  We evaluate the $a_1(1260) \to \pi \sigma (f_0(500))$ decay width from the
perspective that the $a_1(1260)$ resonance is dynamically generated from the
pseudoscalar-vector interaction and the $\sigma$ arises from the
pseudoscalar-pseudoscalar interaction. A triangle mechanism with $a_1(1260) \to
\rho \pi$ followed by $\rho \to \pi \pi$ and a fusion of two pions within the
loop to produce the $\sigma$ provides 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 $\pi\sigma$ channel in recent lattice QCD
calculations of the $a_1$.
