By studying the ηc decays exclusively to double glueballs, we introduce a model to mimic phenomenologically the gluon-pair-vacuum interaction vertices, namely the 0 model. Based on this model, we study glueball production in ηc decay, explicitly ηc → f0(1500)η(1405). Among them f0(1500) is well-known scalar glueball candidate and η(1405) is thought of a candidate for pseudoscalar glueball. We discuss the possibility of finding these light glueballs in their production via the 0 model. We also discuss the heavier glueball production in ηb decays, which might be detectable in the LHCb and Belle-II experiments.

中文翻译：

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完全减少两环五光子散射幅度中的积分

通过专门研究 ηc 衰减到双胶球，我们引入了一个模型来模拟现象学上胶子对真空相互作用的顶点，即 0 模型。基于这个模型，我们研究了 ηc 衰变中胶球的产生，明确地 ηc → f0(1500)η(1405)。其中 f0(1500) 是众所周知的标量胶球候选，而 η(1405) 被认为是伪标量胶球的候选。我们讨论了通过 0 模型在他们的生产中找到这些轻胶球的可能性。我们还讨论了 ηb 衰变中较重的胶球产生，这可能在 LHCb 和 Belle-II 实验中检测到。