1301.2992 (Sheng-Quan Wang et al.)

$J/ψ+χ_{cJ}$ Production at the $B$ Factories under the Principle
of Maximum Conformality    [PDF]

Sheng-Quan Wang, Xing-Gang Wu, Xu-Chang Zheng, Jian-Ming Shen, Qiong-Lian Zhang

Under the conventional scale setting, the renormalization scale uncertainty usually constitutes a systematic error for a fixed-order perturbative QCD estimation. While, the recently suggested principle of maximum conformality (PMC) provides a principle to eliminate such scale ambiguity in a step-by-step way. We make a detailed PMC analysis for both the polarized and the unpolarized cross sections for the charmonium production processes, $e^{+}+e^{-}\to J/ \psi (\psi') + \chi_{cJ}$ with $(J=0,1,2)$, up to next-to-leading order (NLO), and compare our predictions with the measurements at the $B$ factories and the theoretical estimations obtained in the literature. It is found that all the PMC scales for the polarized and the unpolarized cross sections are almost independent of the initial renormalization scale. Then, the scale uncertainty for both the polarized and the unpolarized cross sections are greatly suppressed even at the NLO level. It is found that the charmonium production processes are dominated by J=0 channel. After PMC scale setting, we obtain $\sigma(J/\psi+\chi_{c0}) = 12.14^{+2.67}_{-2.43}$ fb and $\sigma(\psi'+\chi_{c0}) =5.14^{+1.13}_{-1.02}$ fb, where the squared average errors are caused by the bound state parameters as $m_c$, $|R_{J/\psi}(0)|$ and $|R'_{\chi_{cJ}}(0)|$.

View original: http://arxiv.org/abs/1301.2992