1 / 28

K -  + s -wave System from D + Meson Decays to K - p + p + in E791

K -  + s -wave System from D + Meson Decays to K - p + p + in E791. Brian Meadows University of Cincinnati. Outline. What is known about s-wave K -  + scattering Results from D + ! K -  +  + Decays Model Independent Partial Wave Analysis Comparison with the Watson theorem

neron
Download Presentation

K -  + s -wave System from D + Meson Decays to K - p + p + in E791

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. K-+s-wave System from D+ Meson Decays to K-p+p+ in E791 Brian Meadows University of Cincinnati Brian Meadows, U. Cincinnati.

  2. Outline • What is known about s-wave K-+ scattering • Results from D+!K-++ Decays • Model Independent Partial Wave Analysis • Comparison with the Watson theorem • Summary and Discussion Brian Meadows, U. Cincinnati

  3. Kp Scattering in Heavy Quark Decays • Understanding the structure of the s-wave Kp system is important to many analyses, and of vital interest to an understanding of the spectroscopy of scalar mesons. • It may be possible to learn more from the large amounts of data on D and B decays now available. • The applicability of the Watson theorem can be tested. • E791 is the first to try this by making a Model Independent Partial Wave Analysis of the s-wave in the decay D+!K-p+p+ (and cc). Brian Meadows, U. Cincinnati

  4. Kp Scattering • Most information on K-p+ scattering comes from the LASS experiment (SLAC, E135) Data from: K-p!K-p+n and K-p!K0p-p NPB 296, 493 (1988) No data below 825 MeV/c2 Brian Meadows, U. Cincinnati

  5. {12} {23} {13} 1 1 1 2 2 2 3 3 3 1 3 “Traditional” Dalitz Plot Analyses • The “isobar model” has been widely used, with Breit-Wigner resonant terms, over the past 15 years. • Amplitude for channel {ij}: • Each resonance “R” (mass MR, width R) assumed to have form NR 2 D form factor R form factor spin factor NR Constant Brian Meadows, U. Cincinnati

  6. E791 D+!K-p+p+ ~138 % c2/d.o.f. = 2.7 Brian Meadows, U. Cincinnati

  7. E791 D+!K-p+p+ ~89 % c2/d.o.f. = 0.73 (95 %) Probability Mk = 797 § 19 § 42 MeV/c2 Gk = 410 § 43 § 85 MeV/c2 Brian Meadows, U. Cincinnati

  8. E791 D+!K-p+p+ Dalitz Plot • Most interesting feature: • K*(892) bands dominate • Asymmetry in K*(892) bands ! Interference with large s–wave component • Also: • Structure at » 1430 MeV/c2 mostly K0*(1430) • Some K2*(1420)? or K1*(1410)?? • Perhaps some K1*(1680)? • So At least the K*(892) can act as interferometer for s–wave Perhaps other resonances can fill in some gaps too. Brian Meadows, U. Cincinnati

  9. Helicity angle q in K-p+ system Asymmetry: Asymmetry in K*(892) K- q + p q cosq = p¢q + tan-1m00/(m02-sK) !P - s is -750 relative to elastic scattering Brian Meadows, U. Cincinnati

  10. s–wave fromD+!K-p+p+ Dalitz Plot? • Divide m2(K-+) into slices • Find s–wave amplitude in each slice (two parameters) • Use remainder of Dalitz plot as an interferometer • For s-wave: • Interpolate between (ck, k) points: • Model P and D S (“partial wave”) Brian Meadows, U. Cincinnati

  11. Reference Waves • For p- and d-waves: • Use “traditional” Breit-Wigner isobar model: • Unbinned maximum likelihood fit: • Use 40 (ck, k) points for S • Float (d1680, 1680) and (d1430, 1430) ! 40 x 2 + 4 = 84 free parameters. P (“partial wave”) D (“partial wave”) K892 defines reference phase Brian Meadows, U. Cincinnati

  12. Fit E791 Data for s-wave Phase Magnitude Float P and D parameters and find S: • General appearance similar to isobar model fit: • Magnitudes at low mass differ • Phases above K0*(1430) • Tests with many MC samples of this size (15K events), produced to simulate the isobar model, produce similar differences in ~15% of the cases • Major source of systematic uncertainty: • Contribution of reference waves in region between K*(892) and K*(1680). S P D Brian Meadows, U. Cincinnati

  13. Comparison with Data S 2/NDF = 272/277 (48%) Brian Meadows, U. Cincinnati

  14. Comparison with Elastic Scattering (LASS) • S is related to elastic scattering amplitude T obtained from LASS by • In elastic scattering K-p+!K-p+ the amplitude is unitary • In D+ decays, the Kp can come from many sources so we expect the magnitude to differ from sind(sKp). • If applicable to these decays, the Watson theorem requires phases d(sKp) for each wave to be the same, up to the elastic limit (1454 MeV/c2). K.M. Watson, Phys. Rev. 88, 1163 (1952) Brian Meadows, U. Cincinnati

  15. Phases for S, P and D waves are compared with those from LASS. s-wave phase fs for E791 is shifted by –750 wrt LASS. fs energy dependence differs below 1100 MeV/c2. fp does not match well between K*(892) and K*(1680) resonances fd match is excellent up to elastic limit. Watson Theorem - a direct test S Elastic limit Kh’ threshold (1454 MeV/c2) P D Brian Meadows, U. Cincinnati

  16. Summary • A new technique is used to fit the amplitude describing a Dalitz plot distribution • It can provide model independent measurements of the complex amplitude of the K-p+ s-wave system, provided a good model for the p- and d-waves is used. • Such measurements are possible at masses below the limit of existing ones. • The Watson theorem does not apply to D+!K-++ decays. • This technique will play a role in analyses of the large samples of heavy meson decays becoming available from B factories, CLEO-c and the TeVatron collider. Brian Meadows, U. Cincinnati

  17. Back up Slides Brian Meadows, U. Cincinnati

  18. A Different Approach • Instead of expanding the Dalitz plot amplitude in BW’s (or pole terms in a K matrix) for each resonance, expand in partial waves. • For a D decay, barrier factors preclude all but s-, p- and d- waves. • Treat the s-wave, at least, as having completely unknown dependence on invariant mass. • p- and d-waves can be expanded as resonances of appropriate spin Brian Meadows, U. Cincinnati

  19. Does this Work? Simulate 150K MC events with isobar model parameters Find S for them: Phase Magnitude S S P D Brian Meadows, U. Cincinnati

  20. Milestones in Dalitz Plot Analyses 1993-7: E691/687 find large non-resonant (NR) fraction in Decays D+!-++ and D+!K-++ 2001: E791 find that broad, low mass scalar isobars can soak up most of the NR contribution !NR is not constant 2004: Focus collaboration use data from K-matrix fit to large number of hadron interactions involving +- production in analysis of D+!-++. ! No new broad scalars required? Brian Meadows, U. Cincinnati

  21. Milestones in Dalitz Plot Analyses 2005: Lots more data is on the way Clearly, we may be able to learn which scalar resonances really exist Other information is required from the data We need new, less model-dependent ways to analyze it. ! One possibility is Energy Independent Partial Wave Analysis (EIPWA). E791 is the first to try. Brian Meadows, U. Cincinnati

  22. E791 D+!p-p+p+ No “s(500)” Brian Meadows, U. Cincinnati

  23. E791 D+!p-p+p+ Brian Meadows, U. Cincinnati

  24. Kp Scattering • Most information on K-p+ scattering comes from the LASS experiment (SLAC, E135) Data from: K-p!K-p+n and K-p!K0p-p NPB 296, 493 (1988) a – scattering length b – effective range p – momentum in CM Parametrize s-wave (I=1/2) by Brian Meadows, U. Cincinnati

  25. E791 D+! K-p+p+ Brian Meadows, U. Cincinnati

  26. Does this Work? Phase Magnitude Fit the E791 data: • Fix P and D parameters at  model • Find S: • Fix S and D parameters at  model • Find P: • Fix S and P parameters at  model • Find D: The method works. S P S D Brian Meadows, U. Cincinnati

  27. Comparison with Data Moments Masses S 2/NDF = 272/277 (48%) Brian Meadows, U. Cincinnati

  28. Other Solution Phase Magnitude • Qualitative agreement with data • BUT does not give acceptable c2. • This solution violates the Wigner causality condition. S S E. P. Wigner, Phys. Rev. 98, 145 (1955) P D Brian Meadows, U. Cincinnati

More Related