I.M. Barbour

Problems with Finite Density Simulations of Lattice QCD

We present a discussion of problems that have arisen in attempts to understand the behavior of lattice QCD at high densities. The effects observed in the lattice simulations do not seem to be consistent with what we expect from the usual ideas of chiral symmetry breaking. In particular, at zero quark mass, there does not seem to be a massive baryon at finite density.

RESULTS ON FINITE DENSITY QCD

A brief summary of the formulation of QCD at finite chemical potental, μ, is presented. The failure of the quenched approximation to the problem is reviewed. Results are presented for dynamical simulations of the theory at strong and intermediate couplings. We find that the problems associated with the quenched theory persist: the onset of non-zero quark number does seem to occur at a chemical potential ≈ m x 2 . However analysis of the Lee-Yang zeros of the grand canonical partition function in the complex fugacity plane, (eμ/T), does show signals of critical behaviour in the expected region of chemical potential. Results are presented for a simulation at finite density of the Gross-Neveu model on a 163 lattice near to the chiral limit. Contrary to our simulations of QCD no pathologies were found when μ passed through the value m x 2 .

The critical points of strongly coupled lattice QCD at nonzero chemical potential

We study QCD at nonzero quark density, zero temperature, infinite coupling using the Glasgow algorithm. An improved complex zero analysis gives a critical point

Complex zeros of the partition function for lattice QCD

{\ensuremath{\mu}}_{c}

Analysis of single pion photoproduction at high and low energies

in agreement with that of chiral symmetry restoration computed with strong coupling expansions, and monomer-dimer simulations. We observe, however, two unphysical critical points: the onset for the number density

Simulations with lattice QCD at finite density

{\ensuremath{\mu}}_{0}

CHARGED PION PHOTOPRODUCTION IN THE QUARK MODEL.

, and

The Lanczos Method in Lattice Gauge Theories

{\ensuremath{\mu}}_{s}

The\(N\bar N\) and ππ decay modes of baryonium

the saturation threshold, coincident with pathological onsets observed in past quenched QCD calculations. An analysis of the probability distributions for particle number supports our physical interpretation of the critical point

CHIRAL SYMMETRY RESTORATION AND REALISATION OF THE GOLDSTONE MECHANISM IN THE U(1) GROSS-NEVEU MODEL AT NON-ZERO CHEMICAL POTENTIAL

{\ensuremath{\mu}}_{c},