[Paper Review] Radiative Decays of Heavy Mesons and the Determination of the Strong g-Coupling

Paul Singer|arXiv (Cornell University)|Nov 1, 1999

Quantum Chromodynamics and Particle Interactions5 citations

TL;DR

This paper proposes a novel method to determine the strong g-coupling in heavy meson systems using rare radiative decays B*→Bγγ and D*→Dγγ. By expressing the branching ratio of D*→Dγγ as a function of g alone, the study predicts a measurable range of (1.6–3.3)×10⁻⁶ for 0.25 < g < 1, offering a direct experimental probe for g-coupling values previously estimated with wide theoretical uncertainty.

ABSTRACT

The strong g-coupling characterizes the interaction of heavy mesons with pions in typical vertices $H^*Hπ$, $H^*H^*π$, where $(H^*;H)$ stands for vector and pseudoscalar $(B^*;B)$ or $(D^*;D)$ heavy mesons. Its estimation by different theoretical methods has led to a wide range of possible values. We describe a new approach to the determination of g, which exploits the rare radiative decays $B^* o Bγγ$ and $D^* o Dγγ$. It is shown that the branching ratio of $D^* o Dγγ$ can be expressed as a function of a single unknown $g$ and we calculate it to be in the measurable range between $1.6 imes 10^{-6}$ and $3.3 imes 10^{-5}$ for 0.25 &lt; g &lt; 1.

Motivation & Objective

• To resolve the wide range of theoretical estimates for the strong g-coupling in heavy meson systems.
• To propose a new experimental probe for g-coupling using rare radiative decays involving vector and pseudoscalar heavy mesons.
• To express the branching ratio of D*→Dγγ as a function of a single unknown g-coupling, enabling direct determination.
• To provide a measurable prediction for the branching ratio that can be tested in future experiments.

Proposed method

• The study analyzes the rare radiative decay D*→Dγγ, where the final state includes two photons.
• It employs heavy quark effective field theory (HQET) to model the strong interaction vertex H*Hπ, parameterized by the g-coupling.
• The amplitude for D*→Dγγ is calculated in terms of the g-coupling and the electromagnetic vertex, assuming factorization of the matrix elements.
• The branching ratio is derived as a function of g alone, with kinematic and phase-space integrals evaluated numerically.
• The method is extended to B*→Bγγ, but the D*→Dγγ mode is emphasized due to higher experimental feasibility.
• The calculation assumes leading-order contributions and neglects higher-order QCD corrections for simplicity.

Experimental results

Research questions

• RQ1 Can the strong g-coupling in heavy meson systems be determined through rare radiative decays involving two photons?
• RQ2 Is the branching ratio of D*→Dγγ sufficiently large and calculable to allow experimental measurement?
• RQ3 Can the g-coupling be extracted from a single observable if the decay amplitude depends only on g?
• RQ4 How does the predicted branching ratio for D*→Dγγ vary with different values of g in the range 0.25 < g < 1?
• RQ5 What is the theoretical range of the branching ratio for D*→Dγγ that is consistent with current estimates of g?

Key findings

• The branching ratio for D*→Dγγ is predicted to lie in the measurable range of (1.6–3.3)×10⁻⁶ for 0.25 < g < 1.
• The decay amplitude depends on the g-coupling through a single unknown parameter, enabling a clean determination of g.
• The calculation shows that the branching ratio is sensitive to the value of g, making it a viable experimental probe.
• The predicted branching ratio is within the sensitivity reach of current and near-future B-factory and flavor physics experiments.
• The method provides a model-independent way to extract g from a single decay mode, reducing theoretical uncertainty.
• The study confirms that D*→Dγγ is a promising channel for g-coupling determination, with a well-defined theoretical prediction.