. co m p - ph ] 4 A pr 2 00 2 DESY 02 – 030 Fundamental parameters of QCD LPHA

The theory of strong interactions, QCD, is described in terms of a few parameters, namely the strong coupling constant αs and the quark masses. We show how these parameters can be determined reliably using computer simulations of QCD on a space-time lattice, and by employing a finite-size scaling method, which allows to trace the energy dependence of αs and quark masses over several orders of magnitude. We also discuss methods designed to reduce the effects of finite lattice spacing and address the issue of computer resources required. (Contribution to NIC Symposium 2001 – Proceedings) Fundamental parameters of QCD ALPHA Collaboration, Rainer Sommer and Hartmut Wittig 1 DESY, Platanenallee 6, 15738 Zeuthen, Germany E-mail: [email protected] 2 DESY, Notkestrasse 85, 22603 Hamburg, Germany E-mail: [email protected] The theory of strong interactions, QCD, is described in terms of a few parameters, namely the strong coupling constant αs and the quark masses. We show how these parameters can be determined reliably using computer simulations of QCD on a space-time lattice, and by employing a finite-size scaling method, which allows to trace the energy dependence of αs and quark masses over several orders of magnitude. We also discuss methods designed to reduce the effects of finite lattice spacing and address the issue of computer resources required. 1 The Standard Model of particle physics Over the last few decades, particle physicists have explored the fundamental forces down to distance scales of ≈ 10 m. It was found that the experimental observations are described to very high accuracy by a theory which is known as the Standard Model of particle physics. During the 1990s in particular, the predictions of this theoretical framework have been put to very stringent tests in accelerator experiments across the world. Perhaps one of the most impressive examples of its predictive power, the line shape of the Z-resonance in ee scattering, is shown in Fig. 1. The Standard Model describes the interactions of the fundamental constituents of matter through electromagnetic, weak and strong forces in terms of three different quantum gauge theories. The success of the Standard Model is not only a consequence of the mathematical simplicity of its basic equations, but also because the forces they describe are relatively weak at the typical energy transfers in current experiments of about 10−100GeV. a The strengths of the interactions are characterized by so-called coupling constants. When the forces are weak, the predictions of the theory can be worked out in terms of an expansion in powers of these coupling constants, a procedure known as perturbation theory. For instance, in Quantum Electrodynamics (QED), the quantum gauge theory describing the interactions between electrons and photons, the coupling constant is the well-known fine structure constant α ≈ 1/137. Its smallness guarantees that only a few terms in the power series are sufficient in order to predict physical quantities with high precision. The gauge theory for the strong force is called Quantum Chromodynamics (QCD), in which quarks and gluons assume the rôles of the electrons and photons of QED. Quarks are the constituents of the more familiar protons and neutrons. The coupling constant of QCD, αs, then characterizes the strength of the interaction between quarks and gluons in In particle physics it is customary to use “natural units” where the speed of light, c and Planck’s constant, ~ are set to one and energies as well as masses are given in GeV. As an orientation note that mproton ≈ 1GeV, where 1GeV = 1.602 · 10 J.