlander et al., the equation of motion for quark fields was used. For the entropy density in which the equation of motion has no effects, we find that the results using the two-loop coefficients agree well with those using one-loop coefficients. On the other hand, for the trace anomaly which is affected by the equation of motion, we find discrepancies between the one- and two-loop results at high temperatures. By comparing the results of one-loop coefficients with and without using the equation of motion, the main origin of the discrepancies is suggested to be attributed to contamination of O((aT)2)=O(1/Nt2) discretization errors in the equation of motion at Nt≲10.

AB - We study thermodynamic properties of Nf=2+1 QCD on the lattice adopting a nonperturbatively O(a)-improved Wilson quark action and the renormalization group-improved Iwasaki gauge action. To cope with the problems due to explicit violation of the Poincaré and chiral symmetries, we apply the small flow-time expansion (SFtX) method based on the gradient flow, which is a general method to correctly calculate any renormalized observables on the lattice. In this method, the matching coefficients in front of operators in the small flow-time expansion are calculated by perturbation theory thanks to the asymptotic freedom around the small flow-time limit. In a previous study using one-loop matching coefficients, we found that the SFtX method works well for the equation of state extracted from diagonal components of the energy-momentum tensor and for the chiral condensates and susceptibilities. In this paper, we study the effect of two-loop matching coefficients which have been calculated by Harlander et al. recently. We also test the influence of the renormalization scale in the SFtX method. We find that, by adopting the μ0 renormalization scale of Harlander et al. instead of the conventional μd=1/8t scale, the linear behavior at large flow-times is improved so that we can perform the t→0 extrapolation of the SFtX method more confidently. In the calculation of the two-loop matching coefficients by Harlander et al., the equation of motion for quark fields was used. For the entropy density in which the equation of motion has no effects, we find that the results using the two-loop coefficients agree well with those using one-loop coefficients. On the other hand, for the trace anomaly which is affected by the equation of motion, we find discrepancies between the one- and two-loop results at high temperatures. By comparing the results of one-loop coefficients with and without using the equation of motion, the main origin of the discrepancies is suggested to be attributed to contamination of O((aT)2)=O(1/Nt2) discretization errors in the equation of motion at Nt≲10.

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U2 - 10.1103/PhysRevD.102.014510

DO - 10.1103/PhysRevD.102.014510

M3 - Article

AN - SCOPUS:85091863104

VL - 102

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 1

M1 - 014510

ER -