Nuclear Theory Seminars at Texas A&M: Fall 2005

Location: Cyclotron Building (434), Seminar Room

Friday, October 21, 2:00pm

Dr. Stefan Leupold, Gießen University, Germany
Weinberg sum rules, four-quark condensates and chiral restoration

Abstract:

In QCD, weighted averages (moments) of the difference of spectra in the vector and axial-vector channel can be identified as order parameters of chiral symmetry breaking (generalized Weinberg sum rules [1]). One of these moments is connected to a specific four-quark condensate. It is pointed out how this condensate can be evaluated for in-medium situations in the large-N_c limit, where N_c denotes the number of colors [2].

The four-quark condensate is evaluated

1. for low temperature (and vanishing baryo-chemical potential) by approximating the medium by a pion gas;
2. for finite baryo-chemical potential (and vanishing temperature) by approximating the medium by a Fermi sphere of nucleons;
3. for sizable temperature and sizable baryo-chemical potential by approximating the medium by a resonance gas [3].

For the first two cases it is demonstrated that the corrections to the respective large-N_c result can be expected to be small. The third case allows the determination of a transition line to the chirally restored phase as a function of temperature and baryo-chemical potential [4]. The regime of sizable temperature and sizable baryo-chemical potential is especially relevant for the Compressed Baryonic Matter (CBM) project [5] at the future Facility for Antiproton and Ion Research (FAIR) at GSI.

[1] J. I. Kapusta and E. V. Shuryak, Phys. Rev. D 49, 4694 (1994), hep-ph/9312245.
[2] S. Leupold, Phys. Lett. B 616, 203 (2005), hep-ph/0502061.
[3] P. Gerber and H. Leutwyler, Nucl. Phys. B 321, 387 (1989).
[4] S. Leupold, in preparation.
[5] http://www.gsi.de/zukunftsprojekt/experimente/CBM/