Effective - field theories for the = 52 quantum Hall edge state

The quantum Hall state at the filling fraction =5 /2 is the leading candidate to be a physical system supporting excitations with non-Abelian braid statistics. While a direct experimental evidence for the latter is still absent, recent experiments by Radu et al. I. P. Radu, J. B. Miller, C. M. Marcus, M. A. Kastner, L. N. Pfeiffer, and K. W. West, Science 320, 899 2008 yielded results favoring some previously proposed nonAbelian theories over Abelian ones. Here, we systematically investigate candidate theories of the quantum Hall edge at the filling fraction =5 /2. We find a set of candidate theories, both Abelian and non-Abelian, which are equally consistent with the experimental data and cannot therefore be distinguished in the quasihole tunneling experiment only. We discuss what experimental information may be useful in resolving the ambiguity.