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Description
We perform the complete non-perturbative running of the quark mass from hadronic to electroweak scales in $N_f = 3$ massless QCD. In the present work we use the same configuration ensembles used for a similar calculation arXiv 1802.05243, subject to Schrödinger Functional (SF) boundary conditions, whereas we use valence quarks with ($\chi$SF) boundary conditions, which results in O(a) improvement for observables after tuning of boundary counterterms. We establish the optimal tuning strategy for the critical hopping parameter $\kappa_{\rm crit}$ and the $\chi$SF boundary counterterm coefficient $z_{\rm f}$. Following the recent Alpha strategy, we work in two different energy regimes: at high energies ($\mu > $~2GeV) we use a SF-type coupling, while at low energies ($\mu < $~2GeV) a Gradient Flow (GF)-type coupling.