Explaining the annihilation decay of heavy quarks has historically played a key role in establishing the gradual and free-form nature of quantum chromodynamics. About 40 years ago, the pseudoscalar singlet strong decay width under non-relativistic limits The NLO correction has been done independently by two theorists in Italy and Japan. The contribution of the NLO correction is so important that it is natural for the curiosity of the size of the next-order radiation correction. Due to technical challenges, For a long time, NNLO correction of the strong decay width of ηc has never been known.With the rapid development of quantum field theory high-order perturbation calculation technology in recent years, the people of the summer of 2017 finally usher in the long-awaited breakthrough. After several years of unremitting efforts, Jia Yu overcome numerous technical difficulties, and ultimately with the help of the National Supercomputing Center, Guangzhou Tianhe platform to complete the calculation.In this paper, Jia Yu, for the first time specifically verified from QCD first principle The effective field theory of departure - the non-relativistic QCD (NRQCD) factorization holds for the lead in the second order, however, correlates NNLO radiation with known The combination of relativistic corrections found that the most complete NRQCD predictions and experimental measurements of the total width of ηc, in particular, severely diverged from the experimentally measured ηc decay to the two-photon branching ratio, meant that the well-known NRQCD method, despite its theoretical roots Is very sturdy, but for the quark-quark element, the quark-quark quality is not big enough, which leads to very poor convergence of the perturbation unfolding, which makes the validity of the quark quark challenging.On the other hand, the NRQCD method can satisfactorily explain the experimental measurement , The exact prediction of ηb decay to two-photon branching ratio, Br'ηb → γγ '= (4.8 ± 0.7) × 10-5, is yet to be super B factory test.
It is noteworthy that the conclusion of the research is in agreement with the conclusion of Jia Yu and others published in the Physics Review Letters in 2015. That is to say, the NRQCD method is challenged in the application of the method involving 粲 quark conjugation. The NNLO radiation correction of 遍 quark conjugation was calculated, and the variation of γ * ηηc transition shape factor with momentum transfer was studied. The results show that the prediction of the most accurate NRQCD prediction differs greatly from the BaBar experiment when NNLO correction is included.
For the first time, Jia et al. Calculated the NNLO radiation correction for single-decay and over-all generation involving 粲 -quarkson, and found that its contribution is very important. After considering its correction effect, the theoretical prediction seriously agrees with the experimental measurement, In terms of the perturbation of the NRQCD short-range coefficients, the convergence of the perturbations is poor, arguing that the root cause of this problem is that the mass of the quarks is not so large that the strong coupling constants that can be defined are not Small, thus seriously undermining the convergence of perturbation expansion.While the widely used NRQCD factorization method is solidly based on the theory, its validity appears to be a serious challenge for the quark-quark element and still requires further research To find its solution.
Research has been funded by the National Natural Science Foundation of China.
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Theoretical prediction of ηc total width as a function of renormalization energy standard μR. LO, NLO, NNLO corresponding perturbation corresponding to the leading order, sub-leading order, and the second leading theoretical predictions. Is the experimental measurement of the total width of ηc.
NRQCD factorization predicts ηc to two-photon branching ratio as a function of renormalization energy marker μR The blue band diagram in the figure is an experimental measurement of ηc to two-photon branching ratio.
The (normalized) γ * γηc transition shape factor predicted by the NRQCD theory changes with the momentum transfer Q2. The black dots with errors in the figure represent the experimental measurements of BaBar. The dotted, dashed, Under the leadership of the perturbation on the order, second leading, second leading prediction.