We determine from first principles the quark mass anomalous dimension in N f = 3 QCD between the electroweak and hadronic scales. This allows for a fully non-perturbative connection of the perturbative and nonperturbative 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%.

We discuss the issue of global anomalies in chiral gauge theories on the lattice. In Lüscher's approach, these obstructions make it impossible to define consistently a fermionic measure for the path integral. We show that an SU (2) theory has such a global anomaly if the Weyl fermion is in the fundamental representation. The anomaly in higher representations is also discussed. We finally show that this obstruction is the lattice analogue of the SU (2) anomaly first discovered by Witten.

We present a lattice QCD determination of light quark masses with three sea-quark flavours (N f = 2+1). Bare quark masses are known from PCAC relations in the framework of CLS lattice computations with a non-perturbatively improved Wilson-Clover action and a tree-level Symanzik improved gauge action. They are fully non-perturbatively improved, including the recently computed Symanzik counter-term b A − b P . The mass renormalisation at hadronic scales and the renormalisation group running over a wide range of scales are known non-perturbatively in the Schrödinger functional scheme. In the present paper we perform detailed extrapolations to the physical point, obtaining (for the four-flavour theory) m u/d (2 GeV) = 3.54(12)(9) MeV and m s (2 GeV) = 95.7(2.5)(2.4) MeV in the MS scheme. For the mass ratio we have m s /m u/d = 27.0(1.0)(0.4). The RGI values in the three-flavour theory are M u/d = 4.70(15)(12) MeV and M s = 127.0(3.1)(3.2) MeV.

We present the open-source package openQ*D-1.0 [1], which has been primarily, but not uniquely, designed to perform lattice simulations of QCD+QED and QCD, with and without C * boundary conditions, and O(a) improved Wilson fermions. The use of C * boundary conditions in the spatial direction allows for a local and gauge-invariant formulation of QCD+QED in finite volume, and provides a theoretically clean setup to calculate isospin-breaking and radiative corrections to hadronic observables from first principles. The openQ*D code is based on openQCD-1.6 [2] and NSPT-1.4 [3]. In particular it inherits from openQCD-1.6 several core features, e.g. the highly optimized Dirac operator, the locally deflated solver, the frequency splitting for the RHMC, or the 4th order OMF integrator.

As first realized by Witten an SU (2) gauge theory coupled to a single Weyl fermion suffers from a global anomaly. This problem is addressed here in the context of the recent developments on chiral gauge theories on the lattice. We find Witten's anomaly manifests in the impossibility of defining globally a fermion measure that reproduces the proper continuum limit. Moreover, following Witten's original argument, we check numerically the crossing of the lowest eigenvalues of Neuberger's operator along a path connecting two gauge fields that differ by a topologically non-trivial gauge transformation.