Quark mass RG-running for $N_f$ =3 QCD in a $\chi SF$ setup

Abstract

We compute the nonperturbative quark mass RG-running in the range ${\Lambda }_{QCD}⪅\mu ⪅M_W$ for $N_f=3$ massless QCD with a mixed action approach: sea quarks are regularised using nonperturbatively $O(a)$-improved Wilson fermions with Schrödinger 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 Schrödinger 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 $z_{\mathrm{f}}$. We work in two energy regimes with two different definitions of the coupling: SF-coupling for 2 GeV $⪅\mu ⪅M_W$ and GF-coupling for ${\Lambda }_{QCD}⪅\mu ⪅2GeV$.

Comments: 8 pages, 5 figures, presented at the 38th International Symposium on Lattice Field Theory, LATTICE2021, 26th-30th July, 2021. Updated acknowledgements