论文标题
NF = 2+1 QCD热力学，使用两环匹配系数进行梯度流动
Nf=2+1 QCD thermodynamics with gradient flow using two-loop matching coefficients
论文作者
论文摘要
我们研究了NF = 2+1 QCD在采用O（A）改良的Wilson Quark Action和Iwasaki仪表作用的晶格上的热力学特性。为了应对由于明确违反庞加罗和手性对称性而引起的问题，我们基于梯度流进行了较小的流动时间扩展（SFTX）方法，这是一种通用方法，可以正确计算晶格上的任何重新分配的可观察结果。在这种方法中，通过扰动理论计算了少量流动时间扩展中运算符前的匹配系数。在先前使用一环匹配系数的研究中，我们发现SFTX方法适合于状态，手性冷凝物和敏感性的方程式。在本文中，我们研究了Harlander等人的两环匹配系数的效果。我们还测试了SFTX方法中重新归一化量表的影响。我们发现，通过采用Harlander等人的MU_0重归其化量表。代替了常规的MU_D = 1/sqrt {8T}刻度，而是改进了大t的线性行为，以便我们可以更自信地执行SFTX方法的t-> 0外推。在Harlander等人的两环匹配系数的计算中，使用了夸克场运动方程。对于运动方程没有影响的熵密度，我们发现使用两环系数的结果与使用一环系数的系数非常吻合。另一方面，对于受运动方程影响的痕量异常，我们发现在高温下，一环和两循环结果之间存在差异。通过有或不使用运动方程的一环系数的结果，建议将差异的主要起源归因于o（（at）^2）= o（1/n_t^2）在N_T = <10的运动方程中的离散误差。
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.
