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The eigenvalue spectrum $rho(lambda)$ of the Dirac operator is numerically calculated in lattice QCD with 2+1 flavors of dynamical domain-wall fermions. In the high-energy regime, the discretization effects become significant. We subtract them at the leading order and then take the continuum limit with lattice data at three lattice spacings. Lattice results for the exponent $partiallnrho/partiallnlambda$ are matched to continuum perturbation theory, which is known up to $O(alpha_s^4)$, to extract the strong coupling constant $alpha_s$.
The determination of renormalization factors is of crucial importance. They relate the observables obtained on finite, discrete lattices to their measured counterparts in the continuum in a suitable renormalization scheme. Therefore, they have to be
We review the long term project of the ALPHA collaboration to compute in QCD the running coupling constant and quark masses at high energy scales in terms of low energy hadronic quantities. The adapted techniques required to numerically carry out the
Recent developments in non-perturbative renormalization for lattice QCD are reviewed with a particular emphasis on RI/MOM scheme and its variants, RI/SMOM schemes. Summary of recent developments in Schroedinger functional scheme, as well as the summa
We propose a fully non-perturbative method to compute inelastic lepton-nucleon ($ell N$) scattering cross sections using lattice QCD. The method is applicable even at low energies, such as the energy region relevant for the recent and future neutrino
We compute the spectral density of the (Hermitean) Dirac operator in Quantum Chromodynamics with two light degenerate quarks near the origin. We use CLS/ALPHA lattices generated with two flavours of O(a)-improved Wilson fermions corresponding to pseu