Non-perturbative Test of the Witten-Veneziano Formula from Lattice QCD

Abstract

We compute both sides of the Witten-Veneziano formula using lattice techniques. For the one side we perform dedicated quenched simulations and use the spectral projector method to determine the topological susceptibility in the pure Yang-Mills theory. The other side we determine in lattice QCD with $N_f=2+1+1$ dynamical Wilson twisted mass fermions including for the first time also the flavour singlet decay constant. The Witten-Veneziano formula represents a leading order expression in the framework of chiral perturbation theory and we also employ leading order chiral perturbation theory to relate the flavor singlet decay constant to the relevant decay constant parameters in the quark flavor basis and flavor non-singlet decay constants. After taking the continuum and the SU$(2)$ chiral limits we compare both sides and find good agreement within uncertainties.

30 pages, 7 figures, version accepted for publication

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• Etaprime and Eta Mesons with Connection to Anomalous Glue
• Topology in full QCD at high temperature: a multicanonical approach
• $\theta$ dependence in $SU(3)$ Yang-Mills theory from analytic continuation
• Flavor-singlet meson decay constants from $N_f=2+1+1$ twisted mass lattice QCD
• Topological susceptibility of $N_f=2+1$ QCD from staggered fermions spectral projectors at high temperatures
• The Large $N_c$ limit of QCD on the lattice
• Fate of the ${\eta }^{\prime }$ in the Quark Gluon Plasma
• Topology via Spectral Projectors with Staggered Fermions
• Different faces of confinement
• $\eta$-glueball mixing from $N_f=2$ lattice QCD
• $U_A(1)$ symmetry restoration at high baryon density
• Strong CP Violation and large-$N_c$ spin-flavor symmetry
• Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
• Topological susceptibility and excess kurtosis in SU(3) Yang-Mills theory
• $\eta$ and ${\eta }^{\prime }$ mesons from $N_f=2+1$ lattice QCD at the physical point using topological charge operators
• Testing the Witten-Veneziano Formula on the Lattice