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K -  + Scattering Using D + Decays from B ABAR

K -  + Scattering Using D + Decays from B ABAR. Brian Meadows University of Cincinnati. {12}. {23}. {13}. 1. 1. 1. 2. 2. 2. 3. 3. 3. 1. 3. “Traditional” Dalitz Plot Analysis.

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K -  + Scattering Using D + Decays from B ABAR

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  1. K-+ Scattering Using D+ Decays from BABAR Brian Meadows University of Cincinnati

  2. {12} {23} {13} 1 1 1 2 2 2 3 3 3 1 3 “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 NR 2 NRConstant R form factor D form factor spin factor

  3. Traditional E791 DD+!KK-p+p+ ~138 % c2/d.o.f. = 2.7 Flat “NR” term does not give good description of data. Phys.Rev.Lett.89:121801,2002

  4. “Traditional”  Model for S-wave - E791 ~89 % c2/d.o.f. = 0.73 (95 %) Probability Mk = 797 § 19 § 42 MeV/c2 Gk = 410 § 43 § 85 MeV/c2 E. Aitala, et al, PRL 89 121801 (2002)

  5. E791 (WMD) “Model-Independent”Partial-Wave Analysis (MIPWA) • Make partial-wave expansion of decay amplitude in angular momentum of K-+ system produced D form-factor • “Partial Wave:” • Describes invariant • Mass dependence of • K-+ system • -> Related to K-+ • scattering ML(p,q)

  6. MIPWA • Define S–wave amplitude at discrete points sK=sj. Interpolate elsewhere.  model-independent - two parameters (ccj, j) per point • P- and D-waves are defined by known K* resonances and act as analyzers for the S-wave.

  7. MIPWA – E791 Mass Distributions E791 15,079 signal events 94% purity 2/NDF = 272/277 (48%) S Phys.Rev.D73:032004,2006

  8. BaBar Sample • K-p+p+ invariant mass distribution from Rolf’s sample. • A likelihood is based on PDFS (signal - MC) and PDFB (background - data sidebands) for each of the following quantities: • Signed D+ decay length SDZ= l¥ l/sl • c2 probability for vertex • PLAB for D+ • Likelihood is product: Skim all with L>2

  9. Rolf’s Skim • K-p+p+ invariant mass vs. likelihood (L) (NOTE log scale).

  10. Max. Likelihood Fit • Likelihood function covers 3-dimensions: • sK1, sK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. • Makes it possible to overlay Dalitz plot for sideband data directly on signal • Greatly simplifies computation of efficiency. • is efficiency Subscript s is signal Subscript b is background

  11. Background Model • K-p+p+ invariant mass distribution from sample with L > 3 • Dalitz plot distributions in lower side-band, signal region and upper side-band (log. Scale) • Used directly as input to background function. PDF1b - bin-by-bin interpolation

  12. Second Background • Probable origin Lost

  13. Efficiency • Efficiency (%) over the Dalitz plot for various laboratory momentum ranges.

  14. Efficiency vs. pLAB • Efficiency (%) vs laboratory momentum. • Lab. momentum for Data (black). • Lab. momentum for reconstructed, signal MC (red).  No need to use efficiency as function of pLAB

  15. D+ K-++ Dalitz Plot • Obviously large S-wave content Interferes with K*(890) (and anything else in P-wave). • D-wave also present

  16. “Traditional”  Model for S-wave - BaBar 2/NDF = 1443/624 – poor fit

  17. Partial Waves from  Model Fit Phase Magnitude Width of lines represents 1

  18. E791 S-Wave Fit (on BaBar data) • S-wave is spline with 30 equally spaced points • P-wave is as in  model fit. • D-wave also as in  model fit.

  19. Spline Model for S-wave - BaBar 2/NDF = 1007/574 – still a poor fit

  20. What to do with P-wave? • S-wave solution depends on P-wave reference. • Could add K1*(1410) • BUT this crowds the wave. • Try a spline: • Sn(s) = splinen(s) - spline defined by n points. • Pm(s) = RBW[K*(890)] x splinem(s) • Not much progress yet •  Uniqueness problem ??

  21. Double Spline Fit - n x m = 40 x 20 2/NDF = 843/574 – better, but still a poor fit

  22. Double Spline Fit - n x m = 40 x 20 • S-wave is spline with 40 equally spaced points • P-wave is also a spline with 20 equally spaced points x RBW[K*(890)]. • D-wave just as in  model fit.

  23. Double Spline Fit - n x m = 50 x 15 2/NDF = 867/518 – just better, but still a poor fit

  24. Double Spline Fit - n x m = 50 x 15 • S-wave is spline with 40 equally spaced points • P-wave is also a spline with 20 equally spaced points x RBW[K*(890)]. • D-wave just as in  model fit.

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