Consistent Dalitz plot analysis of Cabibbo-favored D+→Kˉππ+D^+ \to \bar{K} \pi \pi^+ decays

We resume the study of the Cabibbo-favored charmed-meson decays $D^+ \to \bar{K} \pi \pi^+$ 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 $D^+ \to K_S \pi^0 \pi^+$ Dalitz plot obtained by the BESIII collaboration as well as the $D^+ \to K^- \pi^+ \pi^+$ 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.Comment: 8 pages, 2 figures; v2: discussion extended, references added, matches published versio

Dispersion-theoretical analysis of the D^+ --> K^- pi^+ pi^+ Dalitz plot

We study the Dalitz plot of the Cabibbo-favored charmed-meson decay $D^+\to K^-\pi^+\pi^+$ 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.Comment: 32 pages, 7 figures, version published in JHE

Dispersive analysis of charmed meson decays

The Standard Model comprises most of today's knowledge of particle physics and is overall well tested and understood. However the dynamics of strong interactions, given by Quantum Chromodynamics (QCD), are still a challenge at low energies. The running coupling constant prevents a direct perturbative calculation of QCD at the hadronic scale and therefore other methods have to be employed. In this thesis we apply dispersion theory to study strong final-state interactions in three-particle decays and investigate the J/ψ → π0 γ* transition form factor. In the first part of this thesis we introduce a dispersive framework for three-body decays, based on Khuri—Treiman equations, that satisfies analyticity, unitarity, and crossing symmetry by construction and includes crossed-channel rescattering effects. We explicitly display the derivation of the Khuri—Treiman equations on general vector-meson decays into three pions V → 3π with V∈{ω, Φ, J/ψ}. These decays provide an ideal test case as the equations are of simple form. In this context we study the general dependence of the resulting amplitude on the vector-meson mass and investigate the employed iterative solution strategy and its convergence. Building on the obtained J/ψ → 3π amplitude we study the J/ψ transition form factor. The transition form factors of light vector mesons have been of great interest over the last years because of their importance in the theoretical determination of the anomalous magnetic moment of the muon. However the available experimental data is difficult to understand theoretically. With the larger phase space available, the J/ψ → π0 γ* transition may shed light onto the lighter vector-meson transition form factors. In the second part we resume our study of three-particle decays on the Cabibbo-favored D+ → K π π+ decays. Heavy-flavor three-body decays into light mesons provide a valuable source for Standard Model tests and beyond. They play an important role due to their richer kinematic structure compared to two-body decays which can be exploited e.g. in CP-violation studies. So far the Khuri—Treiman-type equations have been applied successfully to light meson decays but not to heavy-flavor decays. Thus the Cabibbo favored D+ → K π π+ decays provide an ideal test to establish the framework in the open-charm sector. We introduce a new numerical method to solve the Khuri—Treiman-type equations, compare the obtained decay amplitudes to the data from the CLEO, FOCUS, and BES III collaboration as well as previous theoretical studies and discuss the impact of crossed-channel rescattering effects in these decays

Dispersive analysis of omega --> 3pi and phi --> 3pi decays

We study the three-pion decays of the lightest isoscalar vector mesons, omega and phi, 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 phi --> 3pi Dalitz plot by the KLOE and CMD-2 collaborations. Dalitz plot parameters for future precision measurements of omega --> 3pi are predicted. We also calculate the pi-pi P-wave inelasticity contribution from omega-pi intermediate states.Comment: 23 pages, 18 figures; discussion extended, Appendix D added, matches version published in EPJ

Dispersive analysis of the pion transition form factor

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 $e^+e^-\to 3\pi$ cross section, generalizing previous studies on $\omega,\phi\to3\pi$ decays and $\gamma\pi\to\pi\pi$ scattering, and verify our result by comparing to $e^+e^-\to\pi^0\gamma$ data. We perform the analytic continuation to the space-like region, predicting the poorly-constrained space-like transition form factor below 1 GeV, and extract the slope of the form factor at vanishing momentum transfer $a_\pi=(30.7\pm0.6)\times 10^{-3}$. 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.Comment: 13 pages, 5 figures, journal versio

omega --> pi0 gamma* and phi --> pi0 gamma* Transition form factors in dispersion theory

We calculate the omega --> pi0 gamma* and phi --> pi0 gamma* 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 omega --> pi0 mu+ mu- decay spectrum by the NA60 collaboration, and strongly encourage experimental investigation of the Okubo-Zweig-Iizuka-forbidden phi --> pi0 l+ l- decays in order to understand the strong deviations from vector-meson dominance found in these transition form factors.Comment: 11 pages, 8 figures; references updated, version published in Phys. Rev.

Dispersive analysis of the pion transition form factor

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 e⁺e⁻→3π cross section, generalizing previous studies on ω,ϕ→3π decays and γπ→ππ scattering, and verify our result by comparing to e⁺e⁻→π⁰γ data. We perform the analytic continuation to the space-like region, predicting the poorly-constrained space-like transition form factor below 1GeV, and extract the slope of the form factor at vanishing momentum transfer aπ=(30.7±0.6)×10⁻³. 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

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

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