The $U_A(1)$ Problem on the Lattice

Abstract

If the expression of the topological charge density operator, suggested by fermions obeying the Ginsparg--Wilson relation, is employed, it is possible to prove on the lattice the validity of the Witten--Veneziano formula for the ${\eta }^{\prime }$ mass. Recent numerical results from simulations with overlap fermions in 2 (abelian Schwinger model) and 4 (QCD) dimensions give values for the mass of the lightest pseudo-scalar flavour-singlet state that agree with theoretical expectations and/or experimental data.

Comments: 3 pages, talk presented by G.C. Rossi at Lattice2001(theorydevelop)