Witten-Veneziano Formula Research Articles

Evidence for η′-π splitting in unquenched lattice QCD

We perform an extrapolation from negative to positive flavour numbers of full QCD lattice estimates of the η′ mass. The extrapolations are carried out by keeping ϱ and π masses at fixed values. We find an η′-π splitting which shows a flavour dependence consistent with the Witten-Veneziano formula based on the U(1) anomaly. The quantitative splitting is consistent with the estimates made in the quenched approximation.

Screening of the topological charge in a correlated instanton vacuum.

Screening of the topological charge due to he fermion-induced interactions is an important phenomenon, closely related with the resolution of the strong CP and U(1) problems. We study the mechanism of such screening in a 'correlated instanton vacuum', as opposed to the 'random' one. Both scalar and pseudoscalar gluonic correlators are analyzed by means of an observable that minimizes finite size effects. Screening of the topological charge is established. This allows us to calculate the $\eta'$ mass without having to invert the Dirac operator. We suggest that this method might be used in lattice QCD calculations as well. Our results for the screening of the topological charge are in agreement with the chiral Ward identities, and the scalar gluonic correlator satisfies a low energy theorem first derived by Novikov et al. \cite{Novikov-etal}. We also propose to evaluate the topological susceptibility in the Witten-Veneziano formula not in an infinite box in an world $without$ fermions but in an infinitesimal box in a world $with$ fermions.

The effects of aU(1) chiral condensate on the mass spectrum of the light pseudoscalar mesons

The possibility that a new order parameter for theU(1) chiral symmetry could exist is discussed. In particular we analyse the effects that one should observe on the mass spectrum of the (light) pseudoscalar mesons. A generalized “Witten-Veneziano formula” is found for the mass of the lightestSU(3) singlet pseudoscalar meson (the η′), making use of an effective Lagrangian formalism which also includes the new order parameter.

Renormalized Ward-Takahashi relations and topological susceptibility with staggered fermions

Local (axial) vector currents and (pseudo) scalar fields are constructed, renormalized and used to derive Ward-Takahashi relations for staggered fermions in lattice QCD. With the help of these a lattice derivation is given of the Witten-Veneziano formula for the flavor singlet pseudoscalar particle. We discuss how the ensuing topological susceptibility is to be evaluated and argue that it is finite.