https://doi.org/10.1140/epjc/s10052-018-6378-8
Regular Article - Theoretical Physics
Solving integral equations in 
1
Albert Einstein Center for Fundamental Physics, Institut für theoretische Physik, Universität Bern, Sidlerstr. 5, 3012, Bern, Switzerland
2
Helmholtz-Institut für Strahlen- und Kernphysik (Theorie) and Bethe Center for Theoretical Physics, Universität Bonn, Nussallee 14-16, 53115, Bonn, Germany
* e-mail: rusetsky@hiskp.uni-bonn.de
Received:
24
September
2018
Accepted:
27
October
2018
Published online:
9
November
2018
A dispersive analysis of 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 
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© The Author(s), 2018
