Berlin 2005 – scientific programme
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HK: Physik der Hadronen und Kerne
HK 12: Theorie
HK 12.9: Talk
Friday, March 4, 2005, 18:45–19:00, TU MA041
Volume Dependence of the pion mass from Renormalization Group flows. — •Bertram Klein1, Jens Braun2, and Hans-Juergen Pirner2 — 1GSI, Planckstr.1, 64291 Darmstadt — 2Institut fuer Theoretische Physik, Universitaet Heidelberg, Philosophenweg 19, 69120 Heidelberg
We investigate finite volume effects on the pion mass and the pion decay constant. An understanding of such effects is necessary in order to interpret results from lattice QCD and extrapolate reliably from finite lattice volumes to infinite volume.
We consider the quark-meson-model in a finite 3+1 dimensional volume. In order to break chiral symmetry in the finite volume, we introduce a small current quark mass. In the corresponding effective potential for the meson fields, the chiral O(4) symmetry is broken explicitly, and the sigma and pion fields are treated individually. Using the proper-time renormalization group (RG), we derive renormalization group flow equations in the finite volume and solve these equations in the local potential approximation.
We calculate the volume dependence of pion mass and pion decay constant and investigate the influence of different boundary conditions for the quark fields on the result.
We compare our results with results from chiral perturbation theory in finite volume and with results from lattice QCD.