On the role of final-state interactions in Dalitz plot studies

Abstract

The study of Dalitz plots of heavy-meson decays to multi-hadron final states has received intensified interest by the possibility to gain access to precision investigations of CP violation. A thorough understanding of the hadronic final-state interactions is a prerequisite to achieve a highly sensitive, model-independent study of such Dalitz plots. We illustrate some of the theoretical tools, predominantly taken from dispersion theory, available for these and related purposes, and discuss the low-energy decays omega, phi --> 3pi in some more detail.Comment: 5 pages, 5 figures; to appear in the proceedings of the International Workshop on e+e- collisions from Phi to Psi, September 19-22, 2011, Novosibirsk, Russia; partial textual overlap with arXiv:1108.586

“Could charm (& τ) transitions be the ‘poor princess’ providing a deeper understanding of fundamental dynamics ?” or: “Finding novel forces”

“…The usual Breit-Wigner parametrization does not describe the impact of broad resonances such as σ/f 0 (500) & κ/K * 0 (800) [60][61][62][63][43][44][45] on both charm (& beauty) hadronic FS well, for various reasons. The interference of narrow and broad resonances cannot be described as being simply "inside" and "outside" the centers of the narrow resonances.…”

“…FSI by strong forces cannot be calculated from first principles at present. Yet, one can relate these factors using nontrivial theoretical tools incorporating chiral symmetry and refined dispersion relations [60][61][62][63][43][44][45], which are based on data concerning low-energy pion and kaon collisions. The crucial strength in this approach is that we cannot depend on the best fitted data, but rather on correlations with other transitions based on tested theories.…”

“…We require further thought, redefined tools and, in particular, consideration of correlations with other FS based on CPT invariance. In the future, dispersion relations [43][44][45][60][61][62][63] based on lowenergy collisions of two hadrons will be used; their power lies in combining data with experimental & theoretical tools.…”

Dispersion Theory Methods for Transition Form Factors

“…Dispersion relations allow for a model-independent description of these transition form factors. 2 The π 0 transition form factor of fixed isoscalar photon virtuality (q 2 = M 2 ω/φ ) can be extracted from ω/φ → π 0 + − ( = e/µ), and a dispersive analysis of this process has previously been reported. 3 An extension of the framework to include arbitrary isoscalar photon virtualities will enable a full-fledged dispersive analysis of the doubly-virtual transition form factor.…”