Renormalization of quark propagator, vertex functions, and twist-2 operators from twisted-mass lattice QCD at\({N}_{f}=4\)

We present the analytical calculation of the four-loop QCD beta-function within the minimal subtraction scheme.

We present the analytical calculation of the four-loop quark mass anomalous dimension in Quantum Chromodynamics within the minimal subtraction scheme. On the basis of this result we find that the so-called invariant quark mass is a very good reference mass for the accurate evolution of the running MS-bar quark mass in phenomenological applications. We also obtain for the first time a complete 4-th order perturbative QCD expression for a physical quantity, the total Higgs boson decay rate into hadrons, and analyze the infrared fixed point for this case.

We propose a non-perturbative method for computing the renormalization constants of generic composite operators. This method is intended to reduce some systematic errors, which are present when one tries to obtain physical predictions from the matrix elements of lattice operators. We also present the results of a calculation of the renormalization constants of several two-fermion operators, obtained, with our method, by numerical simulation of \(QCD\), on a \(16^3 \times 32\) lattice, at \(\beta=6.0\). The results of this simulation are encouraging, and further applications to four-fermion operators and to the heavy quark effective theory are proposed.