Non-perturbative quark mass renormalisation and running in $N_f=3$ QCD

We determine from first principles the quark mass anomalous dimension in $N_{\scriptstyle \mathrm{f}}=3$ QCD between the electroweak and hadronic scales. This allows for a fully non-perturbative connection of the perturbative and non-perturbative regimes of the Standard Model in the hadronic sector. The computation is carried out to high accuracy, employing massless $\text{ O }(a)$ -improved Wilson quarks and finite-size scaling techniques. We also provide the matching factors required in the renormalisation of light quark masses from lattice computations with $\text{ O }(a)$ -improved Wilson fermions and a tree-level Symanzik improved gauge action. The total uncertainty due to renormalisation and running in the determination of light quark masses in the SM is thus reduced to about $1\%$ .