Quark mass RG-running for Nf =3 QCD in a χSF setup

We compute the nonperturbative quark mass RG-running in the range $Lambda_{QCD}lessapproxmulessapprox M_W$ for $N_f=3$ massless QCD with a mixed action approach: sea quarks are regularised using nonperturbatively $O(a)$-improved Wilson fermions with Schr"odinger functional (SF) boundary conditions, employing the configurations of 1802.05243, while valence quarks are regularised using nonperturbatively $O(a)$-improved Wilson fermions with chirally rotated Schr"odinger functional boundary conditions ($chi$SF). Our result is compatible with its SF counterpart of ref.1802.05243, confirming the universality of $chi$SF and SF in the continuum limit. We also establish the optimal tuning strategy for the critical hopping parameter $kappa_c$ and the $chi$SF boundary counterterm coefficient $z_{ m f}$. We work in two energy regimes with two different definitions of the coupling: SF-coupling for 2 GeV $lessapproxmulessapprox M_W$ and GF-coupling for $Lambda_{QCD} lessapproxmulessapprox 2 GeV$.