30 research outputs found
Solving integral equations in
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 .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
Quark-mass dependence in decays
We study the quark-mass dependence of decays, based on a
dispersion-theoretical framework. We rely on the quark-mass-dependent
scattering phase shift for the pion-pion -wave extracted from unitarized
chiral perturbation theory. The dispersive representation then takes into
account the final-state rescattering among all three pions. The described
formalism may be used as an extrapolation tool for lattice QCD calculations of
three-pion decays, for which can serve as a paradigm case.Comment: 12 pages, 8 figures; v2: added two references, version published in
EPJ