Sign problem in QCD

The revised version of our paper 0808.2987 is up on arXiv now. Special thanks to Kim Splittorff, Mark Alford, Bob Sugar, Phillippe de Forcrand and many others for comments. See earlier discussion.

On the sign problem in dense QCD

http://arXiv.org/abs/0808.2987

S. Hsu and D. Reeb

We investigate the Euclidean path integral formulation of QCD at finite baryon density. We show that the partition function Z can be written as the difference between two sums Z+ and Z-, each of which defines a partition function with positive weights. If the ratio Z-/Z+ is nonzero in the infinite volume limit the sign problem is said to be severe. This occurs only if, and generically always if, the associated free energy densities F+ and F- are equal in this limit. In an earlier version of this paper we conjectured that F- is bigger than F+ in some regions of the QCD phase diagram, leading to domination by Z+. However, we present evidence here that the sign problem may be severe at almost all points in the phase diagram, except in special cases like exactly zero chemical potential (ordinary QCD), which requires a particular order of limits, or at exactly zero temperature and small chemical potential. Finally, we describe a Monte Carlo technique to simulate finite-density QCD in regions where Z-/Z+ is small.