1112.3625 (Ying Fan et al.)

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

Ying Fan, Jin-Zhao Li, Ce Meng, Kuang-Ta Chao

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 $\eta_{c2}$.

View original: http://arxiv.org/abs/1112.3625