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Topological quantization of vector meson anomalous couplings

Chao-Qiang Geng, Chia-Wei Liu, Yue-Liang Wu

TL;DR

The paper addresses how anomalous vector-meson couplings can be topologically quantized within an extended hidden local symmetry framework by adding a Wess–Zumino–Witten–like term that introduces integers $N_h$ and $N_h'$ subject to $N_h' + N_h = N_c$. This leads to quantized predictions for the low-energy constants $c_i$, specifically $c_1-c_2 = \frac{N_h}{2N_c}$, $c_3 = \frac{1}{3}\frac{N_h}{N_c}$, and $c_4 = \frac{2}{3}\frac{N_h}{N_c}$, with $N_h'$ chosen as $N_c - N_h$. Phenomenologically, $N_h/N_c = 2$ is favored by the $\pi^0\to\gamma\gamma^*$ slope and the $\eta^{(\prime)}$ transition form factors, suggesting partial saturation of vector-meson dominance and a specific $q^2$–dependence distinct from conventional VMD. The framework also identifies experimental channels, such as $\eta^{(\prime)}\to e^+e^-\mu^+\mu^-$ and $\eta^{(\prime)}\to \pi^+\pi^-\ell^+\ell^-$, as decisive tests to confirm the quantized-HLS picture and to probe dynamics beyond the original HLS setup.

Abstract

We uncover a new anomalous term in hidden local symmetry that enforces the topological quantization of vector-meson anomalous couplings. Unlike existing formulations in the literature, which introduce several unquantized coefficients, our term removes this freedom by fixing the couplings to quantized, topologically determined values. We further conjecture that it saturates the anomaly, explaining the success of vector-meson dominance while pinpointing where saturation must fail. High-precision measurements of $η^{(\prime)}\toπ^+π^-γ^*$ form factors at BESIII and the Super $τ$-Charm Facility can provide a definitive experimental discriminator of this quantized picture.

Topological quantization of vector meson anomalous couplings

TL;DR

The paper addresses how anomalous vector-meson couplings can be topologically quantized within an extended hidden local symmetry framework by adding a Wess–Zumino–Witten–like term that introduces integers and subject to . This leads to quantized predictions for the low-energy constants , specifically , , and , with chosen as . Phenomenologically, is favored by the slope and the transition form factors, suggesting partial saturation of vector-meson dominance and a specific –dependence distinct from conventional VMD. The framework also identifies experimental channels, such as and , as decisive tests to confirm the quantized-HLS picture and to probe dynamics beyond the original HLS setup.

Abstract

We uncover a new anomalous term in hidden local symmetry that enforces the topological quantization of vector-meson anomalous couplings. Unlike existing formulations in the literature, which introduce several unquantized coefficients, our term removes this freedom by fixing the couplings to quantized, topologically determined values. We further conjecture that it saturates the anomaly, explaining the success of vector-meson dominance while pinpointing where saturation must fail. High-precision measurements of form factors at BESIII and the Super -Charm Facility can provide a definitive experimental discriminator of this quantized picture.
Paper Structure (4 sections, 22 equations, 2 figures)

This paper contains 4 sections, 22 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Formalism
  3. Numerical results and discussions
  4. Conclusion

Figures (2)

  • Figure 1: (a) Schematic of the one-point compactification $M^5 \cup \{\infty\} \simeq S^5$: the outer surface is identified as a single point, while the striped region denotes the ordinary Lorentz spacetime $S^4$. (b) A two-dimensional cartoon showing $w_5 [ {\color{blue}\xi_L^\dagger}{\color{red}\xi_R}] = w_5[ {\color{blue}\xi_L^\dagger}] + w_5[ {\color{red}\xi_R}].$ The polar angle $\theta$ is used as a schematic parameter along $S^5$, while the radial direction is purely illustrative. The blue and red curves represent the maps $\xi_L^\dagger$ and $\xi_R$ from $S^5$ to the $SU(3)$ group manifold, each with unit winding. Consequently, the product $\xi_L^\dagger$$\xi_R$ has winding $w_5=2$.
  • Figure 2: Example diagrams contributing to $\omega \to \pi^0\pi^+\pi^-$ and $\omega \to \pi^0\gamma^*$ at next-to-leading order are expected to be of relative size $(m_V/\Lambda_\chi)^2 \simeq 50\%$.