NRQCD Predictions of D-Wave Quarkonia 3DJ(J=1,2,3)^3D_{J}(J=1,2,3) Decay into Light Hadrons at Order αs3\alpha_{s}^{3}

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.Comment: 12 figures, references added, published version in PR

B-meson Semi-inclusive Decay to 2−+2^{-+} Charmonium in NRQCD and X(3872)

The semi-inclusive B-meson decay into spin-singlet D-wave $2^{-+}$ charmonium, $B\to \eta_{c2}+X$, is studied in nonrelativistic QCD (NRQCD). Both color-singlet and color-octet contributions are calculated at next-to-leading order (NLO) in the strong coupling constant $\alpha_s$. The non-perturbative long-distance matrix elements are evaluated using operator evolution equations. It is found that the color-singlet $^1D_2$ contribution is tiny, while the color-octet channels make dominant contributions. The estimated branching ratio $B(B\to \eta_{c2}+X)$ is about $0.41\,\times10^{-4}$ in the Naive Dimensional Regularization (NDR) scheme and $1.24\,\times10^{-4}$ in the t'Hooft-Veltman (HV) scheme, with renormalization scale $\mu=m_b=4.8$\,GeV. The scheme-sensitivity of these numerical results is due to cancelation between ${}^1S_0^{[8]}$ and ${}^1P_1^{[8]}$ contributions. The $\mu$-dependence curves of NLO branching ratios in both schemes are also shown, with $\mu$ varying from $\frac{m_b}{2}$ to $2m_b$ and the NRQCD factorization or renormalization scale $\mu_{\Lambda}$ taken to be $2m_c$. Comparison of the estimated branching ratio of $B\to \eta_{c2}+X$ with the observed branching ratio of $B \to X(3872)+K$ may lead to the conclusion that X(3872) is unlikely to be the $2^{-+}$ charmonium state $\eta_{c2}$.Comment: Version published in PRD, references added, 26 pages, 9 figure

Relativistic corrections to J/ψJ/\psi exclusive and inclusive double charm production at B factories

In order to clarify the puzzling problems in double charm production, relativistic corrections at order $v^{2}$ to the processes $e^{+}e^{-}\to J/\psi+\eta_{c}$ and $e^{+}e^{-}\to J/\psi+c\bar{c}$ at B factories are studied in non-relativistic quantum chromodynamics. The short-distance parts of production cross sections are calculated perturbatively, while the long-distance matrix elements are estimated from $J/\psi$ and $\eta_c$ decays up to errors of order $v^4$. Our results show that the relativistic correction to the exclusive process $e^{+}e^{-}\to J/\psi+\eta_{c}$ is significant, which, when combined together with the next-to-leading order $\alpha_{s}$ corrections, could resolve the large discrepancy between theory and experiment; whereas for the inclusive process $e^{+}e^{-}\to J/\psi+c\bar{c}$ the relativistic correction is tiny and negligible. The physical reason for the above difference between exclusive and inclusive processes largely lies in the fact that in the exclusive process the relative momentum between quarks in charmonium substantially reduces the virtuality of the gluon that converts into a charm quark pair, but this is not the case for the inclusive process, in which the charm quark fragmentation $c\to J/\psi+c$ is significant, and QCD radiative corrections can be more essential.Comment: Version to appear in PRD. In the summary an explicit statement added: "for the J/\psi eta_c cross section the relativistic correction alone gives an enhancement factor of 1.7 while the combination of relativistic correction with QCD radiative correction results in a much larger enhancement factor of 9". One reference added. A few typos correcte

Nonfactorizable B→χc0KB\to\chi_{c0}K decay and QCD factorization

We study the unexpectedly large rate for the factorization-forbidden decay $B\to \chi_{c0}K$ within the QCD factorization approach. We use a non-zero gluon mass to regularize the infrared divergences in vertex corrections. The end-point singularities arising from spectator corrections are regularized and carefully estimated by the off-shellness of quarks. We find that the contributions arising from the vertex and leading-twist spectator corrections are numerically small, and the twist-3 spectator contribution with chiral enhancement and linear end-point singularity becomes dominant. With reasonable choices for the parameters, the branching ratio for $B\to\chi_{c0}K$ decay is estimated to be in the range $(2-4)\times 10^{-4}$, which is compatible with the Belle and BaBar data.Comment: Appendix added; it is emphasized that in the dominant twist-3 spectator corrections the end-point singularity contributions may be estimated by the off-shellness of the charm quark (by the binding energy in charmonium) and the gluon (by the transverse momentum of the light quark in the kaon

Synthesis and crystal structure of the first 6a-thiathiophthen metal complex [Mo(CO)_5PPh_(2]2)(µ-C_5H_2S_3)

The first 6a-thiathiophthen metal complex was prepared by treating M(CO_)5[PPh_2CS_2CH_2C≡CH] with a catalytic amount of secondary amine or tertiary amine; the structure of the 6a-thiathiophthen molybdenum complex is confirmed by an X-ray diffraction analysis

Υ\Upsilon radiative decays to light quark jets and color octet mechanism

We study radiative decays of $\Upsilon$ to light quark jets in nonrelativistic QCD by taking both the color singlet and color octet $b\bar b$ operators into consideration. The cut for quark jet energy and cut for the angle between two quark jets are introduced. The sensitivity to the soft and collinear singularities in the loop integrals are greatly reduced by these cuts. With the jet energy cut of about 1 GeV, and the jet angle cut of about $36^\circ$, the branching ratio for $\Upsilon\to\gamma q\bar q$ is found to be $8.2\times 10^{-4}$ from color singlet contributions. The color octet contributions could be much larger than that of color singlet, depending on the estimate of the color octet matrix elements. This process may provide a new test for the color octet mechanism in nonrelativistic QCD.Comment: journal version; a few references adde