Benefiting from rapid technical advances in multi-loop computation in recent years, Prof. JIA Yu's group succeeded in accomplishing the challenging calculation of the complete NNLO correction for the inclusive decay rate of ηc, with the help of the National Tianhe Supercomputing Center in Guangzhou.
In this study, the researchers clearly verified, for the first time, that the effective-field-theory approach based on the first principles of QCD, the nonrelativistic QCD (NRQCD) factorization, still remains valid at NNLO for this inclusive decay process. Nevertheless, when combining this new NNLO piece with existing relativistic corrections, they found that, the state-of-the-art NRQCD predictions are in severe tension with the measured ηchadronic width, and in particular, with the measured branching fraction of ηc decay to two photons.
These discrepancies indicated that, though the influential NRQCD approach has solid theoretical ground, the charm quark mass may not be viewed as truly large. Therefore the utility of NRQCD, when applied to charmonium, appears to face serious challenges. On the other hand, NRQCD approach appears to be capable of reliably accounting for the measured ηb hadronic width.
The research group's conclusion is compatible with their earlier study published in Physical Review Letters in 2015, namely that the NRQCD approach faces some crisis when applied to charmonium exclusive production process.
This study was supported in part by the National Natural Science Foundation of China.
The predicted ηc total width as a function of renormalization scale μR. The blue band denotes the measured ηc hadronic width. The curves labeled by LO, NLO, NNLO represent the various perturbative accuracies in NRQCD predictions. The green band characterizes the theoretical uncertainty brought by varying the NRQCD factorization scale μΛ (Image by the research group)
The predicted branching fraction for ηc decay to two photons as a function of renormalization scale μR. The blue band represents the measured value. The curves labeled by LO, NLO, NNLO represent the various perturbative accuracies in NRQCD predictions. (Image by the research group)
NRQCD predictions for the (normalized) γ*γηc transition form factor as a function of Q2. The solid black dots with error bar represent the BaBar data. The dotted, dashed, and solid curves represent the LO, NLO and NNLO predictions in the nonrelativistic limit. (Image by the research group)
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