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Investigation of the $D^{\ast}_{s}D_{s} η^{(\prime)}$ and $B^{\ast}_{s}B_{s} η^{(\prime)}$ vertices via QCD sum rules

E. Yazici, E. Veli Veliev, K. Azizi, H. Sundu

TL;DR

The paper addresses the nonperturbative determination of strong coupling constants at the heavy-strange meson vertices involving η and η′ by applying QCD sum rules to three-point correlation functions for off-shell configurations. It develops the QCD-side expressions via the operator product expansion, includes perturbative and condensate contributions, computes spectral densities with Cutkosky rules, and uses a double Borel transform with quark–hadron duality while neglecting η–η′ mixing due to its small angle. The authors derive explicit sum-rule expressions for the form factors and extract the corresponding couplings for the vertices D_s^*D_sη, D_s^*D_sη′, B_s^*B_sη, and B_s^*B_sη′, reporting uncertainties from parameter choices. These results yield testable predictions for heavy-flavor strong interactions and have potential implications for interpreting heavy-meson decays and exploring the QCD vacuum structure.

Abstract

The strong coupling constants among mesons are very important quantities as they can provide useful information on the nature of strong interaction among hadrons as well as the QCD vacuum. In this article, we investigate the strong vertices of the $D^{\ast}_{s}D_{s} η^{(\prime)}$ and $B^{\ast}_{s}B_{s} η^{(\prime)}$ in the framework of the QCD sum rule approach choosing the $η$ or $D_{s} (B_{s})$ meson as an off-shell state. We obtain the results $g_{D_s^*D_sη}=(1.46\pm 0.30)GeV^{-1}$, $g_{D_s^*D_sη^{\prime}}=(0.74\pm 0.16)GeV^{-1}$, $g_{B_s^*B_sη}=(5.29\pm 1.06)GeV^{-1}$ and $g_{B_s^*B_sη^{\prime}}=(2.29\pm 0.48)GeV^{-1}$ for the strong coupling constants under consideration, which can be checked in future experiments.

Investigation of the $D^{\ast}_{s}D_{s} η^{(\prime)}$ and $B^{\ast}_{s}B_{s} η^{(\prime)}$ vertices via QCD sum rules

TL;DR

The paper addresses the nonperturbative determination of strong coupling constants at the heavy-strange meson vertices involving η and η′ by applying QCD sum rules to three-point correlation functions for off-shell configurations. It develops the QCD-side expressions via the operator product expansion, includes perturbative and condensate contributions, computes spectral densities with Cutkosky rules, and uses a double Borel transform with quark–hadron duality while neglecting η–η′ mixing due to its small angle. The authors derive explicit sum-rule expressions for the form factors and extract the corresponding couplings for the vertices D_s^*D_sη, D_s^*D_sη′, B_s^*B_sη, and B_s^*B_sη′, reporting uncertainties from parameter choices. These results yield testable predictions for heavy-flavor strong interactions and have potential implications for interpreting heavy-meson decays and exploring the QCD vacuum structure.

Abstract

The strong coupling constants among mesons are very important quantities as they can provide useful information on the nature of strong interaction among hadrons as well as the QCD vacuum. In this article, we investigate the strong vertices of the and in the framework of the QCD sum rule approach choosing the or meson as an off-shell state. We obtain the results , , and for the strong coupling constants under consideration, which can be checked in future experiments.

Paper Structure

This paper contains 3 sections, 20 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. QCD Sum Rules for strong Coupling form factors
  3. Numerical results

Figures (4)

  • Figure 1: Diagrams considered in the calculations.
  • Figure 2: Left:$g^{(D_s)}_{D_s^*D_s\eta}(Q^2=1~GeV^2)$ as a function of the Borel mass parameter $M^2$. Right:$g^{(\eta)}_{D_s^*D_s\eta}(Q^2=1~GeV^2)$ as a function of the Borel mass $M^2$.
  • Figure 3: Left:$g^{(B_s)}_{B_s^*B_s\eta^{\prime}}(Q^2=1~GeV^2)$ as a function of the Borel mass $M^2$. Right:$g^{(\eta^{\prime})}_{B_s^*B_s\eta^{\prime}}(Q^2=1~GeV^2)$ as a function of the Borel mass parameter $M^2$.
  • Figure 4: Left:$g_{D_s^*D_s\eta}(Q^2)$ as a function of $Q^2$. Right:$g_{B_s^*B_s\eta^{\prime}}(Q^2)$ as a function of $Q^2$.