In this article, the analyticity of triangle loop integral with complex masses of internal particles is discussed in a new perspective, based on which we obtain the explicit width dependence of the absorptive part of the triangle amplitude. We reanalyze the decay pattern of ηð1405=1475Þ with the width effects included in the triangle singularity (TS) mechanism. Based on the present experimental information, we provide a selfconsistent description of the KKπ, ηππ, and 3π decay channels for ηð1405=1475Þ. Our results confirm the claim that the TS mechanism plays a decisive role in the understanding of the ηð1405Þ and ηð1475Þ puzzle. Namely, the observed differences of η resonances within the mass region of 1.40-1.48 GeV are originated from the same state. For the isospin violated process J=ψ → γηð1405=1475Þ → f 0 ð980Þπ → 3π, we identify an additional contribution to the a 0 ð980Þ − f 0 ð980Þ mixing via the TS mechanism.

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