Pseudoscalar Meson Decay Constants and Couplings, the Witten-Veneziano Formula beyond large N_c, and the Topological Susceptibility

Abstract

The QCD formulae for the radiative decays $η,η'\to\c\c$, and the corresponding Dashen--Gell-Mann--Oakes--Renner relations, differ from conventional PCAC results due to the gluonic $U(1{)}_A$ axial anomaly. This introduces a critical dependence on the gluon topological susceptibility. In this paper, we revisit our earlier theoretical analysis of radiative pseudoscalar decays and the DGMOR relations and extract explicit experimental values for the decay constants. This is our main result. The flavour singlet DGMOR relation is the generalisation of the Witten-Veneziano formula beyond large $N_c$, so we are able to give a quantitative assessment of the realisation of the $1/N_c$ expansion in the $U(1{)}_A$ sector of QCD. Applications to other aspects of ${\eta }^{\prime }$ physics, including the relation with the first moment sum rule for the polarised photon structure function $g_1^\c$, are highlighted. The $U(1{)}_A$ Goldberger-Treiman relation is extended to accommodate SU(3) flavour breaking and the implications of a more precise measurement of the $\eta$ and ${\eta }^{\prime }$-nucleon couplings are discussed. A comparison with the existing literature on pseudoscalar meson decay constants using large-$N_c$ chiral Lagrangians is also made.

arXiv comment27 pages, 4 figures

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Cited by in corpus (22)

• SU(N) gauge theories at large N
• Theta dependence of SU(N) gauge theories in the presence of a topological term
• Etaprime and Eta Mesons with Connection to Anomalous Glue
• A study of the eta and eta' mesons with improved staggered fermions
• $\eta$ and ${\eta }^{\prime }$ mesons in the Dyson-Schwinger approach at finite temperature
• Methods for Pseudoscalar Flavour-Singlet Mesons with Staggered Fermions
• ${\eta }^{\prime }$ and $\eta$ mesons at high T when the U_A(1) and chiral symmetry breaking are tied
• The Polarised Photon $g_1^{\gamma }$ Sum Rule at the Linear Collider and High Luminosity B Factories
• A $U_A(1)$ symmetry restoration scenario supported by the generalized Witten-Veneziano relation and its analytic solution
• Axial and pseudoscalar current correlators and their couplings to eta and etaprime mesons
• Temperature Dependence of the Axion Mass in a Scenario Where the Restoration of Chiral Symmetry Drives the Restoration of the $U_A(1)$ Symmetry
• Eta-nucleon and eta-prime-nucleon coupling constants in QCD and the role of gluons
• Eta-nucleon coupling constant in QCD with SU(3) symmetry breaking
• $\eta$ and ${\eta }^{\prime }$ mesons in the Dyson-Schwinger approach using a generalization of the Witten-Veneziano relation
• A Dyson-Schwinger model beyond isospin limit prepared for investigating U_A(1)-breaking temperature dependence
• Master formula approach to broken chiral U(3)xU(3) symmetry
• The U(1)_A Anomaly and QCD Phenomenology
• Quark distributions and gluon contents of eta and etaprime
• Aspects of model dependence of eta'-eta complex treated by going beyond the isospin limit
• Regularities in electromagnetic decay widths
• Eta-Eta' mixing and the derivative of the topological susceptibility at zero momentum transfer
• Polarized Structure Functions and Two-Photon Physics at Super-B