1. 8th December 2007CLEO physics fest1 Coherence factor analyses Jim Libby, Andrew Powell and Guy Wilkinson (University of Oxford)

2. 8th December 2007 CLEO physics fest 2 Outline The ADS technique to measure γ  Using D→Kπππ: introducing the coherence factor Measuring the coherence factor at CLEOc Status of the D→Kπππ coherence factor analysis  700 pb -1 results  New CP tags First steps with D→Kππ 0 coherence analysis Conclusion and plans

3. 8th December 2007 CLEO physics fest 3 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 These measurements are theoretically clean  No penguin  CKM standard candle  largest correction is sub-degree from D-mixing Number of strategies to study such decays Introduction B ± →DK ± Ratio of absolute amplitudes of colour/CKM suppressed to favoured (~0.1) Strong phase difference

4. 8th December 2007 CLEO physics fest 4 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) With knowledge of the relevant efficiencies and BRs, the normalisation constants (N K , N hh ) can be related to one another Important constraint from CLEOc σ(cos  D K   Overconstrained: 6 observables and 5 unknowns ADS method h=π or K

5. 8th December 2007 CLEO physics fest 5 Four-body ADS B→D(K πππ)K can also be used for ADS style analysis However, need to account for 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  Introduce coherence parameter R K3π which dilutes interference term sensitive to γ R K3π ranges from 1=coherent (dominated by a single mode) to 0=incoherent (several significant components) Can slice and dice phase space to find most coherent regions

6. 8th December 2007 CLEO physics fest 6 Measurements of the rate of K3 π versus different tags at CLEO-c allows direct access to R K3π and δ K3π 1. Normalisation from CF K − π + π + π − vs. K + π − π − π + and K − π + π + π − vs. K + π − 2. CP eigenstates: 3. K − π + π + π − vs. K − π + π + π − : 4. K − π + π + π − vs. K − π + : Determining the coherence factor

7. 8th December 2007 CLEO physics fest 7 Jingoistic selection Analyzed data sets 31-33, 35-37 and 43-45  ~700 pb -1 Standard selection based on ΔE and m bc  K s veto to remove dominant    s      and        s peaking background  ‘Flat’ background from sidebands  Peaking from generic MC  Efficiencies from dedicated signal MC  Details in Andrew’s Sept. PTA talk A B D D C S All Truth-matched

8. 8th December 2007 CLEO physics fest 8 Yields and efficiencies Mode Vs K - 3  SComb. Bkg Peaking bkg YieldEfficiency    (Opp Sign) 334075.9 ± 6.910.83253 ± 58(20.4±0.1)%    (Same Sign) 281.8 ± 1.13.023.2 ± 5.2(20.4±0.1)% KK 4416.8 ± 1.64.4430 ± 21(24.1±0.7)%  1993.5 ± 1.41.7194 ± 14(32.1±1.3)% Ks0Ks0 5975.5 ± 1.84.2587 ± 24 (12.4±0.7)% (includes π 0 eff corr)    (Opp Sign) 433025.3 ± 3.913.04292 ± 66(28.9±0.1)%    (Same Sign) 320 ± 01.730.3 ± 5.7(28.9±0.1)%

9. 8th December 2007 CLEO physics fest 9 Coherence factor extraction To extract coherence factor and strong phase from these double-tag yields requires branching fractions  All BF from PDG’07 except K s  0  K s  0 from recent CLEO-c pub arXiv:0711.1463v1 [hep-ex]   efficiency systematic uncertainties cancels  Systematic uncertainties dominated by knowledge of branching fractions except for K + π − where the  K   assumption dominates

10. 8th December 2007 CLEO physics fest 10 Coherence factor: preliminary results Tag mode R K3π cos  K3π ±σ stat ±σ syst Weight in average KK −1.01±0.51±0.450.15  −0.53±0.70±0.420.09 Ks0Ks0 −0.70±0.36±0.500.26  −0.06±0.16±0.310.50 Combination−0.41±0.14±0.20 χ 2 /ndf=1.1

11. 8th December 2007 CLEO physics fest 11 Coherence factor: preliminary results  K3π R K3π 1 σ bounds Will benefit from more modes First selection results today with additional K S modes For the future K L modes R K3π cos  K3π Allowed K3π likesign Preliminary

12. 8th December 2007 CLEO physics fest 12 Additional CP tags Looked into 5 other CP tags:  K S  (  +  -  0 )  K S  0  0  K S  (K + K - )  K S  ’(      )  K S  (  ) and K S  (  +  -  0 ) Mass fit applied to  →  +  −  0 and  ’ →      Backgrounds as for earlier modes Signal efficiencies not calculated yet for all modes

13. 8th December 2007 CLEO physics fest 13 KS(+-0)KS(+-0) DATA MC

14. 8th December 2007 CLEO physics fest 14 K S  (  ) DATA MC

15. 8th December 2007 CLEO physics fest 15 New CP tags Mode Vs K - 3  SComb. Bkg Peaking bkgYieldEfficiency SS 2152.3 ± 1.37.1206 ± 15? S00S00 23812.2 ± 3.13.8222 ± 15 ? KSKS 5000.649 ± 76.1%  S  2500.624 ± 5?  S  γγ) 1143.4 ± 1.24.5106 ±11?  S  +  −  0 ) 351.0± 0.7034 ± 6? 50% increase in the number of CP tags

16. 8th December 2007 CLEO physics fest 16 Kππ 0 selection Another ADS mode but multiple intermediate states so need to calculate coherence factor Generated, reconstructed and D-skimmed samples of 50k Kππ 0 vs {Kππ 0, Kπ,ππ,KK, K S π 0 } Determine efficiencies for these channels:  ΔE selection 3σ with single tag resolutions taken from DTag CBX  Require π 0 daughters satisfy standard ECAL shower shape cuts for single photons

17. 8th December 2007 CLEO physics fest 17 Efficiencies and expected yields TagMC EfficiencyExpected yields from 800 pb -1 Kππ 0 (13.1±0.2)%4.4k KπKπ (23.2±0.2)%7k KK (20.6±0.2)%800 ππ (25.4±0.2)%300 KSπ0KSπ0 (10.6±0.1)%900 Efficiencies are a couple of % higher than in Dhad BF analysis – no corrections

18. 8th December 2007 CLEO physics fest 18 Conclusion and plans Analyzed majority of the ψ  data and evaluated coherence factor and strong phase difference  50% more CP tags to be added  K L X to be added Kππ 0 coherence started  Predicted yields indicate slightly better sensitivity than K3 π  Add other modes already studied for K3 π Aim to publish first measurements of these parameters globally (no division of phase space to find the coherent regions) asap  CBX and request committee early in ’08  Full data-set Later longer paper with binned analysis and K S ππ tags (Nov PTA)  Binned analysis will be guided by full amplitude analysis (next talk) Other modes of interest for γ measurements  D→K 0 S K + K − and D→K 0 S K + π −  D→K − K + π + π − and D→K 0 S π − π + π 0