QCD and the eta prime Mass: Instantons or Confinement?

Abstract

We argue that lattice calculations of the ${\eta }^{\prime }$ mass in QCD with $N_c=2$ colors performed at non-zero baryon chemical potential can be used to study the mechanism responsible for the mass of the ${\eta }^{\prime }$. QCD with two colors is an ideal laboratory because it exhibits confinement, chiral symmetry breaking and a would-be $U(1{)}_A$ Goldstone boson at all densities. Since the instanton density and the confinement scale vary with density in a very different way, instantons are clearly distinguishable from other possible mechanisms. There is an instanton prediction for the ${\eta }^{\prime }$ mass at large density that can be compared to lattice results. The density dependence of the instanton contribution is a simple consequence of the integer topological charge carried by the instanton. We also argue that $N_c=3$ color QCD at finite isospin density can be used in order to study the origin of OZI-violation in the scalar sector.

6 pages, 2 figures

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