Sensitivity to g with B ® D(KK pp )K Decays

1. Sensitivity tog with B ®D(KKpp)KDecays • Introduction • B ® DKDalitz Analysis • Summary of Selection & Bkg Results • Model • Signal Acceptance Across Phase Space • Background Distributions in Phase Space • Simulation • Overview • Results Jim Libby, Andrew Powell, Jonas Rademacker, Guy Wilkinson CP Working Group Meeting - Thursday, 19th April 2007

2. Introduction Four-Body Dalitz [Phys. Lett. B 647 (2007) 400] • Extension to conventional three-body technique • Jonas and Guy’s initial sensitivity study performed with NO background ~or detector effects incorporated • Assuming signal sample of 1,000 events, rB = 0.1, Following results of the B ®D(KKpp)K DC04 selection and background study (CP WG meeting – 14th December) , we now perform an LHCb specific sensitivity study Selection Results [LHCb 2007-004 PHYS] Background per 2fb-1 Signal Yield per 2fb-1 Reflections 400 ± 136 Partially Reco. 262 ± 185 Combinatoric 840 ± 593 S = 1,700 events BTot 1,500 ± 640

3. Selection Efficiency Across Phase Space Question: Do we need to incorporate an acceptance function into our study? Example plots: s24 • Compare the distributions formed in the ~10 kinematic projections (sij, sijk) of: • Original MC generator level events • Corresponding reconstructed offline events 100k MC events (uniform in phase space) 2,012 offline reconstructed events • Two tests of similarity: • ratio of distributions (bottom plot) • Kolmogorov-Smirnov (K-S) test Ratio plots, given the limited reco. statistics, suggests a flat acceptance K-S testconfirms this, returning probabilities of between 0.9 – 0.7 that the reco. distribution is a subset of the MC truth distribution Answer: No.

4. Background Description in Phase Space I To do this, we first classify the background into the following 3 categories: • Reflection Event: • Combinatoric Event: • Combinatoric Event: 1. Reflection EventB ® Dp • Dangerous! 10xBR(B ® DK) • Controlled with RICH PID: B/S = 0.24 • The interference between these paths is ~greatly suppressed due to the additional ~CKM suppression (DCS) • Effective suppression , thus, ~ignore interference (no CPV) and only ~consider favoured modes Therefore, PDFs for this background:

5. Background Description in Phase Space II 2. Combinatoric Kaon: • Genuine D meson, generally from a D* cascade decay, combined with a ~combinatoric K meson (either true or fake) • Equal probability of either a K- or K+ being wrongly associated with the ~D0/D0 • Incorporate with B/S = 0.32 3. Combinatoric D • Naively expect this background to ~occupy phase space un-biasedly • Need to check explicitly • Appears to be the case: • Model, therefore, with a flat PDF in ~phase space • Incorporate with B/S = 0.32

6. Fit Likelihood Function • Simultaneous likelihood fit to B- and B+ with the following overall PDF: • Fit fractions: fDp, ffakeK, fPS • Fixed in fit (not free parameters) • Justified, since these values will ~be known from sideband studies ~and a Dp control sample • Use RooFit based framework written by Jonas Rademaker to generate and ~fit toy experiments • Each toy experiment generates 1,700 signal events with appropriate ~quantities of background • Input values: g = 60°, dB = 130°, rB = 0.10 • Several studies performed: • Individual backgrounds incorporated separately at nominal levels • All backgrounds incorporated at nominal, (2 x nominal) and ~(½ x nominal) levels w.r.t signal

7. Results

8. Considering Backgrounds Separately • Generate 100 toy experiments for each background configuration Example:Accumulated plots for fits incorporating just Dp background

9. Considering Backgrounds Together Nominal Background (S/B =1.1) B- B+ B+ B-

10. Considering Backgrounds Together • 300 toy experiments with ALL backgrounds included at ‘nominal’ levels Example:Accumulated plots for fits to g

11. Considering Backgrounds Together 2 x Nominal Background (S/B =0.57) B- B+ B+ B-

12. Considering Backgrounds Together • 100 experiments with ALL backgrounds included at ‘2 x nominal’ levels Example:Accumulated plots for fits to g

13. Considering Backgrounds Together ½ x Nominal Background (S/B =2.27) B- B+ B+ B-

14. Considering Backgrounds Together • 100 experiments with ALL backgrounds included at ‘½ x nominal’ levels Example:Accumulated plots for fits to g

15. Summary • The sensitivity to g using B ® D(KKpp)K decays with a four-body ~Dalitz amplitude analysis at LHCb has been studied • Various configurations of the background about its estimated nominal ~contribution have been simulated within 2fb-1 data sets: • A public note fully documenting this sensitivity study is in preparation