Relative scale setting for two-color QCD with $N_f=2$ Wilson fermions

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.