Nf=2+1采用双环匹配系数的梯度流动QCD热力学

Y. Taniguchi, S. Ejiri, K. Kanaya, M. Kitazawa, Hiroshi Suzuki, T. Umeda
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引用次数: 15

摘要

采用O(a)-改进的Wilson夸克作用和Iwasaki规范作用研究了晶格上Nf=2+1 QCD的热力学性质。为了解决由于显式违反庞加莱对称性和手性对称性而引起的问题,我们采用了基于梯度流的小流时展开(SFtX)方法,该方法是正确计算晶格上任何重归一化观测值的通用方法。该方法利用微扰理论计算小流时展开中算子前的匹配系数。在之前使用单环匹配系数的研究中,我们发现SFtX方法对状态方程、手性凝聚物和磁化率都有很好的效果。本文研究了Harlander等人的双环匹配系数的影响。我们还测试了重整化尺度在SFtX方法中的影响。我们发现,通过采用Harlander等人的mu_0重整化尺度而不是传统的mu_d=1/sqrt{8t}尺度,改善了大t下的线性行为,使我们可以更自信地执行SFtX方法的t ->外推。Harlander等人在计算双环匹配系数时,采用了夸克场的运动方程。对于不受运动方程影响的熵密度,我们发现使用双环系数的结果与使用单环系数的结果吻合得很好。另一方面,对于受运动方程影响的轨迹异常,我们发现高温下的一环和双环结果存在差异。通过对比使用运动方程和不使用运动方程的单回路系数结果,认为差异的主要原因是运动方程在N_t =< 10时的离散误差为O((aT)^2)=O(1/N_t^2)。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Nf=2+1 QCD thermodynamics with gradient flow using two-loop matching coefficients
We study thermodynamic properties of Nf=2+1 QCD on the lattice adopting O(a)-improved Wilson quark action and Iwasaki gauge action. To cope with the problems due to explicit violation of the Poincare 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. In a previous study using one-loop matching coefficients, we found that the SFtX method works well for the equation of state, chiral condensates and susceptibilities. In this paper, we study the effect of two-loop matching coefficients by Harlander et al. We also test the influence of the renormalization scale in the SFtX method. We find that, by adopting the mu_0 renormalization scale of Harlander et al. instead of the conventional mu_d=1/sqrt{8t} scale, the linear behavior at large t 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 O((aT)^2)=O(1/N_t^2) discretization errors in the equation of motion at N_t =< 10.
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