Abstract
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%.
Highlights
We will employ the Schrödinger Functional [32,33] as an intermediate renormalisation scheme that allows to make contact between the hadronic scheme used in the computation of bare quark masses and the perturbative schemes used at high energies, and employ well-established finite-size recursion techniques [34,35,36,37,38,39,40,41,42,43,44,45] to compute the Renormalisation Group (RG) running nonperturbatively
In order to make the connection with renormalisation group invariants (RGI) masses, as spelled out in our strategy in Sect. 2, we could apply next-to-leading order (NLO) perturbation theory directly at an energy scale μpt at the higher end of our data-covered range – e.g., the one defined by g
For the purpose of the latter computation, we have provided a precise computation of the matching factors required to obtain renormalised quark masses from partially conserved axial current (PCAC) bare quark masses obtained from simulations based on CLS Nf = 2 + 1 ensembles [89,90]
Summary
Nf. The renormalisation group functions β and τ admit perturbative expansions of the form β(g). Note that the integrands are finite at g = 0, making the integrals well defined (and zero at universal order in perturbation theory). It is easy to check, that they are Nf -dependent but μindependent. They can be interpreted as the integration constants of the renormalisation group equations. The values of Mi can be checked to be independent of the renormalisation scheme. The value of QCD is instead scheme-dependent, but the ratio QCD/ QCD between its values in two different schemes can be calculated exactly using one-loop perturbation theory
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