A dispersive analysis of η→3π decays has been performed in the past
by many authors. The numerical analysis of the pertinent integral equations is
hampered by two technical difficulties: i) The angular averages of the
amplitudes need to be performed along a complicated path in the complex plane.
ii) The averaged amplitudes develop singularities along the path of integration
in the dispersive representation of the full amplitudes. It is a delicate
affair to handle these singularities properly, and independent checks of the
obtained solutions are demanding and time consuming. In the present article, we
propose a solution method that avoids these difficulties. It is based on a
simple deformation of the path of integration in the dispersive representation
(not in the angular average). Numerical solutions are then obtained rather
straightforwardly. We expect that the method also works for ω→3π.Comment: 11 pages, 10 Figures. Version accepted for publication in EPJC. The
ancillary files contain an updated set of fundamental solutions. The
numerical differences to the former set are tiny, see the READMEv2 file for
detail