Feng Feng, Jia Yu, Sang Wen-Long
Institute of High Energy Physics and Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences, Beijing 100049, China.
China University of Mining and Technology, Beijing 100083, China.
Phys Rev Lett. 2017 Dec 22;119(25):252001. doi: 10.1103/PhysRevLett.119.252001. Epub 2017 Dec 20.
We compute the next-to-next-to-leading-order QCD corrections to the hadronic decay rates of the pseudoscalar quarkonia, at the lowest order in velocity expansion. The validity of nonrelativistic QCD (NRQCD) factorization for inclusive quarkonium decay process, for the first time, is verified to relative order α_{s}^{2}. As a by-product, the renormalization group equation of the leading NRQCD four-fermion operator O_{1}(^{1}S_{0}) is also deduced to this perturbative order. By incorporating this new piece of correction together with available relativistic corrections, we find that there exists severe tension between the state-of-the-art NRQCD predictions and the measured η_{c} hadronic width and, in particular, the branching fraction of η_{c}→γγ. NRQCD appears to be capable of accounting for η_{b} hadronic decay to a satisfactory degree, and our most refined prediction is Br(η_{b}→γγ)=(4.8±0.7)×10^{-5}.
我们在速度展开的最低阶下，计算了赝标量夸克偶素强子衰变率的次下一个领头阶QCD修正。首次将包含性夸克偶素衰变过程的非相对论QCD（NRQCD）因子化的有效性验证到了相对阶α_s^2。作为副产品，领头的NRQCD四费米子算符O_1(^1S_0)的重整化群方程也被推导到了这个微扰阶。通过将这一新的修正与现有的相对论修正相结合，我们发现，最先进的NRQCD预测与测量到的η_c强子宽度，特别是η_c→γγ的分支比之间存在严重矛盾。NRQCD似乎能够令人满意地解释η_b强子衰变，我们最精确的预测是Br(η_b→γγ)=(4.8±0.7)×10^-5。
