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K-?+ Scattering from D+ ? K-?+?+ Antimo Palano INFN, Bari R. Andreassen, Brian Meadows University of Cincinnati D. Aston, J. Coleman, W. Dunwoodie, K. Suzuki, D. Leith Group B, SLAC “Traditional” Dalitz Plot Analysis The “isobar model”, with relativistic Breit-Wigner (RBW) resonant terms, is widely used in studying 3-body decays of heavy quark mesons. Amplitude for channel {ij}: Each resonance “R” (mass MR, width ?R) assumed to have form E791 (WMD) “Model-Independent”Partial-Wave Analysis (MIPWA) Make partial-wave expansion of decay amplitude in angular momentum of K-?+ system produced MIPWA (a la WMD / E791) Define S – wave amplitude at discrete points sK?=sj. Interpolate elsewhere. ? model-independent - two parameters (cj, ?j) per point P- and D- waves are parametrized by known K* resonances Unbinned Max. Likelihood Fit Likelihood function covers 3-dimensions: s(K?1), s(K?2) and also the reconstructed 3-body mass MK?? Factorize MK?? dependence: All events used in signal as well as sidebands have a D+ mass constraint. Can then overlay Dalitz plot for sideband data directly on signal Greatly simplifies computation of efficiency. E791 MIPWA of K-p+ S-wave Compare E791 K-p+ S-wave with E791 Compare E791 K-p+ S-wave with LASS The BaBar Sample of D+?K-?+?+ Skim carried out by Rolf Andreassen. A likelihood is based on PDFS (signal - MC) and PDFB (background - data sidebands) for each of the following quantities: Signed D+ decay length l/s l c2 probability for vertex PLAB for D+ Likelihood is product: Skim all with L2 D+ ? K-?+?+ Dalitz Plot Plot includes 500K events (~97% purity) ~13K are background. Obviously large S-wave content Interferes with K*(890) (and anything else in P-wave). Some D-wave also present Three Isobar Model Fits to BaBar Data E791 S-Wave Fit (on BaBar data) S-wave is spline with 30 equally spaced points P-wave is as in ? model fit, with complex coefficients floated. D-wave also as in ? model fit – complex coefficient floated.