This exploratory study computes two-photon decay widths of pseudo-scalar ( ) and scalar ( ) charmonium using two ensembles of twisted mass lattice QCD gauge configurations. The simulation is performed using two lattice ensembles with lattice spacings fm with size and fm with size . The decay widths for the two charmonia are obtained within the expected ballpark, but are however smaller than the experimental ones. Possible reasons for these discrepancies are discussed.

Within the framework of three-channel Ross-Shaw effective range theory, we derive the constraints among different parameters of the theory in the case of a narrow resonance close to the threshold of the third channel, which is relevant for the resonancelike structure Z c ð3900Þ. The usage of these constraint relations, together with the multichannel Lüscher formula in lattice QCD calculations are also discussed and the strategies are outlined.

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The three-photon decay rate of J=ψ is studied using two N f ¼ 2 twisted-mass gauge ensembles with lattice spacings a ≃ 0.085 and 0.067 fm. Using a new method, only the correlation functions directly related to the physical decay width are computed with all polarizations of the initial and final states summed over. The final result can be obtained after a naive extrapolation to the continuum limit. To be specific, the result for such rare decay is given as BðJ=ψ → 3γÞ ¼ ð2.13 AE 0.14 AE 0.29Þ × 10 −5 , where the first error is statistical and the second is an estimate of the systematics. We also propose a method to analyze the Dalitz plot of the corresponding process based on the lattice data which can provide direct information for the relevant experiments.

Modelling based on multi-agent system (MAS) was built for the current production management and process of Shenyang Songyang Paper Cup Co., Ltd. It can transmit the information instantly via order agent (OA), manager agent (MA), production agent (PA), and service agent (SA), and realize information sharing. The PA is also built on MAS, and it includes two agents, task agent (TA), and resource agent (RA). It has been found that the modelling is superior to the old one. It can improve the working flow and production efficiency, and shorten the time of delivery.

We have corrected the decay width for the two photon decay widths for scalar and pseudo-scalar Charmonium in [Chinese Physics C Vol.44,No.8(2020)083108]. The decay widths are now in better agreement with the experiment values.