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

Abstract

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 ${}^1{D}_2$ contribution is tiny, while the color-octet channels make dominant contributions. The estimated branching ratio $B(B\to {\eta }_{c2}+X)$ is about $0.41\times 10^{-4}$ in the Naive Dimensional Regularization (NDR) scheme and $1.24\times 10^{-4}$ 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 ${}^1{S}_0^{[8]}$ and ${}^1{P}_1^{[8]}$ 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 ${\eta }_{c2}$.

Version published in PRD, references added, 26 pages, 9 figures

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Cited by in corpus (9)

• Hadronic molecules
• X(3872) is not a true molecule
• Description of the ${\Xi }_c$ and ${\Xi }_b$ states as molecular states
• EM Decay of X(3872) as the $1{}^1{D}_2(2^{-+})$ charmonium
• 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 ${\eta }_b$
• Hadronic decays of the spin-singlet heavy quarkomium under the principle of maximum conformality
• Study on ${\eta }_{c2}({\eta }_{b2})$ electromagnetic decay into double photons
• $\mathcal{O}({\alpha }_s)$ corrections to $e^{+}{e}^{-}\to J/\psi +{\eta }_{c2}({\chi }_{c1}^{\prime })$ at $B$ factories