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 $\eta'$ 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.
Giusti, L., Rossi, G., Testa, M., Veneziano, G. (2002). The UA (1) problem on the lattice. NUCLEAR PHYSICS B-PROCEEDINGS SUPPLEMENTS, 106, 1001-1003 [10.1016/S0920-5632(01)01910-7].
The UA (1) problem on the lattice
GIUSTI, LEONARDO;
2002
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 $\eta'$ 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.
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