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  1. Abstract

    We evaluate the$$a_1(1260) \rightarrow \pi \sigma (f_0(500))$$a1(1260)πσ(f0(500))decay width from the perspective that the$$a_1(1260)$$a1(1260)resonance is dynamically generated from the pseudoscalar–vector interaction and the$$\sigma $$σarises from the pseudoscalar–pseudoscalar interaction. A triangle mechanism with$$a_1(1260) \rightarrow \rho \pi $$a1(1260)ρπfollowed by$$\rho \rightarrow \pi \pi $$ρππand a fusion of two pions within the loop to produce the$$\sigma $$σprovides the mechanism for this decay under these assumptions for the nature of the two resonances. We obtain widths of the order of 13–22 MeV. Present experimental results differ substantially from each other, suggesting that extra efforts should be devoted to the precise extraction of this important partial decay width, which should provide valuable information on the nature of the axial vector and scalar meson resonances and help clarify the role of the$$\pi \sigma $$πσchannel in recent lattice QCD calculations of the$$a_1$$a1.