Radiative Decays of Vector Mesons with Light-Cone Sum Rules

TL;DR

This work uses light-cone sum rules (LCSR) to compute magnetic-dipole (M1) radiative decays of vector mesons, covering $K^{*-}\rightarrow K^-\gamma$, $D^*\rightarrow D\gamma$, $B^*\rightarrow B\gamma$, $D^{*+}_s\rightarrow D^+_s\gamma$, $B_s^*\rightarrow B_s\gamma$, and the excited-state transition $\psi(2S)\rightarrow\eta_c(2S)\gamma$. Transition form factors $F_{VP}$ are derived within the LCSR framework using correlation functions, light-cone distribution amplitudes (LCDAs), and Borel transforms, with explicit expressions for both heavy-light and charmonium channels. The study reports $F_{VP}(0)$ values and corresponding decay widths, finding good agreement with experimental data for the kaon channel and reasonable agreement for the excited state, while providing concrete predictions for unmeasured decays. A key finding is a universal linear scaling of the decay width with a kinematic function $A(x)$, evaluated at $x\approx2.1$ in the relation $\log\Gamma \propto \log A(2.1)$, suggesting a common underlying dynamics across ground-state $V\to P\gamma$ transitions and offering a potential lens to understanding broader hadronic radiative phenomena.

Abstract

Hadronic electromagnetic form factors and radiative decay properties offer a crucial window into the nonperturbative dynamics of Quantum chromodynamics (QCD). In this work, we employ the light-cone sum rules (LCSR) method to systematically investigate the M1 radiative decay of vector mesons. Our study covers processes including $K^{*-}\rightarrow K^-γ$, $D^*\rightarrow Dγ$, $B^*\rightarrow Bγ$, $D^{*+}_s\rightarrow D^+_sγ$, and $B_s^*\rightarrow B_sγ$, and further extends to the excited charmonium state $ψ(2S)$. Our calculations yield decay widths for $K^*$ and $ψ(2S)$ that are in excellent agreement with experimental data. For the charm and bottom meson decays, where precise measurements are lacking, we provide theoretical predictions and compare them with other theoretical approaches. Most notably, our analysis reveals a universal linear dependence of the decay width on a function A(x) in the logarithmic coordinate system, which originates from the two-body decay dynamics and the ratio of the initial and final state decay constants. This relationship holds for the ground state $V \rightarrow P γ$ processes here and suggests a broader applicability to radiative decays of ground-state vector mesons.

Figures (19)

• Figure 1: The dependence of the form factors for $K^{*-}\rightarrow K^-\gamma$ and $\psi(2S)\rightarrow\eta_c(2S)\gamma$ processes on the threshold $s_0$ and Borel parameter $M^2$.
• Figure 2: The dependence of the form factors for $D^*\rightarrow D\gamma$ and $D^{*+}_s\rightarrow D^+_s\gamma$ processes on the threshold $s_0$ and Borel parameter $M^2$.
• Figure 3: The dependence of the form factors for $B^*\rightarrow B\gamma$ and $B^*_s\rightarrow B_s\gamma$ processes on the threshold $s_0$ and Borel parameter $M^2$.
• Figure 4: The dependence of the decay widths for $K^{*-}\rightarrow K^-\gamma$ and $\psi(2S)\rightarrow\eta_c(2S)\gamma$ processes on the threshold $s_0$ and Borel parameter $M^2$.
• Figure 5: The dependence of the decay widths for $D^*\rightarrow D\gamma$ and $D^{*+}_s\rightarrow D^+_s\gamma$ processes on the threshold $s_0$ and Borel parameter $M^2$.