Determining the Coherence Factor, R, of D ® K3 p Decays

1. Determining the Coherence Factor, R, of D ®K3pDecays • Motivation Reminder • B ® DK: Access to CKM g • Use of DCS D0 Decays: ‘ADS’ Approach • Coherence Factor, R • Status with Preliminary Measurements • Reconstruction Efficiencies • Background Estimations (Data and MC) • Sensitivities: Present Status and Prospects Andrew Powell (University of Oxford) On behalf of the UK group D-Hadronic PTA, CLEO-c Collaboration Meeting, July 9th 2007

2. gfromB±®DK ± • Extraction through interference between b c and b u transitions ColourSuppressed • Requireandto decay to a common final state,f(D) Common starting point for a variety of methods to extractg

3. ‘ADS’ Strategy: D ® hh Large interference possible if amplitudes of similar magnitude f(D) = non-CP Eigenstate(e.g. K+p-) DCS Decay CF Decay Interference is now large when looking at ‘wrong sign’ decays: (2) & (4) (1) (2) (3) (4) These + other rates (e.g. D®KK, pp) allow unknowns to be fitted.

4. ‘ADS’ Strategy: D ® Multi-Body • Using the same approach, the final state can also be considered. • Neglecting the resonant sub-structure for the 4-body decay would mean rate (2) would look like: where we introduce the additional parameters rDK3p and dDK3p • Considering the resonant sub-structure modifies the above by introducing a dilution term (value: 0-1) called the ‘Coherence’ factor, RK3p. dD then becomes an ‘averaged’ strong phase difference, z : [ Atwood & Soni, Phys Rev D 68 (2003) 033003 ] • The above paper details how one could measure RK3p at a charm factory. We are now making first measurements here at CLEO-c …

5. MeasuringRK3p • To measure RK3p we need to analyse the following double tagged y(3770)data samples and simply count the events observed: • 1) • 2) • 3) • 4) Opposite Sign Kaon CP even CP odd Same Sign Kaon Why These Tags? • Provides normalisation factor • & 3) : 4) : Therefore, can get separate measurements of and

6. Preliminary K3p vs Tags Selection Results

7. MC Reconstruction Efficiencies • Since last time, have followed Alexander Scott’s TQCA CBX note (in preparation)and have applied the following: • Best candidate according to • |DE| cuts and Signal-Box in MBC(K3p) vs MBC(Tag) (MBC(K3p), MBC(Tag)) = (1.86 : 1.87, 1.86 : 1.87) eRec (%) MC Assoc. MC Events |DE| Cut (GeV) Tag Reco Events 5,000 0.0177 1,427 KK 1,379 24.3 pp 0.024 764 739 2,000 32.6 Ksp0 13.8 2,650 2,456 0.048 15,000 Kppp 22.3 0.015 22,324 25,260 100,000

8. Non-Peaking Background In Data As shown last time, Jim Libby has run a selection for these 5 modes over the 281pb-1 data set. Applying the same techniques as quoted in Alexander Scott’s CBX note, Jim has estimated the non-peaking, combinatoric, background from analysing the Mbc sidebands. • Definitions: • S: signal box • A: lower signal Mbc sideband • signal mis-reconstruction • B: lower tag Mbc sideband • tag mis-reconstruction • C: lower mispartition Mbc sideband • particles swapped between D candidates • |Mbc(K3π)−Mbc(Tag)|<3.5 MeV/c2 • D: non DD combinatoric • |Mbc(K3π)−Mbc(Tag)|>5.5 MeV/c2 K3π vs K3π(Opp. Sign) A S C D B D

9. K3π vs K0S π0 K3π vs K3π (likesign) The Other Modes … K3π vs π+π− K3π vs K+K−

10. Counting Signal + Non-Peaking Bkg Assessing the events found for each mode within these defined sideband regions results in the following signal and estimated background numbers: Avoids double counting of combinatoric background In order to determine sources of peaking background, we have looked at the generic DDbar MC…

11. MC Background Studies • As a ‘preliminary’ study, we have run over the 10 x lumi. corresponding to dataset 37 (10 x 111.105pb-1). • All results are consistent with Jim’s estimates, except for a notable peaking background seen in the Ksp0 tag from: • r+(p+p0)p- • p+p-p0 • r0(p+p-)p0 Observed ratios (I : II : III) = (10 : 4 : 1) • This is a consequence of a relatively loose Ksp0 mass window (30 MeV) • Intend to tighten this in future to 10 – 7.5 MeV • An additional peaking background has been observed in the K3p tag: • No Flight-Significance cut is currently applied. Intend to apply this to reject the Ks background. • K*-(Ksp-)K+ • K*0(K-p+)Ks

12. RK3p cos(z ) : Sensitivity Predictions

13. With Current Data Set & Implementation • With the current 281pb-1y(3770)sample and using the set of tags currently being investigated we calculate a statistical uncertainty on the quantity RK3p cos(z )as being: • This corresponds to the shaded region in parameter space (right). • However, this can be improved … sstat= 0.36 Above plot generated using an “Illustrative” value: RK3p cos(z ) = -0.5

14. With Final Data Set & Additional Tags • With a (predicted) 750 pb-1y(3770)sample and using the current set of tags along with additional CP tags (including KL) it is possible to further reduce this uncertainty: • Further improvements possible by considering ‘pseudo-CP’ tags (K0pp) sstat~ 0.15 Above plot generated using an “Illustrative” value: RK3p cos(z ) = -0.5

15. ‘Non-Global’ Determination of RK3p cos(z ) • We expect RK3p to be small when considering events integrated over all the allowable decay phase-space, as we are doing now. (i.e. ‘Global’ measurement). • Given this, we intend to investigate considering only those events in localised regions of decay phase-space (i.e. a binned analysis) where a known resonance is dominant (e.g. K* or r). • Through intelligent binning, one would expect greater coherence and a value of RK3p much closer to 1. This would then have obvious benefits towards use in ADS type measurements at experiments like LHCb. • This is something we intend to perform and most likely conduct in parallel with the ‘global’ measurement of RK3p cos(z ).

16. Summary • Determination of RK3p is invaluable for use as an external constraint in ‘ADS’ type g extraction strategies at LHCb. • Progress is being made with the current 281pb-1 CLEO-c dataset to measure the quantity RK3p cos(z ). • Once further understanding of our backgrounds has been made, a first determination will be possible. • Much improved measurements should be achievable by considering additional CP tags and KL as well as Ks. • A ‘binned’ analysis is also foreseen to be performed. • Not forgetting that the other technique, an amplitude analysis of the four-body final state, will begin in earnest soon.