B -meson semi-inclusive decay to 2 − + charmonium in nonrelativistic QCD and X ( 3872 )
B -meson semi-inclusive decay to 2 − + charmonium in nonrelativistic QCD and X ( 3872 )
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DOI：
10.1103/physrevd.85.034032
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发表时间：
2011-12
影响因子：
5
通讯作者：
Ying-Ying Fan-Ying;Jin-Zhao Li;C. Meng;K. Chao
中科院分区：
文献类型：
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作者：
Ying-Ying Fan-Ying;Jin-Zhao Li;C. Meng;K. Chao
在非相对论QCD(NRQCD)中研究了半包含型B介子衰变为自旋单重态D波$2^-+$Charmonium，$BTO{c2}+X$.色单重态和色八重态的贡献都是在强耦合常数α_S中的次前级(NLO)下计算的。利用算符演化方程对非微扰长距离矩阵元进行了计算。结果表明，色单重态的贡献很小，而色八重态的贡献占主导地位。在简约维正则(NDR)方案和t‘Hooft-Veltman(HV)方案中，估计的分支比$B(BtoETA_(C2)+X)$分别约为$0.41，×10^-4}和$1.24，×10^-4}，重整化尺度为$\u=m_b=4.8$，GeV。这些数值结果的格式敏感性是由于${}^1S_0^{[8]}$和${}^1P_1^{[8]}$之间的抵消。文中还给出了两种方案中NLO分支比的$-MU-关系曲线，其中$\MU$从$FRAC{m_b}{2}$变化到$2M_b$，NRQCD分解或重整化标度$\MU_{\Lambda}$取为$2M_c$。将估算的分枝比$B与观测到的分枝比$B与X(3872)+K进行比较，可以得出结论：X(3872)不太可能是$2^-+$查尔蒙正态$ETA{c2}$。
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 $\eta_{c2}$.