This project addresses the problem of reducing systematic errors due to ontinuum limit corrections, which affect the phenomenological results of Lattice Quantum Chromodynamics (QCD) simulations. Lattice simulations in particle physics have stimulated many developments in computational techniques and even the realization of dedicated hardware. This research proposal would contribute to a theoretical framework towards an optimized exploitation of available computer resources, in order to obtain more and more reliable physical predictions from numerical simulations. In particular, the project consists of three main subjects :
i) the extension of the ideas of non-perturbative renormalization to th computation of the strong coupling constant ;
ii) the study, in the context of non-perturbative renormalization, of t 4-fermion operator relevant for the investigation of the hI = 1/2 rule, to understand the origin of the observed experimental enhancement ;
iii) the extension of the 'improvement' method to higher orders, in the case of heavy quark masses.