Lattice QCD and the Phase Diagram of Quantum Chromodynamics Theory of Strongly Interacting Matter

Abstract

Quantum chromodynamics (QCD) is the theory of strong interactions. The elementary particles of QCD –contrary to the other particles described by the Standard Model (SM) of particle physics– can not be observed directly. The Lagrangian of QCD is given by quarks and gluons. Instead of free quarks and gluons we observe bound state hadrons. One of the most important features of QCD is asymptotic freedom. At small energies the coupling is strong, the value of the coupling constant is large. For large energies the coupling constant decreases and approaches zero. Since the coupling constant is large at small energies, we can not use one of the most powerful methods of particle physics, the perturbative approach. For large enough energies the coupling gets smaller, thus asymptotic freedom opens the possibility to use perturbative techniques. In this regime scattering processes can be treated perturbatively. The results are in good agreement with the experiments. At small energies (below about 1 GeV) the bound states and their interactions can be described only by non-perturbative methods. The most systematic non-perturbative technique today is lattice field theory. The field variables of the Lagrangian are defined on a discrete space-time lattice. The continuum results are obtained by taking smaller and smaller lattice spacings (a )a nd extrapolating the results to vanishing a. Though lattice field theory has been an active field for 30 years, the first continuum extrapolated full results appeared only recently. Another consequence of asymptotic freedom is that the coupling decreases for high temperatures (they are also characterized by large energies). According to the expectations at very high temperatures (Stefan-Boltzmann limit) the typical degrees of freedom are no longer bound state hadrons but freely moving quarks and gluons. Since there are obvious qualitative differences between these two forms of matter, we expect a phase transition between them at a given temperature Tc .T he value ofTc can be estimated to be the typical QCD scale (≈ 200 MeV). At large baryonic densities the Fermi surface is at large energy, thus we observe a similar phenomenon, the typical energies are large, the coupling is small. Also in this case we expect a phase transition between the phases characterized by small and large energies. In QCD the thermodynamic observables are related to the grand canonical partition function. Therefore, the baryonic density can be tuned by tuning the baryonic chemical potential (μ). If we increase the chemical potential the corresponding Tc values decrease. Thus, one obtains a non-trivial phase diagram on the T –μ plane.