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Journal of High Energy Physics

, 2015:20 | Cite as

Non-perturbative test of the Witten-Veneziano formula from lattice QCD

  • The ETM collaboration
  • Krzysztof Cichy
  • Elena Garcia-Ramos
  • Karl Jansen
  • Konstantin Ottnad
  • Carsten Urbach
Open Access
Regular Article - Theoretical Physics

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.

Keywords

Lattice QCD Lattice Gauge Field Theories 1/N Expansion QCD 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • The ETM collaboration
  • Krzysztof Cichy
    • 1
    • 2
    • 3
  • Elena Garcia-Ramos
    • 2
    • 4
  • Karl Jansen
    • 2
  • Konstantin Ottnad
    • 5
  • Carsten Urbach
    • 5
    • 6
  1. 1.Goethe-Universität, Institut für Theoretische PhysikFrankfurt a.M.Germany
  2. 2.NIC, DESYZeuthenGermany
  3. 3.Adam Mickiewicz University, Faculty of PhysicsPoznanPoland
  4. 4.Humboldt Universität zu BerlinBerlinGermany
  5. 5.Institut für Strahlen- und Kernphysik (Theorie)BonnGermany
  6. 6.Bethe Center for Theoretical PhysicsBonnGermany

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