1/15 Sensitivity to  with B  D(KK  )K Decays CP Working Group Meeting - Thursday, 19 th April 2007 Introduction B  DK  Dalitz 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

2/15 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, r B = 0.1, Following results of the B  D(KK  )K DC04 selection and background study (CP WG meeting – 14 th December), we now perform an LHCb specific sensitivity study Selection Results [LHCb PHYS] S = 1,700 events Signal Yield per 2fb -1 Reflections Reflections 400 ± 136 Partially Reco. Partially Reco. 262 ± 185 Combinatoric Combinatoric 840 ± 593 1,500 ± 640 B Tot Background per 2fb -1

3/15 Selection Efficiency Across Phase Space Question: Do we need to incorporate an acceptance function into our study? Compare the distributions formed in the ~10 kinematic projections (s ij, s ijk ) 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 test confirms this, returning probabilities of between 0.9 – 0.7 that the reco. distribution is a subset of the MC truth distribution Example plots: s 24 Answer: No.

4/15 Background Description in Phase Space I To do this, we first classify the background into the following 3 categories: 1.Reflection Event: 2.Combinatoric Event: 3.Combinatoric Event: 1. Reflection Event B  D  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:

5/15 Background Description in Phase Space II 3. Combinatoric D 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 ~D 0 /D 0 2. Combinatoric Kaon: 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

6/15 Fit Likelihood Function Simultaneous likelihood fit to B - and B + with the following overall PDF: Fit fractions: f D , f fakeK, f PS Fixed in fit (not free parameters) Justified, since these values will ~be known from sideband studies ~and a D  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:  = 60°,  B = 130°, r B = 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

7/15 Results

8/15 Considering Backgrounds Separately Example: Accumulated plots for fits incorporating just D  background Generate 100 toy experiments for each background configuration

9/15 Considering Backgrounds Together Nominal Background (S/B =1.1) B-B- B-B- B+B+ B+B+

10/15 Example: Accumulated plots for fits to  300 toy experiments with ALL backgrounds included at ‘nominal’ levels Considering Backgrounds Together

11/15 Considering Backgrounds Together 2 x Nominal Background (S/B =0.57) B-B- B-B- B+B+ B+B+

12/15 Considering Backgrounds Together 100 experiments with ALL backgrounds included at ‘2 x nominal’ levels Example: Accumulated plots for fits to 

13/15 Considering Backgrounds Together ½ x Nominal Background (S/B =2.27) B-B- B-B- B+B+ B+B+

14/15 Considering Backgrounds Together 100 experiments with ALL backgrounds included at ‘ ½ x nominal’ levels Example: Accumulated plots for fits to 

15/15 Summary The sensitivity to  using B  D(KK  )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