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Hadronic Substructure and Dalitz Analyses at CLEO

This presentation discusses the significance of charm Dalitz plot analyses and results from the CLEO experiment. It covers key decay channels such as D0 → K+K-p0 and D0 → p+p-p0, and explores the potential contributions of CLEO-c to the study of the CKM angle γ/f3. The importance of understanding final state interactions and the complexities of modeling multi-body decays are emphasized. The presentation includes details on the CLEO evolution, extraction methods for CKM parameters, and significant findings relevant to the determination of f3, highlighting the intricate interference effects within charm decays.

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Hadronic Substructure and Dalitz Analyses at CLEO

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  1. Hadronic Substructure & Dalitz Analyses at CLEO Mats Selen, University of IllinoisHEP 2005, July 22, Lisboa, Portugal

  2. Outline • Why the interest in charm Dalitz Plot (DP) analyses? • Results from CLEO • D0 → K+K-p0 • D0  p+p-p0 • D0  Ks00 • What CLEO-c will do for CKM angle g/f3.

  3. CLEO Evolution CLEO II.V (9/fb) New RICH New Drift Chamber New silicon New Trigger & DAQ CLEO III (14/fb) Replace siliconwith a wire vertex chamber CLEO-c (281/pb)

  4. Why bother? • Need to understand the brown muck. • Final state interactions are tricky • Relative amplitudes and phases hard to calculate – must measure. • Need to sort out the best way to model ≥ 3 body decays • Isobar, K-matrix, … • People have not always agreed on best approach  • Important engineering measurement for getting the most out of b-factory data. • For example, extracting f3 from BDK

  5. The power of the DP approach • Interference is a beautiful thing ! • Phase sensitivity is a very important handle Example: D0 K- p+ p0

  6. 4.1% K*(1430)0 79% r(770) 16% K*(892)- 13% K*(892)0 3.3% K*(1430)- 5.7% r(1700) 7.5% non-res 1.3% K*(1680)- + a3 a1 eif3 + a4 + a2 eif4 eif1 eif2 eif8 + a5 eif7 eif5 + a6 + a7 + a8 eif6 =

  7. Relevance to f3 • There are several schemes to access g/f3 by exploiting interference in the decays of charged B mesons to charm: B  DK • D  K*K • Grossman, Ligeti, Soffer PRD 67 (2003) • Suprun, Rosner PRD 68 (2003) • CLEO analysis of D0 K+K-p0 • D  3-body/Dalitz • Giri, Grossman, Soffer, Zupan PRD 68 (2003) • CLEO analysis of D0 KSp+p-, p+p-p0

  8. D0K+K-p0 • Method for measuring CKM phase f3 by looking at B± → (K*+ K-)DK ± and B± → (K*- K+)DK ± • Needs a measurement of the strong phase difference dD between D0 → K*+ K– and D0 → K*– K+. • Dalitz analysis of D0 → K+K-p0 will yield dD d=180 d=0

  9. D0K+K-p0 CLEO III ¡(4S) Region: 8.965/fb D*+ → p+ D0 → K+ K–p0 → gg K±Kmp0 signal region mK+p02 (GeV/c2)2 (after selection criteria) f Signal Fraction » 77.4% Signal Events »565 (in the signal region) K*+ K*- mK-p02 (GeV/c2)2 mK+K-p0 (GeV/c2)

  10. D0K+K-p0 Preliminary Fit Statistical errors only

  11. Fit projections reveal a feature/problem… K*- K*+ mK+p02 (GeV/c2)2 mK-p02 (GeV/c2)2 dips  are we missing some physics ?? Exploring K-p P-wave K-matrix approach

  12. f3 from 3-body final states s b c u b s c u u u u u Access f3 via interference between B±  D0K± and B±  D0K± favored suppressed KS, p0 p+ p- B± K±

  13. Amplitude differences willbe sensitive to f3. ~ ~ D+ D- Where is the amplitude of the D0 matrix element at the point on the Dalitz Plot, and Once has been determined (where we come in) then D+ and D- Dalitz plots can be fit to determine f3. ~ ~ ~ D  KS-+ BELLE 253/fb m- m- (From B± decays) m+ m+

  14. D0p+p-p0 • Useful for studying f3 in charged B decays. • Like D0KSp-p+(discussed later) • Good system for CP violation search. • Some predictions as high as 0.1% (ref) • Compare to D+p+p-p+ • Has large S-wave component (FOCUS ref)

  15. 0 1 2 3 m2(p+p0) (GeV2) D0p+p-p0 S/(S+B) ~ 80% S ~ 1100 9.0/fb m2(p+p0) (GeV2) m2(p+p-) (GeV2) 0 1 2 3 0 1 2 3 m2(p+p-) (GeV2) m2(p-p0) (GeV2)

  16. p+p- proj < 6.4 @ 95% CL 0 1 2 3 GeV2 < 0.21 @ 95% CL 0 1 2 3 GeV2 See Au, Morgan, Pennington PRD 35, 1633 (1987) < 1.9 @ 95% CL 0 1 2 3 GeV2

  17. D0p+p-p0 • Only rp contributions plus small non-resonant component are required to fit Dalitz plot. • Very small D0p+p-p0 S-wave fit fraction (<0.9%) compared to FOCUS (56%) for D+p+p-p+ • D+p+p-p+ / D0p+p-p0 S-wave ratio > 36@95%CL • Tree level estimate = • Flavor tagged D0 and D0 Dalitz plots also fit separately to limit DP integrated CP asymmetry: • ACP =

  18. S/(S+B) ~ 70% S ~ 700 D0 Ks00 m2(p0p0) (GeV2) • Lots of brown muck • Complement KSp-p+ analyses • Good place to search for low mass pp • No r00 to get in the way! m2(KSp0)RS (GeV2) K*(890) + K0(1430) + f0 + NR K*(890) + K0(1430) + f0 + NR + s 0 1 2 0 1 2 m2(p0p0) (GeV2) m2(p0p0) (GeV2)

  19. CLEO-c data (165 pb-1) CLEO-II.V & III (~15 fb-1) S/(S+B) ~ 70% S ~ 700 S/(S+B) ~ 72% S ~ 1500 m2(p0p0) (GeV2) m2(KSp0)RS (GeV2)

  20. What CLEO-c will do for f3 The determination of is presently the limiting systematic • Belle and BaBar have studied the dependence of f3 on the D decay model (analysis used D0  Ks+-) • Belle - Phys.Rev.D70:072003,2004 hep-ex/0406067 • BaBar – ICHEP04 paper hep-ex/0408088 D Decay Model Systematic Uncertainty

  21. 2 0 1 2 3 0 1 2 3 0 1 2 3 m2(KSp-) (GeV2) m2(KSp+) (GeV2) m2(p-p+) (GeV2) S/(S+B) ~ 98% S ~ 5300 CLEO-II.V D0 Ks+- Rather low statistics compared to… m2(p-p+) (GeV2) 1 0 0 3 2 1 m2(KSp)RS (GeV2)

  22. BaBar data with“CLEO” modelnot so good 2.27x108 BB pairs BELLE fits look like BaBar

  23. Fit with additional resonances much better. This includes BW s1 and s2 with ~10% fit fractions. Causes big systematicuncertainty !

  24. CLEO-c can help • Do simultaneous CP tagged and flavor tagged analysis of D0  Ks+- [only at ’’(3770)] • Suppose we write • We will extract as well as in a model independent way. • This is exactly what the f3 analyses need.

  25. Many other CLEO-c Dalitz plot analyses are in the works: K-p+h p-p+p0 KSKSp0 K-p+p0 KSKp KSK+K- KSp+p0 p+p+p- etc…many others

  26. Conclusions • CLEO has done (and continues to do) groundbreaking work on charm Dalitz analyses. • K-p+p0,p+p-p0,KSp+p-,KSp0,K-K+p0,KSp0p0, ... • Implementation of K-Matrix amplitudes in fits • CLEO-c will open a new window on the charm sector by exploiting quantum correlations: • CP tagged Dalitz Plot analyses • f3, mixing, CP violation, … • Double correlated Dalitz analyses (i.e. DP vs DP) • Stay tuned

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