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

TL;DR

This paper uses NRQCD to calculate D-wave quarkonia decay rates into light hadrons at order αs^3, providing predictions that differ from potential models for charmonium but agree for bottomonium.

Contribution

It presents the first comprehensive calculation of D-wave quarkonia light hadron decays at order αs^3 within the NRQCD framework, including operator evolution and matrix element estimates.

Findings

NRQCD predicts larger decay widths for charmonium D-wave states than potential models.

For bottomonium, NRQCD and potential models agree on decay width estimates.

Predicted decay widths vary significantly among J=1,2,3 states.

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 $^3D_J(J=1,2,3)$ 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 $\psi(1^3D_J)$ predicted by NRQCD is about $2\sim3$ times larger than the phenomenological potential model results, while for the $b\bar{b}$ system the two theoretical estimations of $\Gamma(\Upsilon(1^3D_J)\to LH)$ are in coincidence with each other. Our predictions for $\psi(1^3D_J)$ LH decay widths are $\Gamma(\psi(1^3D_J)\to LH)=(0.43,0.05,0.17)$MeV for J=1,2,3; and for $\Upsilon(1^3D_J)$, $\Gamma(\Upsilon(1^3D_J)\to LH)=(6.91,0.75,2.75)$KeV for J=1,2,3.