Abstract. We study the three-pion decays of the lightest isoscalar vector mesons, ω and φ, in a dispersive framework that allows for a consistent description of final-state interactions between all three pions. Our results are solely dependent on the phenomenological input for the pion-pion P-wave scattering phase shift. We predict the Dalitz plot distributions for both decays and compare our findings to recent measurements of the φ → 3π Dalitz plot by the KLOE and CMD-2 collaborations. Dalitz plot parameters for future precision measurements of ω → 3π are predicted. We also calculate the ππ P-wave inelasticity contribution from ωπ intermediate states. PACS

We analyze the pion transition form factor using dispersion theory. We calculate the singly-virtual form factor in the time-like region based on data for the cross section, generalizing previous studies on decays and scattering, and verify our result by comparing to data. We perform the analytic continuation to the space-like region, predicting the poorly-constrained space-like transition form factor below , and extract the slope of the form factor at vanishing momentum transfer . We derive the dispersive formalism necessary for the extension of these results to the doubly-virtual case, as required for the pion-pole contribution to hadronic light-by-light scattering in the anomalous magnetic moment of the muon.

We calculate the ! ! 0 Ã and ! 0 Ã electromagnetic transition form factors based on dispersion theory, relying solely on a previous dispersive analysis of the corresponding three-pion decays and the pion vector form factor. We compare our findings to recent measurements of the ! ! 0 þ À decay spectrum by the NA60 collaboration, and strongly encourage experimental investigation of the OkuboZweig-Iizuka forbidden ! 0 ' þ ' À decays in order to understand the strong deviations from vectormeson dominance found in these transition form factors.

Abstract:We study the Dalitz plot of the Cabibbo-favored charmed-meson decay D + → K − π + π + using dispersion theory. The formalism respects all constraints from analyticity and unitarity, and consistently describes final-state interactions between all three decay products. We employ pion-pion and pion-kaon phase shifts as input, and fit the pertinent subtraction constants to Dalitz plot data by the CLEO and FOCUS collaborations. Phase motions of resonant as well as nonresonant amplitudes are discussed, which should provide crucial input for future studies of CP violation in similar three-body charm decays.

We resume the study of the Cabibbo-favored charmed-meson decays D + →Kππ + in a dispersive framework that satisfies unitarity, analyticity, and crossing symmetry by construction. The formalism explicitly describes the strong final-state interactions between all three decay products and relies on pion-pion and pion-kaon phase shift input. For the first time, we show that the D + → K S π 0 π + Dalitz plot obtained by the BESIII collaboration as well as the D + → K − π + π + Dalitz plot data by CLEO and FOCUS can be described consistently, exploiting the isospin relation between the two coupled decay channels that provides better constraints on the subtraction constants.