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Mixing and Decay Constants of Pseudoscalar Mesons

T. Feldmann, P. Kroll, B. Stech

TL;DR

The paper presents a predictive framework for eta-eta' mixing by adopting a quark-flavor basis in which decay constants follow state mixing. By using the divergences of axial-vector currents and the U(1)_A anomaly, it derives a mass matrix quadratic in meson masses and fixes key parameters to leading order in SU(3)_F breaking, relating the mixing angle to decay-constant ratios. Phenomenological analyses across multiple processes yield a consistent mixture angle and decay constants ($\phi \approx 39.3^\circ$, $f_q \approx 1.07 f_\pi$, $f_s \approx 1.34 f_\pi$) in agreement with ChPT constraints. The framework is extended to include the charmed state, yielding small charm admixtures in $\eta$ and $\eta'$, with testable predictions for radiative $J/\psi$ decays, thereby offering a coherent, parameter-efficient description aligned with experiment.

Abstract

We propose a new eta-eta' mixing scheme where we start from the quark flavor basis and assume that the decay constants in that basis follow the pattern of particle state mixing. On exploiting the divergences of the axial vector currents - which embody the axial vector anomaly - all basic parameters are fixed to first order of flavor symmetry breaking. That approach naturally leads to a mass matrix, quadratic in the masses, with specified elements. We also test our mixing scheme against experiment and determine corrections to the first order values of the basic parameters from phenomenology. Finally, we generalize the mixing scheme to include the eta(c). Again the divergences of the axial vector currents fix the mass matrix and, hence, mixing angles and the charm content of the eta and eta'.

Mixing and Decay Constants of Pseudoscalar Mesons

TL;DR

The paper presents a predictive framework for eta-eta' mixing by adopting a quark-flavor basis in which decay constants follow state mixing. By using the divergences of axial-vector currents and the U(1)_A anomaly, it derives a mass matrix quadratic in meson masses and fixes key parameters to leading order in SU(3)_F breaking, relating the mixing angle to decay-constant ratios. Phenomenological analyses across multiple processes yield a consistent mixture angle and decay constants (, , ) in agreement with ChPT constraints. The framework is extended to include the charmed state, yielding small charm admixtures in and , with testable predictions for radiative decays, thereby offering a coherent, parameter-efficient description aligned with experiment.

Abstract

We propose a new eta-eta' mixing scheme where we start from the quark flavor basis and assume that the decay constants in that basis follow the pattern of particle state mixing. On exploiting the divergences of the axial vector currents - which embody the axial vector anomaly - all basic parameters are fixed to first order of flavor symmetry breaking. That approach naturally leads to a mass matrix, quadratic in the masses, with specified elements. We also test our mixing scheme against experiment and determine corrections to the first order values of the basic parameters from phenomenology. Finally, we generalize the mixing scheme to include the eta(c). Again the divergences of the axial vector currents fix the mass matrix and, hence, mixing angles and the charm content of the eta and eta'.

Paper Structure

This paper contains 5 sections, 34 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. The ${\rm q}\overline{\rm q}$ -- ${\rm s}\overline{\rm s}$ mixing scheme
  3. The phenomenological values of $\phi$, $f_{\rm{q}}$, $f_{{\rm{s}}}$
  4. Generalizing to $\eta$--$\eta'$--$\eta_{{\rm{c}}}$ mixing
  5. Summary

Figures (1)

  • Figure 1: a) Electromagnetic contribution to $J/\psi \to \rho \eta,\eta'$. b) Pole ansatz for the $D_{{\rm{s}}}\to P \ell \nu$ semi-leptonic decay.