Radiative $h_{c/b}$ decays to $\eta$ or ${\eta }^{\prime }$

Abstract

Motivated by recent measurements of the radiative decay rates of the \emph{P}-wave spin singlet charmonium $h_c$ to the light meson $\eta$ or ${\eta }^{\prime }$ by the BESIII Collaboration, we investigate the decay rates of these channels at order $\alpha {\alpha }_s^4$. The photon is radiated mainly from charm quark pairs in the lowest order Feynman diagrams, since the diagrams where a photon radiated from light quarks are suppressed by ${\alpha }_s$ or the relative charm quark velocity $v$, due to Charge parity conservation. The form factors of two gluons to $\eta$ or ${\eta }^{\prime }$ are employed, which are the major mechanism for $\eta$ and ${\eta }^{\prime }$ productions. $\eta ({\eta }^{\prime })$ is treated as a light cone object when we consider that the parent charmonium mass is much heavier than that of the final light meson. We obtain the branching ratio $\mathcal{B}(h_c\to \gamma {\eta }^{\prime })=(1.94_{-0.51}^{+0.70})\times 10^{-3}$ in the nonrelativistic QCD approach, which is in agreement with the BESIII measurement. The prediction of the branching ratio of $h_c\to \gamma \eta$ is also within the range of experimental error after including the larger uncertainty of the total decay width ${\Gamma }_{h_c}$. The applications of these formulae to the radiative decays to $\eta ({\eta }^{\prime })$ of the \emph{P}-wave spin singlet bottomonium $h_b(nP)$ are presented. These studies will shed some light on the $\eta -{\eta }^{\prime }$ mixing effects, the flavor SU(3) symmetry breaking, as well as the nonperturbative dynamics of charmonium and bottomonium.

arXiv comment6 pages, 2 figures, and 1 table;To appear in Physical Review D

References in corpus (21)

• Rigorous QCD Analysis of Inclusive Annihilation and Production of Heavy Quarkonium
• Automatized One-Loop Calculations in 4 and D dimensions
• Heavy quarkonium: progress, puzzles, and opportunities
• Mixing and Decay Constants of Pseudoscalar Mesons
• Quarkonium Wave Functions at the Origin
• Quarkonium Production at High-Energy Colliders
• Automatic Loop Calculations with FeynArts, FormCalc, and LoopTools
• Spectroscopy and Regge trajectories of heavy quarkonia and B_c mesons
• Next-to-Leading Order QCD Correction to ${\mathbf{e}}^{+}{\mathbf{e}}^{-}\to \mathbf{J}/\mathbf{\psi }+{\mathbf{\eta }}_{\mathbf{c}}$ at $\sqrt{s}=10.6$GeV}
• $B_c$ Exclusive Decays to Charmonium and a Light Meson at Next-to-Leading Order Accuracy
• The ${\eta }^{\prime }{g}^{\ast }{g}^{\ast }$ vertex with arbitrary gluon virtualities in the perturbative QCD hard scattering approach
• ${\eta }^{\prime }-g^{\ast }-g$ Transition Form Factor with Gluon Content Contribution Tested
• Factorization in exclusive quarkonium production
• Factorization theorems for exclusive heavy-quarkonium production
• Implications on $\eta$-${\eta }^{\prime }$-glueball mixing from $B_{d/s}\to J/\Psi {\eta }^{{(}^{\prime })}$ Decays
• Exclusive Double Charmonium Production from ${\rm Y}$ Decay
• Observation of $h_c$ radiative decay $h_c\to \gamma {\eta }^{\prime }$ and evidence for $h_c\to \gamma \eta$
• Understanding the cross section of $e^{+}{e}^{-}\to \eta J/\psi$ process via nonrelativistic QCD
• The Exclusive Decay of Upsilon into $h_c$, the $X(3940)$ and $X(4160)$
• ${\bar{B}}_s^0\to ({\pi }^0{\eta }^{(\ast )},{\eta }^{(\ast )}{\eta }^{(\ast )})$ decays and the effects of next-to-leading order contributions in the perturbative QCD approach
• Factorization for radiative heavy quarkonium decays into scalar Glueball

Cited by in corpus (4)

• Model independent investigation of the $R_{J/\psi ,{\eta }_c}$ and ratios of decay widths of semileptonic $B_c$ decays into a P-wave charmonium
• Revisiting the $P$-wave charmonium radiative decays $h_c\to \gamma {\eta }^{(\prime )}$ with relativistic corrections
• Radiative decays of $h_c$ to the light mesons ${\eta }^{(\prime )}$: A perturbative QCD calculation
• QCD analysis of electromagnetic Dalitz decays $J/\psi \to {\eta }^{(\prime )}{\ell }^{+}{\ell }^{-}$