1. Gagan Mohanty University of Warwick Dalitz Plot Analysis in the Charmless three-body B decays @ Representing

2. 12/1/2006Gagan Mohanty2 Outline of the talk Introduction Theoretical Framework Experiment & Dataset Event Selection DP Analysis Methodology Results and Discussion Conclusions and Outlook (*) DP = Dalitz Plot

3. 12/1/2006Gagan Mohanty3 Introduction: Timeline (1993) 1 st observation of charmless B decays by CLEO  Since then… PRL 71, 3922 (1993)

4. 12/1/2006Gagan Mohanty4 Introduction: Timeline (2006) A vast amount of results in the charmless sector is pioneering: A natural extension: quasi-two-body B decays to three-body final states test of QCD factorization direct CP search for new physics BaBar: PRL 93, 131801 K+π-K+π- K-π+K-π+

5. 12/1/2006Gagan Mohanty5 Theoretical Framework b → s penguin transition contributes only to final states with odd number of kaons due to presence s quark e.g. Kππ, KKK b → u tree and b → d penguin transitions contribute mainly to final states with even number of kaons such as πππ, KKπ. Contribution to odd number kaon states is Cabibbo suppressed [~ sin θ c ] “wrong flavor” final states such as K + K + π - and K - π + π + are expected to be exceedingly small at o(10 -11 ) in the Standard Model, and offer an excellent window for new physics  The dominant contributions to charmless three-body final state: b → u b → s/d

6. 12/1/2006Gagan Mohanty6 Typical final states Shall focus on the Dalitz Plot analysis of above five charmless three-body decay modes from BaBar

7. 12/1/2006Gagan Mohanty7 PEP-II asymmetric B factory Daily luminosity Run 5 9 GeV e - →Υ(4S)← 3.1 GeV e + γβ = 0.56 ~ 260 μm L int > 300 fb -1 (10% off-peak) This talk includes

8. 12/1/2006Gagan Mohanty8 Design = 3x10 33 cm -2 sec -1 ~ 3x Design ~ 100 pb -1

9. 12/1/2006Gagan Mohanty9 BaBar Detector Cerenkov Detector (DIRC) 144 Quartz bars and 11000 PMTs 1.5T solenoid Electromagnetic Calorimeter 6580 CsI(Tl) Crystals Drift Chamber 40 layers Instrumented Flux Return Resistive Plate Chamber → Limited Streamer Tube Silicon Vertex Tracker 5 layers, double strip e + (3.1GeV) e - (9GeV) e  ID  reco.   & K L ID High quality tracking (fiducial volume: 041 <  < 2.54)  (p T )/p T = 0.13% P T  0.45%  E /E = 2.32% E -1/4  1.85% Particle ID

10. 12/1/2006Gagan Mohanty10 Event Selection Wish to select B → hhh (h=K/ π ) event out of sea of continuum and other type B events Done in several steps:  Continuum rejection (Event topology)  π vs. K vs. e/ μ (Particle flavour Identification)  Reconstruct K s / π 0 from their decay products  on vs. off resonance (Kinematical variables)  Veto on charmed resonances: D, J/ ψ, ψ (2S)

11. 12/1/2006Gagan Mohanty11 Continuum Rejection B’ s are produced at rest (spherical) vs. jetty udcs events Cuts on event thrust & Fisher discriminant/NN constructed out of the topological variables BackgroundSignal

12. 12/1/2006Gagan Mohanty12 Particle Identification PID is crucial for the analyses –distinguish K vs. π (DIRC) –veto the electron (DCH/EMC) Reconstruct π 0 [ → γγ ] (EMC) and K s [ → ππ ]

13. 12/1/2006Gagan Mohanty13 Kinematical Variables Utilize precise beam energy information & (E,p) conservation B + → K + π + π - Sideband Signal box Background DP fit

14. 12/1/2006Gagan Mohanty14 DP Analysis Technique – 1 Dalitz Plot is a powerful technique relying on Lorentz invariant phase-space variables in a three-body decay B 1 2 3 B 2 1 3 + Resonance {13} s ij = m 2 ij

15. 12/1/2006Gagan Mohanty15 DP Analysis Technique – 2 Extract c i and θ i by performing a max likelihood fit θ i has two terms:  CP violating weak phase (–ve)  CP conserving strong phase same Separate fit of B and B samples B → B {

16. 12/1/2006Gagan Mohanty16 Efficiency Variation B + → π + π + π - Smooth variation of efficiency across the DP Use 2D parameterization in the likelihood fit Combinatorics is very small (mostly ignored) D J/ψ ψ(2S)

17. 12/1/2006Gagan Mohanty17 Background Parameterization B + → π + π + π - Use 2D histogram to model the DP distribution Continuum = off res + on res data sideband and B bkg = Monte Carlo & subtracted from latter Square DP for better describing peaking edge Continuum D J/ψ ψ(2S)

18. 12/1/2006Gagan Mohanty18 B + → π + π + π - : fitting the signal PRD 72, 052002 (2005) B+B+ B-B- Phase-space Coupled BW ρ(770) f 2 (1270) 210 fb -1

19. 12/1/2006Gagan Mohanty19 B + → π + π + π - : Summary PRD 72, 052002 (2005) ρ 0 (770) is the dominant component 3σ indication for f 2 (1270) & NR mode Little evidence for σ (seen by BES)  Can be utilized to measure γ PRL 81, 4067 (1998)

20. 12/1/2006Gagan Mohanty20 B + → π + π + π - : prospect for γ  proposes to use B →χ c0 π, which carries a null weak phase, as the reference mode  However, no indication of the χ c0 π mode  new reference mode needs to be studied Iso-scalar ππ resonances e.g. f 0 (980) are proposed as alternatives Again statistics disallows any meaningful conclusion  L int is the need of the hour! PRL 81, 4067 (1998)

21. 12/1/2006Gagan Mohanty21 B + → K + π + π - : fitting the signal PRD 72, 072003 (2005) B+B+ B+B+ B-B- B-B- qq BB Fit 205 fb -1

22. 12/1/2006Gagan Mohanty22 B + → K + π + π - : Summary PRD 72, 072003 (2005)  Total BF differs significantly from Belle  (Kπ)* 0 => K* 0 (1430) resonance + Effective range NR component (again different in Belle)  Evidence for direct CP violation in ρ 0 (770)K mode

23. 12/1/2006Gagan Mohanty23 Belle BABAR CP in charged B decays? PRD 72, 072003 (2005) hep-ex/0512066 (2005) Large A CP in agreement with predictions based on global SU(2) fits |T/P|~0.3 PRD 69, 034001 (2004)  Eagerly looking forward to more data…

24. 12/1/2006Gagan Mohanty24 B 0 → π + π - π 0 : time-dependent DP  Parameterize B 0 (B 0 ) → π + π - π 0 amplitude in terms of ρ + (→π + π 0 )π -, ρ - (→π - π 0 )π + and ρ 0 (→π + π - )π 0 }  Time-dependent decay rate: f κ (κ = +,-,0) are BW functions dependent on the DP variables PRD 48, 2139 (1993) Determine U κ and I κ (27 → 16 parameters for small ρ 0 π 0 contribution) in the likelihood fit {

25. 12/1/2006Gagan Mohanty25 B 0 → π + π - π 0 : DP fit and result Likelihood built using PDFs for the discriminating variables: ΔE, m ES, NN, Δt & DP variable (square) Extract physics parameters from the fitted U κ and I κ : { Event yield = 1184 ± 58 m’ θ’θ’ hep-ex/0408099 (2004) 192 fb -1

26. 12/1/2006Gagan Mohanty26 B 0 → π + π - π 0 : α and direct CP { Direct CP violation @ 2.9σ level  hep-ex/0408099 (2004) 11 22

27. 12/1/2006Gagan Mohanty27 Overall  from BaBar  from ,  and   from a full CKM fit  K, V ub,  m d,s, sin(2  )) Mirror solutions being disfavored!  mode particularly plays an important role From , ,  (combined) : (preliminary)

28. 12/1/2006Gagan Mohanty28 B 0 → K + π - π 0 : fitting the signal  Gounaris-Sakurai  LASS shape  Uniform phase-space PRL 21, 244 (1968) NP B296, 493 (1988) Fit qq BB hep-ex/0408073 (2004)

29. 12/1/2006Gagan Mohanty29 B 0 → K + π - π 0 : Summary hep-ex/0408073 (2004) 4.2 σ evidence of K* 0 (892) mode, UL from Belle Negligible non-resonant contribution 90% CL UL Measured BF of the benchmark process B 0 → D 0 π 0 in agreement with current world average: (270 ± 80)x10 -6 No significant A CP observed in any of the modes 193 fb -1

30. 12/1/2006Gagan Mohanty30 B 0 → K + K - K s : fitting the signal 1 st attempt to study the K + K - K s Dalitz plot Narrow Φ (1020) signal => use convoluted BW Handful events to claim any other resonances Try combinations of known 0 ++ and non-flat NR model to best parameterize the data f 0 (980) X(1500) NR 210 fb -1

31. 12/1/2006Gagan Mohanty31 B 0 → K + K - K s : Summary X(1500)  NR  c0 D +,D s +  reflections hep-ex/0507094 (2005)  Ad hoc model to describe S-wave  Need theory hand & more data

32. 12/1/2006Gagan Mohanty32 Summary  Charmless three-body decays move to the era of Dalitz plot analysis  Branching fractions of many quasi-two-body decays are measured, some are the 1 st time measurements  Evidence of large CP asymmetry in the ρ 0 (770)K mode of the Kππ final state  Time-dependent Dalitz measurement of B 0 →(ρπ) 0  direct CP violation at 2.9σ level and measured α  Mostly covered from BaBar, competitive results are available from Belle for many modes

33. 12/1/2006Gagan Mohanty33 Backup Slides

34. 12/1/2006Gagan Mohanty34 Future Prospects Double again from 2006 to 2008 ~ 1 ab -1 Double from 2004 to 2006 L int [fb -1 ]

35. 12/1/2006Gagan Mohanty35 Square Dalitz Plot “blow up”  bands & interference regions Jacobian ρ+ρ+ ρ-ρ- ρ0ρ0

36. 12/1/2006Gagan Mohanty36 B →πππ : nominal fit results PRD 72, 052002 (2005)

37. 12/1/2006Gagan Mohanty37 B → K ππ : nominal fit results PRD 72, 072003 (2005)