1. 25/9/2007 LHCb UK meeting 1 ADS determination of γ with B→(Kπ) D K, B→(hh) D K and B→(K3π) D K Jim Libby (University of Oxford)

2. 25/9/2007LHCb UK meeting2 Outline Overview of ADS technique and current sensitivity with B→(Kπ) D K and B→(hh) D K at LHCb Overview of ADS technique and current sensitivity with B→(Kπ) D K and B→(hh) D K at LHCb Extension to B→(K3π) D K Extension to B→(K3π) D K –Introducing the coherence factor –How to measure it at CLEO-c Outlook Outlook Acknowledgements: Mitesh Patel, Andrew Powell and Guy Wilkinson Acknowledgements: Mitesh Patel, Andrew Powell and Guy Wilkinson

3. 25/9/2007LHCb UK meeting3 B→DK decays involve b → c and b → u transitions B→DK decays involve b → c and b → u transitions Access  via interference if D 0 and D 0 decay to the same final state Access  via interference if D 0 and D 0 decay to the same final state Theoretically clean: largest correction is sub-degree from D-mixing Theoretically clean: largest correction is sub-degree from D-mixing Essential to defining ‘tree UT’ to benchmark against `loop UT’ Essential to defining ‘tree UT’ to benchmark against `loop UT’ LHCb looking at a number of strategies to study such decays LHCb looking at a number of strategies to study such decays –B + : Atwood-Dunietz-Soni ('ADS'), 3 and 4 body Dalitz Plot Anal. –B 0 : Gronau-London-Wyler-(Dunietz) ('GLW'), 3 body Dalitz Introduction

4. 25/9/2007LHCb UK meeting4 Look at DCS and CF decays of D to obtain rates that have enhanced interference terms Look at DCS and CF decays of D to obtain rates that have enhanced interference terms Unknowns : r B ~0.1,  B,  D K , , N K , N hh (r D =0.06 well measured) Unknowns : r B ~0.1,  B,  D K , , N K , N hh (r D =0.06 well measured) With knowledge of the relevant efficiencies and BRs, the normalisation constants (N K , N hh ) can be related to one another With knowledge of the relevant efficiencies and BRs, the normalisation constants (N K , N hh ) can be related to one another Overconstrained: 6 observables and 5 unknowns Overconstrained: 6 observables and 5 unknowns ADS method

5. 25/9/2007LHCb UK meeting5 Expected yields ADS measurement is a counting experiment - but suppressed modes have ~10 -7 BRs ADS measurement is a counting experiment - but suppressed modes have ~10 -7 BRs –Principal challenge background suppression Detailed studies in DC04 documented in LHCb- 2006-066 Detailed studies in DC04 documented in LHCb- 2006-066 The suppressed modes have yields varying from 0 to 500 depending on the strong parameters The suppressed modes have yields varying from 0 to 500 depending on the strong parameters –780 background events predicted Channel Signal yield/2 fb -1 B/S B ± →(K ± π ) D K ± 56,0000.6 B ± →(h − h + ) D K ± 82001.8 ±

6. 25/9/2007LHCb UK meeting6 Background composition For favoured mode background dominated by B→Dπ For favoured mode background dominated by B→Dπ –Potential first conf. plot  –Toy MC For suppressed combinatoric dominates For suppressed combinatoric dominates For B→D(hh)K more even mixture of comb. and Dπ For B→D(hh)K more even mixture of comb. and Dπ –B→D(KK)K has significant non- resonant B→KKK component No RICH RICH DK DπDπ 0.5 fb -1 B mass (GeV)

7. 25/9/2007LHCb UK meeting7 Sensitivity from 2-body  D K π = 16.6 o – fit results from 1000 toy 2fb -1 experiments : Without norm. constraintWith norm. constraint

8. 25/9/2007LHCb UK meeting8 Sensitivity from 2-body Resulting  precision from 2fb -1 data (K , KK,  decays): Resulting  precision from 2fb -1 data (K , KK,  decays): This single mode at LHCb will match the expected combined precision of the B-factories at the end of running with 2 fb -1 This single mode at LHCb will match the expected combined precision of the B-factories at the end of running with 2 fb -1 DC06 studies underway (see Mitesh’s plenary talk at Sainte Nectaire): DC06 studies underway (see Mitesh’s plenary talk at Sainte Nectaire): –First analysis of the background suggests a 3 fold increase –Different from DC04 in that it is from misreconstructed PV –Optimistic this will be suppressed with additional cuts and reconstruction improvements (°)  D K π (°)-25-16.6-8.308.316.625   (°) 9.58.67.58.68.69.39.4

9. 25/9/2007LHCb UK meeting9 4-body ADS Studies have also been performed overconstraining the B→D(Kπ)K parameters using B→D(K πππ)K Studies have also been performed overconstraining the B→D(Kπ)K parameters using B→D(K πππ)K You can measure 4 rates analogous to those for D→Kπ with addition of only 1 extra parameter δ K3π You can measure 4 rates analogous to those for D→Kπ with addition of only 1 extra parameter δ K3π [Highlighted regions have ambiguous fit results] DC04 selection studies performed by Andrew (LHCb-2007- 004) DC04 selection studies performed by Andrew (LHCb-2007- 004) Additional information to be harnessed in these modes Additional information to be harnessed in these modes δ D K , δ D K3 

10. 25/9/2007LHCb UK meeting10 Amplitude model However, this simple treatment of ADS method ignores the resonant substructure in D→Kπππ However, this simple treatment of ADS method ignores the resonant substructure in D→Kπππ –made up of D→K*ρ, K − a 1 (1260) +,.,… –in principle each point in the phase space has a different strong phase associated with it - 3 and 4 body Dalitz plot analyses exploit this very fact to extract γ from amplitude fits Atwood and Soni (hep-ph/0304085) show how to modify the usual ADS equations for this case Atwood and Soni (hep-ph/0304085) show how to modify the usual ADS equations for this case –Introduce coherence parameter R K3π which dilutes interference term sensitive to γ –R F ranges from 1 (coherent; dominated by a single mode) to 0 (incoherent; several significant components) –If very incoherent can slice and dice phase space to find most coherent regions

11. 25/9/2007LHCb UK meeting11 The importance of CLEO-c data CLEO-c experiment is collecting events of the type: CLEO-c experiment is collecting events of the type: If one of the neutral D mesons decays to a CP eigenstate the other D is tagged to be of the opposite CP because of the quantum correlation If one of the neutral D mesons decays to a CP eigenstate the other D is tagged to be of the opposite CP because of the quantum correlation Allows determination of R K3π and δ K3π from double- tagged D →K3π vs CP eigenstates or DCS K3π/Kπ Allows determination of R K3π and δ K3π from double- tagged D →K3π vs CP eigenstates or DCS K3π/Kπ As we are not M-theorists only visualise in 2D

12. Tagging technique DD production at threshold: no extra particles, low multiplicity, very clean final state DD production at threshold: no extra particles, low multiplicity, very clean final state Use tagging technique (pioneered by Mark III) to fully reconstruct one (single tag) or both (double tag) D - greatly reduces combinatoric background Use tagging technique (pioneered by Mark III) to fully reconstruct one (single tag) or both (double tag) D - greatly reduces combinatoric background Variables used in the tag reconstruction: Variables used in the tag reconstruction: D + →K − π + π + D − →K + π − π − Single tags D +  K -  +  + or D -  K +  -  - ~81K events e + e - → ψ(3770) → DD PRELIMINARY Cut on ΔE ( ±3  ) and use M bc to extract the signal K3π tag side Expected 800 pb −1 yield K3π CF 4500 Kπ CF 5000 K3π/Kπ DCS 0-40 per mode K0Sπ0K0Sπ0K0Sπ0K0Sπ0650 K+K−K+K−K+K−K+K−500 π+π−π+π−π+π−π+π−200

13. 25/9/2007LHCb UK meeting13 Determining the coherence factor Measurement of R K3π via absolute value of various double tagged rates Measurement of R K3π via absolute value of various double tagged rates Analysis underway 10% effects in CP modes so great care with Analysis underway 10% effects in CP modes so great care with –Background subtraction –Efficiency calculation Estimate of current sensitivity with the addition of K 0 L π 0  Estimate of current sensitivity with the addition of K 0 L π 0  Further CP tags i.e. K 0 S η to be added Further CP tags i.e. K 0 S η to be added Further information in mixed CP SCS tags such as K 0 S π + π − Further information in mixed CP SCS tags such as K 0 S π + π − Binned analysis to determine the most coherent regions Binned analysis to determine the most coherent regions Like sign K3π Other modes Toy MC 800 pb -1 1σ δ K3π (°)

14. 25/9/2007LHCb UK meeting14 Outlook 2-body ADS is well developed 2-body ADS is well developed –Counting experiment therefore likely to be first B→DK measurement of γ –Precision of ~8° expected with 2 fb −1 Additional information in 4-body B→D(K3π)K Additional information in 4-body B→D(K3π)K –Model free determination requires measurement of coherence parameter of the D→K3π final state –Work at CLEO-c has begun to do this and will be complete before first ADS analysis Combine with 3-body decays and all neutral modes for ultimate γ sensitivity in the `tree UT’ Combine with 3-body decays and all neutral modes for ultimate γ sensitivity in the `tree UT’

15. 25/9/2007 LHCb UK meeting 15 Additional slides

16. 25/9/2007LHCb UK meeting16 CLEO-c data samples CLEO-c: Oct. 2003 – Apr. 2008 3686MeV, 54 pb -1, N( ψ(2S))≈ 27M e + e − → ψ(2S) → ππ J/ψ,  c etc. 3773MeV, 560 pb -1 processed, target 800pb -1, ψ(3770) → DD 4170MeV, 195 pb -1 → ~ 300pb -1 → more → ~720pb -1, D (s) ( * ) D (s) ( * ) 3970 – 4260MeV energy scan, 60pb -1 in 12 points PDG-2006