Scale setting from a combination of lattice QCD formulations with Wilson and Wilson twisted mass valence quarks

We report about an update of a scale setting procedure employing a mixed action setup consisting of $N_f=2+1$ flavors of $\mathcal{O}(a)$-improved Wilson sea quarks, based on CLS ensembles, and Wilson twisted mass valence quarks at maximal twist. We employ as external input isoQCD masses and decay constants of pions and kaons, and use the gradient flow scale $t_0$ as an intermediate scale. The analysis includes ensembles in the vicinity of the physical point and five values of the lattice spacing down to $a\approx0.038$ fm. The determination of $t_0$ is carried out using three approaches: the unitary setup where Wilson quarks are used in the sea and valence sectors, the mixed action setup with Wilson twisted mass valence quarks, and by combining the data from the two previous cases. We observe that this combination leads to an improved control over the systematic uncertainties.