1. LHCb Strategies for  from B→DK Yuehong Xie University of Edinburgh for the LHCb Collaboration ADS with B + →DK + and B 0 → DK* 0 Dalitz with B + →DK + and B 0 → DK *0

2. Beauty 2006, Oxford UKYuehong Xie2 Physics Aim  It is generally assumed tree processes are dominated by SM contributions  Disagreement between the tree-determined triangle (|V ub | +  from B→DK) and the loop- determined triangle (  K,  m d,  m s, sin2  … ) indicates new physics.  They are consistent within current measurement precision.  Have big uncertainty in  used for tree fit. Improvement needed!  Require sensitivity of  from tree ~ 5º to match the precision of indirect determination  LHCb:  from B s →D s K is clean and unaffected by new physics, but has sensitivity of 14º with 2 fb -1 of data. We will see B→DK is more promising for LHCb. Loop fit Tree fit  (tree)

3. Beauty 2006, Oxford UKYuehong Xie3 LHCb detector Tracking: Vertex Locator TT T1-T3 Magnet PID: RICH1/RICH2 SPD/PS ECAL HCAL M1-M5 Tracking efficiency 94% for physics tracks with p>10GeV Detector status: Talk by Lluis Garrido Trigger: Talk by Eduardo Rodrigues RICH PID performance 2<p<100 GeV = 93% = 4.7%

4. Beauty 2006, Oxford UKYuehong Xie4 Data simulation  LHCb will start data-taking in 2007.  Full Pythia+Geant4 simulations are used for trigger, reconstruction and event selection studies.  Used event samples include  260m minimum bias events for trigger study,  140m Inclusive bb events for background study,  Dedicated signal events.  Sensitivities are obtained using fast simulations according to efficiencies, resolutions and background level from full simulations.

5. Beauty 2006, Oxford UKYuehong Xie5 Event selection criteria  Hadron particle identification using RICH  Composite particle invariant masses (B, D, K *, K s )  Impact parameters and transverse momentum of B and decay products  Vertex  2 of B, D, K *, K s  Angle between B momentum and flight direction  Event topology Cuts are optimized to reject most background events from a large inclusive bb sample and retain high signal efficiencies. Final B/S ratios are assessed based on a separate bb sample.

6. Beauty 2006, Oxford UKYuehong Xie6 b dbar c ubar s dbar D0D0 b u cbar s dbar D0D0 ubar b c s D0D0 b u cbar s ubar D0D0 B  decays (r B  0.1) B 0 decays (both diagrams colour suppressed → r B  0.4) B→DK decays  Three parameters for CKM favoured B→DK and disfavoured B→DK weak phase difference  = Arg(-(V ub V * cs )/(V cb V * us )) strong phase difference  B and amplitude ratio r B = |A(B→DK )|/|A(B→DK )|  Interference allows to extract , if same D 0 and D 0 final states

7. Beauty 2006, Oxford UKYuehong Xie7 ADS: use Interference  Consider a final state common to D 0 and D 0, e.g. K   Define  There are four possible charged B decays DCS favoured (1)(1) (2)(2) (3)(3) (4)(4) Interference ~ O(1) for suppressed (2) and (4)

8. Beauty 2006, Oxford UKYuehong Xie8 ADS tailored for LHCb  D 0 →K  : 3 observables from the relative rates of the 4 processes depends on 4 unknowns , r B,  B,  D K  r D K  is already well measured may benefit from cos(  D ) measurements in CLEO-c and/or BES III Need another D 0 decay channel to solve for all unknowns  4-body decay D 0 →K  provides 3 observables which depends on 4 unknowns , r B,  B,  D K  – only  D K  new (4-body Dalitz, p.17)  Each CP mode D0→KK/  provides one more observables with no new unknowns The ADS method constrains  only if we can see suppressed decays! Good opportunity for LHCb.

9. Beauty 2006, Oxford UKYuehong Xie9 Example: B + →(K  ) D K +, r B =0.077 Favoured modes –Background from D 0  decays dominates (BR ~13 × D 0 K) Use RICH information to separate D 0 K and D 0  Use dedicated sample of D 0  decays → Expect ~17k bkgrd events/year from D 0  –Use bb sample to assess combinatorial background → Expect ~0.7k bkgrd events/year Suppressed modes –bb sample indicates that the combinatorial contribution dominates : → Expect ~0.7k background events/year –D0  : 17k *R D  BELLE ~ 60 events/year  (K  ) = 93%  (  K  ) = 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 ~530/year B + → (K -  + ) D K + B/S ~ 1.5 ~180/year B - → (K +  - ) D K - B/S ~ 4.3 (depending on r B ) ~28k/year B + → (K +  - ) D K + B/S ~ 0.6 ~28k/year B - → (K -  + ) D K - B/S ~ 0.6

10. Beauty 2006, Oxford UKYuehong Xie10 Performance with B + →DK +  Take  = 60º, r B = 0.077  B = 130º  r D K  = r D K3  = 0.06 -25º< δ D K  < 25º and -180º< δ D K3p <180º  Combine K  with K3  similar yields and background level as K  KK and  modes  (  ) ~ 5º -15º in a year, depending on r B, δ D K  and δ D K3  δ D K , δ D K3  w/o bkgrd estimated bkgrd (Highlighted are RMS quoted for non- Gaussian distribution of fit results due to close ambiguous solutions, will disappear as statistics increase. Global analysis using all modes will also help.) ~4.3k B+→ D0(hh)K+ B/S ~ 1 ~3.3k B- → D0(hh)K- B/S ~ 1

11. Beauty 2006, Oxford UKYuehong Xie11 ADS with D*K Attractive feature –D*→D 0  0 (BR~2/3) – has strong phase δ B –D*→D 0   (BR~1/3) – strong phase δ B +  → if can distinguish the two decays → powerful additional constraint ! Potential –Including D*K without background improves precision to  (  ) = 2º - 5º However –Reconstruction efficiency is small for soft  while background is enormous –Non-trivial to separate D 0  0 and D 0  Fit DK mass shape to get   and  components ignoring neutrals –all favoured modes can reach 10k/year or more with B/S ~ O(1) –Suppressed modes still problematic: under study Idea to use the event topology to reconstruct momentum of  0 /  is being investigated Background dominating: 1 bb event here represents 5k/year! D 0 K mass Charged reconstruction B ± → D*(D 0  0 )K ± B ± → D*(D 0  )K ± bb sample

12. Beauty 2006, Oxford UKYuehong Xie12 ADS with B 0 →DK *0  The same method can be applied to B 0 →D 0 K* with D 0 →K  and KK, (historically treated with “GLW” method)  r B ~ 0.4, big interference in CP modes (r D CP =1) Mode Yields S/B favoured B 0  (K -  + ) D K* 0 + c.c. 3400> 3.3 disfavoured B 0  (K +  - ) D K* 0 + c.c. 500> 0.6 B 0  (K + K - /  +  - ) D K* 0 600> 0.7  (  ) ~ 7º-10  in a year (2 fb -1 ) (55  <  < 105 , r B ~0.4, -20  <  B < 20  )

13. Beauty 2006, Oxford UKYuehong Xie13 Dalitz: B + →(K s     ) D K +  Three body decay D 0 →K s      fully parameterized with two 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 ) 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   ) ] Interference has sensitivity to  Total B decay amplitude as sum of contributions via D 0 and D 0

14. Beauty 2006, Oxford UKYuehong Xie14 Comparison to BELLE data Naïve model amplitude Isobar amp. + non-res. Belle data with model fit

15. Beauty 2006, Oxford UKYuehong Xie15 Performance of B + →(K s     ) D K +  5k events/year assuming “good” K s efficiency at HLT, combinatorial B/S < 0.7, D(K s  )  B/S in (0.11, 12) at 95% C.L.  Need large D(K s  )  sample to clarify  Model parameters from B and charm factories   (  ) ~ 8º + model uncertainty, w/o b.g. and detector effect in fit  Two-fold ambiguity ( ,  B ), (  - ,  B -  ) Current K s problem in HLT: Only 25% of K s decay inside active region of VELO, giving 1.5k events/year. Online reconstruction of the pion tracks from other K s requires special treatment and is challenging due to HLT time limit. Great efforts are being made to speed up the online reconstruction of no-VELO tracks. Depending on how this will be accomplished, annual yield can vary between 1.5k - 5k, leading to  (  )~8º-16º for r B = 0.077. m+m+ m-m- LHCb generator studies  (770) K * and DCS K * for r B = 0.077 Statistical precision depends on r B, e.g.,  (  )~4º for r B =0.15

16. Beauty 2006, Oxford UKYuehong Xie16 Acceptance studies Selection tuned to maximise signal-to-background ratio Flat phase space MC generated Overall acceptance not flat as a result of trigger and offline selection Acceptance evaluation with isobar model in progress – as expected similar acceptance function is indicated. Can be checked with B→D  data. m-m- m-m- m+m+ m+m+ % %

17. Beauty 2006, Oxford UKYuehong Xie17 Dalitz: B +  (K s K + K - ) D K + Same method works for D 0  K s K + K - decay – BR reduced by factor of 6 BR(D 0  K 0 K + K - ) =(1.03±0.10)% – But less background because of two more particle identification constraints from RICH Dalitz model has fewer resonances ( , a 0 ) but complex threshold effects (Babar hep-ex/0507026) Work on event selection and sensitivity ongoing

18. Beauty 2006, Oxford UKYuehong Xie18 “Dalitz”: four-body D decay  ~ 1.5k events in a year  Preliminary number  (  ) ~ 15º w/o b.g. and detector effect B + →(  KK) D K + B + →(  K) D K +  The same channel as used in ADS, but to take into account strong phase dependence on Dalitz space  r B ~r D big interference  Sensitivity under study The idea for 3-body D 0 decays can be extended to 4-body D 0 decays. Need 5 parameters to describe D 0 decays: not really a Dalitz plot. for  =60º,  B =130º, r B =0.08

19. Beauty 2006, Oxford UKYuehong Xie19 Dalitz: B 0  (K S  +  - ) D K* 0  Branching ratio reduced by factor 10 compared with B + mode  Same method as in B +  Annual yield < 600 events  Big interference (r B ~0.4)  Will complement the “GLW” modes D 0 →K , KK and   Also suffers  K S HLT problem PDG ‘04

20. Beauty 2006, Oxford UKYuehong Xie20 Summary of performances: 2 fb -1 B modeD mode ()() B + → DK + K  + KK/  + K3  5º - 15º B + → DK + K s  8º ~ 16º B + → DK + KK  ~ 15º B 0 → DK *0 K  + KK 7º - 10º B 0 → DK *0 K s  Under study More modes are being investigated. Combined precision should not be far away from 5º no b.g., detector effect

21. Beauty 2006, Oxford UKYuehong Xie21 Sources of systematics Dalitz model dependence  Improve D decay model by work of B and Charm factories (LHCb for 4-body) Other contributions to K * region in B→DK *  To be studied Dalitz acceptance not flat  Currently obtained using Mont Carlo simulation, should be calibrated with data Production asymmetry and detection charge asymmetry to be studied D 0 -D 0 mixing and CP violation  CP-conserving D 0 mixing is a very small effect and can be neglected  New physics with big CP violation in D 0 mixing may change the value of  extracted from B→DK. Not really a systematic error but a new physics effect.  D 0 mixing and CP violation can be probed in LHCb. See Raluca Muresan’s talk Friday. As we approach statistical error of 10º, understanding and controlling systematical uncertainty becomes more and more important for LHCb  = 92º ± 41º ± 11º ± 12º (Babar)  = 58º ± 18º ± 3º ± 9º (Belle)

22. Beauty 2006, Oxford UKYuehong Xie22 Conclusions  LHCb will be able to extract  from B→DK to the required 5º precision to match the indirect determination with ~2 fb -1  Comparison of  from B→DK and indirect determination will become a stringent test of the SM  Together with improvement on |V ub | the measured  from B→DK will enable to construct a reference Unitarity Triangle needed for new physics search  A lot of work to do before data-taking

23. Beauty 2006, Oxford UKYuehong Xie23 Offline track finding strategy VELO seeds Long track (forward) Long track (matched) T seeds Upstream track Downstream track T track VELO track Long tracks  highest quality for physics Downstream tracks  needed for efficient K S finding Upstream tracks  lower p, worse p resolution, useful for RICH1 pattern recognition Multiple pass track finding: T seeds Velo seeds

24. Beauty 2006, Oxford UKYuehong Xie24 CKM global fit