NRQCD Predictions of D-Wave Quarkonia ${}^3{D}_J(J=1,2,3)$ Decay into Light Hadrons at Order ${\alpha }_s^3$

Abstract

In this paper, in the framework of NRQCD we study the light hadron (LH) decays of the spin-triplet (S=1) D-wave heavy quarkonia. The short distance coefficients of all Fock states in the ${}^3{D}_J(J=1,2,3)$ quarkonia including D-wave color-singlet, P-wave color-octet and S-wave color-singlet and color-octet are calculated perturbatively at ${\alpha }_s^3$ order. The operator evolution equations of the four-fermion operators are also derived and are used to estimate the numerical values of the long distance matrix elements. We find that for the $c\bar{c}$ system, the LH decay widths of $\psi (1^3{D}_J)$ predicted by NRQCD is about $2\sim 3$ times larger than the phenomenological potential model results, while for the $b\bar{b}$ system the two theoretical estimations of $\Gamma ({\rm Y}(1^3{D}_J)\to LH)$ are in coincidence with each other. Our predictions for $\psi (1^3{D}_J)$ LH decay widths are $\Gamma (\psi (1^3{D}_J)\to LH)=(0.43,0.05,0.17)$MeV for J=1,2,3; and for ${\rm Y}(1^3{D}_J)$, $\Gamma ({\rm Y}(1^3{D}_J)\to LH)=(6.91,0.75,2.75)$KeV for J=1,2,3.

12 figures, references added, published version in PRD

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• The Cosmological Parameters 2006
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• Quarkonia and their transitions
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• Measurements of the cross sections for $e^{+}{e}^{-}\to \mathrm{hadrons}$ at 3.650, 3.6648, 3.773 GeV and the branching fraction for $\psi (3770)\to \mathrm{non}-D\bar{D}$
• Measurements of the braching fractions for psi(3770)--> D0D0-bar,D+D-,DD-bar$ and the resonance parameters of psi(3770) and psi(2S)
• Measurement of sigma(e^+e^- --> psi(3770) --> hadrons) at E_{cm}=3773 MeV
• J/psi plus jet associated production in two-photon collisions at next-to-leading order
• Electromagnetic quarkonium decays at order v^7
• QCD prediction for the non-$D\bar{D}$ annihilation decay of $\psi (3770)$
• J/psi plus prompt-photon associated production in two-photon collisions at next-to-leading order
• Predictions of Light Hadronic Decays of Heavy Quarkonium 1D_2 States in NRQCD

Cited by in corpus (14)

• Heavy quarkonium: progress, puzzles, and opportunities
• Relativistic Correction to J/psi and Upsilon Pair Production
• Relativistic Correction to Color Octet J/psi Production at Hadron Colliders
• ${\alpha }_s{v}^2$ corrections to ${\eta }_c$ and ${\chi }_{cJ}$ production recoiled with a photon at $e^{+}{e}^{-}$ colliders
• Breakdown of NRQCD Factorization in Processes Involving Two Quarkonia and its Cure
• QCD and Relativistic $O({\alpha }_s{v}^2)$ Corrections to Hadronic Decays of Spin-Singlet Heavy Quarkonia $h_c,h_b$ and ${\eta }_b$
• Average speed and its powers $v^n$ of a heavy quark in quarkonia
• B-meson Semi-inclusive Decay to $2^{-+}$ Charmonium in NRQCD and X(3872)
• The electromagnetic decays of $X(3823)$ as the ${\psi }_2(1^3{D}_2)$ state and its radial excited states
• Annihilation Rates of ${}^3{D}_2(2^{--})$ and ${}^3{D}_3(3^{--})$ Heavy Quarkonia
• Search for $C=+$ charmonium and XYZ states in $e^{+}{e}^{-}\to \gamma +H$ at BESIII
• Electronic width of the $\psi (3770)$ resonance interfering with the background
• Overview of charmonium decays and production from Non-Relativistic QCD
• Order-$v^4$ Relativistic Corrections to ${\rm Y}$ Inclusive Decay into a Charm pair