Hadronic Matrix Elements and Weak Decays in Lattice QCD

Abstract

Many important progresses have been done in lattice QCD since the first pioneering numerical calculations were started about 10 years ago. Since then substantial advances have been possible thanks to a great theoretical effort in understanding the lattice quantum field theory and to the extraordinary increase in the available conputer power. Almost all aspects of particle physics are currently studied on the lattice, already with phenomenologically relevant results. Although we are not yet at the point to be able to predict with sufficient accuracy the mass of the proton, many steps forward have been done in the calculation of the hadronic matrix elements. Lattice QCD offers in fact the unique possibility, of computing with the same method many different matrix elements which are of interest in the phenomenology of the Standard Model. Among the other quantities I will report the most recent results obtained for the pion and proton structure functions and electromagnetic form factors, the nucleon G-term, the meson decay constants and the weak hamiltonian matrix elements, including the semileptonic decays of D mesons. These lectures have been conceived to serve as an elementary introduction to this fascinating field and to offer to nonexperts a survey of the most relevant results.