Darmstadt 2008 – scientific programme
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HK: Fachverband Physik der Hadronen und Kerne
HK 28: Theorie
HK 28.2: Talk
Tuesday, March 11, 2008, 11:30–11:45, 2F
Comparison of O(4) scaling behavior and lattice QCD results — •Bertram Klein1 and Jens Braun2 — 1Technische Universität München, Garching — 2TRIUMF, Vancouver, Canada
QCD lattice simulations have established the phase transition order for three quark flavors with a high degree of confidence, but there are still questions for two light quark flavors. While there is a lot of evidence for a second-order transition, some lattice results appear to be incompatible with the expected O(4) scaling behavior.
An analysis of the scaling behavior is necessary to determine the order of a phase transition in a finite-volume system in the presence of symmetry-breaking quark masses. Such an analysis requires knowledge about critical exponents and scaling functions.
We use non-perturbative Renormalization Group methods to calculate scaling functions and finite-size scaling behavior for an O(4) model in 3 dimensions, including a symmetry-breaking external field.
We obtain results for scaling functions for the order parameter and the chiral susceptibility over a wide range of volumes and pion masses and establish infinite-volume as well as finite-size scaling behavior. We find that corrections to the leading-order scaling behavior are already quite large at pion masses comparable to those in current lattice calculations. In addition, corrections to the finite-size scaling behavior also become large at volume sizes comparable to those in current lattice simulations. We compare scaling behavior of QCD lattice results for the phase transition with two flavors to the scaling functions obtained from our non-perturbative RG calculations.