We determine the scale setting function and the pseudo-critical temperature on the lattice in $N_f=2$ two-color QCD using the Iwasaki gauge and Wilson fermion actions. Although two-color QCD does not correspond to the real world, it is very useful as a good testing ground for three-color QCD. The scale setting function gives the relative lattice spacings of simulations performed at different values of the bare coupling. It is a necessary tool for taking the continuum limit. Firstly, we measure the meson spectra for various combinations of ($\beta,\kappa$) and find a line of constant physics in $\beta$--$\kappa$ plane. Next, we determine the scale setting function via $w_0$ scale in the gradient flow method. Furthermore, we estimate the pseudo-critical temperature at zero chemical potential from the chiral susceptibility. Combining these results, we can discuss the QCD phase diagram in which both axes are given by dimensionless quantities, namely, the temperature normalized by the pseudo-critical temperature on the lattice and the chemical potential normalized by the pseudoscalar meson mass. It makes it easy to compare among several lattice studies and also makes it possible to compare theoretical analyses and lattice studies in the continuum limit.

中文翻译：

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Nf = 2 威尔逊费米子的双色 QCD 的相对标度设置

我们使用 Iwasaki 规范和威尔逊费米子作用确定 $N_f=2$ 双色 QCD 中晶格上的标度设置函数和伪临界温度。虽然二色 QCD 与现实世界不对应，但作为三色 QCD 的良好试验场非常有用。比例设置函数给出了在不同裸耦合值下执行的模拟的相对晶格间距。是取连续极限的必备工具。首先，我们测量 ($\beta,\kappa$) 的各种组合的介子谱，并在 $\beta$--$\kappa$ 平面中找到一条恒定物理线。接下来，我们通过梯度流法中的 $w_0$ scale 来确定 scale 设置函数。此外，我们从手性磁化率估计了零化学势下的伪临界温度。结合这些结果，我们可以讨论 QCD 相图，其中两个轴都由无量纲量给出，即由晶格上的伪临界温度归一化的温度和由赝标量介子质量归一化的化学势。它可以轻松地在多个晶格研究之间进行比较，并且还可以在连续介质限制中比较理论分析和晶格研究。