Köln 2004 – wissenschaftliches Programm

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HK: Physik der Hadronen und Kerne

HK 20: Theory III

HK 20.3: Vortrag

Dienstag, 9. März 2004, 16:30–16:45, E

Renormalization Group Flow Equations for the Linear sigma-Model at Finite Volume and Finite Quark Mass — •Bertram Klein, Jens Braun, Lars Jendges, and Hans-Jürgen Pirner — Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 19, 69120 Heidelberg.

The linear sigma-model with quarks provides a valid description of QCD on a scale below approximately 1.3 GeV. It is well suited to describe the physics of the chiral symmetric phase at the UV scale, as well as he physics at low energies characterized by chiral symmetry breaking.

Starting with the theory given at the UV scale, in the renormalization group approach infinitesimal shells of large momentum modes are integrated out and the couplings of the theory are renormalized. In this way, an effective low energy theory is obtained by evolving the couplings towards small momentum scales.

In order to enable a comparison with results from lattice QCD, we consider a renormalization group treatment of the linear sigma model in a finite Euclidean volume. The renormalization group flow equations are derived and solved numerically. Explicit breaking of the chiral symmetry is considered through the introduction of a finite quark mass.

We obtain results for the volume dependence of the chiral condensate. In accordance with the results obtained from finite volume partition functions, the mesonic zero modes are important for the evolution of the couplings at low renormalization scales.