1. Measurements of  at LHCb Mitesh Patel (CERN) (on behalf of the LHCb Collaboration) 14th December 2006

2. Mitesh Patel, CKM 062 Introduction LHCb will use a number of methods to measure  : –“ADS + GLW” B ± →D 0 (K ,KK,  )K ± B 0 →D 0 (K ,KK,  )K *0 –“Dalitz” B ± →D 0 (K S ,K S KK)K ± B 0 →D 0 (K S ,K S KK)K ± –Four body “Dalitz” B ± →D(K  KK  )K ± –B s →D s K –B→hh [Jacopo Nardulli, WG4, Friday, PM-1] Will present : –Expected sensitivity as a function of the relevant parameters –Signal selection/background estimate taking B ± →D 0 (K  )K ± as an example

3. 14th December 2006Mitesh Patel, CKM 063 B - can decay into both D 0 and D 0, diagrams very different amplitudes colour favoured colour suppressed Decays of D 0, D 0 to same final state gives access to interference (doubly) cabibbo suppressedcabibbo favoured For ‘suppressed’ B - →(K +  - ) D K - (+ c.c.) decays : reversed suppression of D decays cf. B decays → ~ equal amplitudes → big interference effects Counting experiment – no need for flavour tagging or  determination [For ‘favoured’ B - →(K -  + ) D K - (+ c.c.) : higher rates, but smaller B ± asymmetry] B ± →DK ± Decays – ADS Method bu s D0D0 u c u s D0D0 b c u uu B-B- B-B- K+ u D0D0 c d s uu -- D0D0 -- d u u s u K+K+ c K-K- K-K-

4. 14th December 2006Mitesh Patel, CKM 064 Interference parameters Interference depends on a number of parameters : –From the B decays :  – because have b→u, b→c interference r B – the ratio in magnitude of two diagrams (≤0.1 for D 0 K ± ) δ B – a CP conserving strong phase difference –From the D decays : r D K  – the ratio in magnitude of two diagrams (0.060) δ D K  – a CP conserving strong phase difference Have 4 B ± →D(K  )K ± rates we can measure : –Two rates are favoured, (1) and (3) –Two rates are suppressed, (2) and (4) but these suppressed rates have order 1 interference effects as r B ~ r D (1)(1) (2)(2) (3)(3) (4)(4) [+CP eigenstates → GLW Method] [+another D decay → ADS Method]

5. 14th December 2006Mitesh Patel, CKM 065 D 0 →K  : 3 observables from the relative rates of the 4 processes depends on the 4 unknowns: , r B,  B,  D K  –r D K  is already well measured –CLEO-c constraining cos(  D K  ) → Need an additional D 0 decay channel to solve for all unknowns D 0 →K  : provides an additional 3 observables which depend only on one additional unknown:  D K3   (r D K3  also well measured) –At present have ignored resonant structure in D 0 →K  and just used rate for illustration, exploitation of sub-structure is under investigation The CP eigenstate decays D 0 →KK/  provide one more observable with no new unknowns: Use the modes D 0 →K , K3 , KK,  together to give best sensitivity B ± →DK ± Strategy : ADS+GLW

6. 14th December 2006Mitesh Patel, CKM 066 Experimental Situation B-factories have not yet observed the suppressed modes Dalitz analyses give r B ~0.2 (BELLE) and r B ~0.1 (BABAR) → Suggest suppressed modes should soon be observed We take r B =0.08 (UTFIT), δ B = 130 o (average B-factory results), r D K  =r D K3  =0.06 (PDG), -25<  D K  <25 o, -180<  D K3  <180 o UTFIT best fit : r B = 0.08 ± 0.03

7. 14th December 2006Mitesh Patel, CKM 067 2fb -1 in 10 7 sec → equivalent to 10 12 bb, 0.4 of which expected to be B ± In both sign combinations signal yields then : 10 12 bb × 0.4 × 2 ×  TOT × BR Our total efficiency,  TOT, and resulting sensitivity depend entirely on our ability to control the background – in very different environment to the B factories Full simulation indicates that acceptance × trigger efficiency × selection efficiency gives  TOT = 0.5% (more in a moment) : –Favoured B ± →D 0 (K  )K ± → ~56,000 events/2fb -1 –Suppressed B ± →D 0 (K  )K ± → ~700 events/2fb -1 Favoured: BR = 1.4×10 -5 Suppressed: BR = 1.8×10 -7 What can LHCb add... ?

8. 14th December 2006Mitesh Patel, CKM 068 Full MC Performance LHCb uses full MC simulation to estimate the signal selection efficiency and the background : –PYTHIA - generation of p-p collisions at √s = 14TeV –GEANT - full detector response/spill-over and tracking through material –on/offline pattern recognition, full trigger chain, selections Signal selection efficiency  TOT ( B ± →D 0 (K  )K ± )=0.5%: 8.2% (geom.) × 87.8% (rec.) × 28.4% (seln.) × 25.0% (trig.) Mass resolutions –B ± ~15 MeV –D 0 ~6.5 MeV 100 cm Interaction region  sensor R sensor Si Sensors RF foils B ± mass /MeV Vertex resolutions –Primary vertex  z ~ 50  m –B decay vertex  z ~ 200  m

9. 14th December 2006Mitesh Patel, CKM 069 From a large sample of minimum bias events find that no events are selected To study background in more detail, focus on bb events where one b decays in 400 mrad – after the application of the trigger most likely source of background Background sample 20 million bb events generated with above condition ( → factor 0.434, sample equivalent to ~46M bb events) Still equivalent to only a few minutes of LHCb running ! Estimating the Background

10. 14th December 2006Mitesh Patel, CKM 0610 Background Studies Favoured Modes –Background from D 0  decays dominates Use RICH PID to separate D 0  and D 0 K Use dedicated sample of D 0  to estimate B/S → Expect ~17k bkgrd events /2fb -1 from D 0  –Use bb sample to assess combinatorial bkgrd → Expect ~0.7k bkgrd events /2fb -1 → ~28k B+ signal events/2fb -1 B/S~0.6 → ~28k B- signal events/2fb -1 B/S~0.6 Suppressed Modes –bb sample → combinatorial bkgrd dominates → Expect ~0.7k bkgrd events /2fb -1 → ~530 B+ signal events/2fb -1 B/S~1.5 → ~180 B- signal events/2fb -1 B/S~4.3  (K  p ) = 93%  (  K  p ) = 4.7% B ± mass /MeV Momentum / GeV Efficiency / % MC B ± →D 0 (K  )  ± events 687 / 580k pass all cuts except B mass 387 / 580k inside 3  B mass cut

11. 14th December 2006Mitesh Patel, CKM 0611 LHCb Sensitivity  D K ,  D K3   D K ,  D K3  w/o bkgrd Estimated bkgrd Toy MC used to generate 2fb -1 data (*) Combine K  with : –K3  – similar yields and identical background level as K  –KK and  : 4300 B +, 3350 B - decays with B/S ~ 2 →   =5–15 o with 2fb -1 data (Non-Gaussian distribution of fit results highlighted …)  = 60º, r B =0.08,  B = 130º, r D K  =r D K3  =0.06, - 25º<δ D K  < 25º and -180º< δ D K3  <180º [degrees]

12. 14th December 2006Mitesh Patel, CKM 0612 LHCb Sensitivity  D K ,  D K3   D K ,  D K3  w/o bkgrd Estimated bkgrd Toy MC used to generate 2fb -1 data (*) Combine K  with : –K3  – similar yields and identical background level as K  –KK and  : 4300 B +, 3350 B - decays with B/S ~ 2 →   =5–15 o with 2fb -1 data (Non-Gaussian distribution of fit results highlighted …)  = 60º, r B =0.08,  B = 130º, r D K  =r D K3  =0.06, - 25º<δ D K  < 25º and -180º< δ D K3  <180º [degrees]

13. 14th December 2006Mitesh Patel, CKM 0613 LHCb Sensitivity  D K ,  D K3   D K ,  D K3  w/o bkgrd Estimated bkgrd Toy MC used to generate 2fb -1 data (*) Combine K  with : –K3  – similar yields and identical background level as K  –KK and  : 4300 B +, 3350 B - decays with B/S ~ 2 →   =5–15 o with 2fb -1 data (Non-Gaussian distribution of fit results highlighted …)  = 60º, r B =0.08,  B = 130º, r D K  =r D K3  =0.06, - 25º<δ D K  < 25º and -180º< δ D K3  <180º [degrees]

14. 14th December 2006Mitesh Patel, CKM 0614 D 0 K mass / MeV B ± → D*(D 0  0 )K ± B ± → D*(D 0  )K ± B ± →D*K ± Decays BB incl sample B ± → D*(D 0  )K ± B ± Mass /MeV Signal/bkgrd arbitary normaln One entry from BB sample corresponds to 5k bkgrd evts/ 2fb -1 B → D*K has attractive feature : –D*→D 0  0 – has CP cons. phase δ B –D*→D 0  – CP cons. phase δ B +  Potentially very powerful : –Adding D* decays (w/o bkgrd) to prev. study:   =5-15 o →   =2-5 o –No phases with non-Gaussian fit results However, reconstruction efficiency for soft  is small → large B/S Ignore neutrals and fit DK mass shape ? –Fav. modes – yields 17k (  0 ) and 9k (  ) / 2fb -1 –Sup. modes – yields similar to D 0 K case - but bkgrd problematic → investigating use of event topology to reconstruct  0,  momentum

15. 14th December 2006Mitesh Patel, CKM 0615 B 0 →DK *0 Decays For B 0 →DK *0 decay r B ~ 0.4 (both diagrams colour suppressed) Treat with the same (“ADS+GLW”) method, so far have used K , KK,  modes Removes  bias from DCS decays seen using traditional ‘ GLW ’ approach →   =7-10 o with 2fb -1 data (taking r B =0.4, -180<  B <180 o, -180<  D K  <180 o ) Mode Yield / 2fb -1 B/S favoured B 0  (K +  - ) D K* 0 + c.c. 3400< 0.3 suppressed B 0  (K -  + ) D K* 0 + c.c. 500< 1.7 B 0  (K + K - /  +  - ) D K* 0 + c.c. 600< 1.4

16. 14th December 2006Mitesh Patel, CKM 0616 B ± →D(K S     )K ± Decays – Dalitz Three body decay D 0 →K s  +  - fully parameterized with parameters m + 2 =m 2 (K s  + ) and m - 2 =m 2 (K s  - ) Use pre-determined model to describe D 0 decay amplitudes as a function of (m + 2, m - 2 ) Total B decay amplitude is sum of contributions via D 0 and D 0 : Interference has sensitivity to  N: number of resonances a j,  j : amplitude and phase parameters from B factories A j : model-dependent parameterization of matrix element  (m - 2,m + 2 ) = |f(m - 2, m + 2 )| 2 + r B 2 |f(m + 2,m - 2 )| 2 + 2 r B Re [ f(m - 2,m + 2 )f*(m + 2,m - 2 ) e i   ) ]

17. 14th December 2006Mitesh Patel, CKM 0617 B ± →D(K S     )K ± – Sensitivity Signal selection gives : –5k events/2fb -1 assuming “good” K S efficiency ( * ) –Combinatorial bkgrd B/S < 0.7 @ 95% C.L. –D(K S  )  bkgrd B/S = 0.2±0.1 → 0.2<B/S<1.0 @ 90% C.L. Model parameters from B and charm factories With r B = 0.08,  (  ) ~ 8º (signal only and w/o acceptance effect in fit) + model uncertainty Similar method will be used for D 0 →K S K + K - decays: reduced BR but less bkgrd (PID from RICH) B 0 →D(K S  +  - )K* 0 decays also under investigation ( * ) Assuming all K S found offline can be reconstructed online  (770) K * and DCS K * LHCb generator studies D 0 /D 0 m + 2( GeV 2 /c 4 ) m - 2 (GeV 2 /c 4 )

18. 14th December 2006Mitesh Patel, CKM 0618 Four-body “Dalitz” Analyses Idea for 3-body D 0 decays can be extended to 4-body D 0 decays Five parameters are then needed to describe the decays Two modes are presently being investigated: –B ± →D(KK  )K ± For  =60º,  B =130º, r B =0.08, expect 1.7k events/2fb -1 B/S=0.9±0.4 (Combinatorial, D 0  ) →  (  ) ~ 15º (signal only) [hep-ph/0611272] –B ± →D(K  )K ± (as used in ADS+GLW analysis) Take into account strong phase dependence across “Dalitz” space Sensitivity under study

19. 14th December 2006Mitesh Patel, CKM 0619 B s →D s K Decays Interference between tree level decays via B s mixing Measures  s (  s from B s  J/   decays) Main background from D s  : –Factor 10 higher branching ratio –Suppressed using kaon id from RICH detectors –B/S < 1 @ 90% CL Expect 5.4k signal events/ 2fb -1 Excellent proper-time resolution (   ~40 fs) allows to resolve B s oscillations →  (  ) ~ 13  from 2fb -1 data [  m s = 17.3 ps –1 ] Parallel analysis possible with B d →D Ŧ  ± (~790k events/2fb -1 with B/S ~ 0.3,  extraction requires r D  or combined B s → D s K U-spin analysis)

20. 14th December 2006Mitesh Patel, CKM 0620 Summary of Performance Combining all modes, with a nominal year of data (~2 fb -1 ), LHCb will be able to extract  from combined analysis B→DK with the ~5º precision required to match the indirect determination Comparison of  from B→DK and indirect determination will become a stringent test of the SM B modeD mode ()() B + →DK + K  + KK/  + K3  5º - 15º B + →D*K + KK Under study B + →DK + K s  8º8º B + →DK + KK  15º B + →DK + K  Under study B 0 →DK *0 K  + KK +  7º - 10º B 0 →DK *0 K s  Under study Bs→DsKBs→DsK KK  13º Signal only, no accep. effect

21. 14th December 2006Mitesh Patel, CKM 0621 Use three body Cabibbo allowed decays of the D 0 /D 0 BR(D 0  K 0 π + π - )=(5.97±0.35)% Large strong phases between the intermediate resonances allow the extraction of r B,  and  by studying the Dalitz distribution of events Measuring  : B +  D 0 (K 0 π + π - )K + where Giri, Grossman, Soffer, Zupan (PRD 68, 054018 (2003))  (770) K * and DCS K * LHCb generator studies D 0 /D 0 m + 2( GeV 2 /c 4 ) m - 2 (GeV 2 /c 4 )