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Decays of the vector charmonium and bottomonium hybrids

B. Barsbay

TL;DR

The paper addresses the decay properties of vector heavy hybrids with $J^{PC}=1^{--}$ by computing their full decay widths from dominant open-flavor channels. It employs the QCD three-point sum-rule method to extract strong couplings at the hybrid-meson–meson vertices, enabling calculation of partial widths for channels such as $H_c \to D^{+}D^{-}$, $D_{0}\bar{D}_{0}$, $D_s^{+}D_s^{-}$, $D^{*+}D^{*-}$, $D^{*0}\bar{D}^{*0}$, $D^{*+}D^{-}$, $D^{*0}\bar{D}^{0}$, $D_s^{*+}D_s^{-}$, and the bottom sector decays $H_b \to B^{+}B^{-}$, $B_{0}\bar{B}_{0}$. The study reports $\Gamma_{H_c}=(309.6\pm39.0)$ MeV and $\Gamma_{H_b}=(78.8\pm15.4)$ MeV, with $H_c$ behaving as a broad resonance and $H_b$ as a relatively narrow state. These predictions provide critical input for identifying and interpreting exotic charmonium- and bottomonium-like hybrids in future experiments and testing nonperturbative QCD dynamics. All mathematical notation is presented with appropriate $...$ delimiters.

Abstract

The full widths of the vector charmonium and bottomonium hybrid mesons $H_{ \mathrm{c}}$ and $H_{\mathrm{b}}$, characterized by the quantum numbers $1^{ \mathrm{--}}$, are determined by analyzing their dominant strong decay modes: $H_{\mathrm{c}} \to D^{+}D^{-}$, $D_{0}\overline{D}_{0}$, $ D_{s}^{+}D_{s}^{-} $ and $H_{\mathrm{b}} \to B^{+}B^{-}$, $B_{0}\overline{B} _{0}$. To evaluate the partial widths of these channels, we employ the QCD three-point sum rule approach, which provides a reliable method for extracting the strong coupling constants at the relevant hybrid-meson-meson interaction vertices. Based on this analysis, the full widths of these hybrid quarkonia are found to be $Γ_{H_{\mathrm{c}}} =(234.1\pm 37.4)~ \mathrm{MeV} $ and $Γ_{H_{\mathrm{b}}} =(78.8\pm 15.4)~\mathrm{MeV} $ . These results are expected to facilitate the interpretation of future experimental data concerning the spectroscopy and decay patterns of exotic charmonium- and bottomonium-like hybrid mesons.

Decays of the vector charmonium and bottomonium hybrids

TL;DR

The paper addresses the decay properties of vector heavy hybrids with by computing their full decay widths from dominant open-flavor channels. It employs the QCD three-point sum-rule method to extract strong couplings at the hybrid-meson–meson vertices, enabling calculation of partial widths for channels such as , , , , , , , , and the bottom sector decays , . The study reports MeV and MeV, with behaving as a broad resonance and as a relatively narrow state. These predictions provide critical input for identifying and interpreting exotic charmonium- and bottomonium-like hybrids in future experiments and testing nonperturbative QCD dynamics. All mathematical notation is presented with appropriate delimiters.

Abstract

The full widths of the vector charmonium and bottomonium hybrid mesons and , characterized by the quantum numbers , are determined by analyzing their dominant strong decay modes: , , and , . To evaluate the partial widths of these channels, we employ the QCD three-point sum rule approach, which provides a reliable method for extracting the strong coupling constants at the relevant hybrid-meson-meson interaction vertices. Based on this analysis, the full widths of these hybrid quarkonia are found to be and . These results are expected to facilitate the interpretation of future experimental data concerning the spectroscopy and decay patterns of exotic charmonium- and bottomonium-like hybrid mesons.

Paper Structure

This paper contains 7 sections, 78 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Decays $H_{\mathrm{c}} \to D^{+}D^{-}$, $D_{0}\overline{D}_{0}$, and $D_{s}^{+}D_{s}^{-}$
  3. Processes $H_{\mathrm{c}}\rightarrow D^{\ast +}D^{\ast -}$, and $D^{\ast 0}\overline{D}^{\ast 0}$
  4. $H_{\mathrm{c}}\rightarrow D^{\ast +}D^{-}$, $D^{\ast 0}\overline{D}^{0}$ and $D_{s}^{\ast +}D_{s}^{-}$
  5. Channels $H_{\mathrm{b}} \to B^{+}B^{-}$, and $B_{0}\overline{B}_{0}$
  6. Summing up
  7. Some expressions in the OPE side of the calculations for the decay $H_{\mathrm{c}}\rightarrow D^{+}D^{-}$

Figures (4)

  • Figure 1: Sample perturbative diagrams corresponding to the strong decay $H_{\mathrm{c}}\rightarrow D^{+}D^{-}$.
  • Figure 2: Sample diagrams of the two-gluon condensate contributions.
  • Figure 3: SR data and functions $\mathcal{F}_{1}(Q^{2})$ (dashed line) and $\mathcal{F}_{3}(Q^{2})$ (solid line). The labels are fixed at the points $Q^{2}=-m_{D}^{2}$ and $Q^{2}=-m_{D_{s}}^{2}$.
  • Figure 4: QCD data and extrapolating function $\mathcal{F}_{4}(Q^{2})$. The red diamond fixes the point $Q^{2}=-m_{B}^{2}$.