  We determine from first principles the quark mass anomalous dimension in Nf=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 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
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%.
