Abstract
(Englisch)
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1. Having completed the parameterization and testing of the chiral symmetric fixed-point action [1,2,3] we performed a large scale numerical simulation using computing power (Hitachi 8000, Munich and IBM SP4, Manno) in the framework of a Bern-Graz-Regensburg collaboration [4]. Due to the good chiral properties of our Dirac operator we were able to explore pion masses down to 210 MeV. This made it possible to identify the logarithmic chiral corrections to the pion mass in quenched QCD and predict the corresponding parameter d = 0.17(2) [2,4]. We studied hadron spectroscopy (pseudoscalar and vector bosons, octet and decouplet baryons) at different lattice resolutions and volumes. Comparing our results with that of the largest earlier studies we found that our action at lattice unit a ' 016 fm has significantly smaller cut-off effects than the Wilson action at a ' 0.05 fm. The finite effects are small, no effect is seen above L = 1.3 fm for mesons and above 1.9 fm for baryons, where L is the size of the box simulated. While no cut-off effect is seen in the energy-momentum dispersion relation of hadrons, we see cut-off effects (although small) on the coarsest lattice when a pure gauge theory scale (r0) is used.
2. Although the quark source used in hadron spectroscopy is not optimal to create two pions we were able to get a signal for the pi-pi scattering length in the isospin = 2 channel [4]. The preliminary results are promising and we continue working on this problem using an improved 2-pion source.
[1] P. Hasenfratz, S. Hauswirth, T. Jörg, F. Niedermayer and K. Holland, Testing the fixed-point QCD action and the construction of chiral curents, hep-lat/0205010.
[2] S. Hauswirth, Light hadron spectroscopy in quenched lattice QCD with chiral fixed-point fermions, Thesis, Bern University, hep-lat/0204015.
[3] T. Jörg, Chiral measurements in quenched lattice QCD with fixed-point fermions, Thesis, Bern University, hep-lat/0206025.
[4] Ch. Gattringer et al. (Bern-Graz-Regensburg collaboration), Quenched QCD with fixed-point and chirally improved fermions, Nucl. Phys. Proc. Suppl. (in print), hep-lat/0209099.
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