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.