1. Prospects for  at LHCb Val Gibson (University of Cambridge) On behalf of the LHCb collaboration Physics at the LHC Split, October 3 rd 2008

2. 3/10/08Prospects for gamma at LHCb2/20 Introduction  plays a unique role in flavour physics —Can be measured via both tree and loop processes Trees —Benchmark Standard Model reference point Loops —Sensitive to New Physics Very impressive measurements from the B factories To fully test SM and unitarity need —   ~ few % precision —measurements in B , B 0 and B s systems K.Trabelsi CKM 2008 V.Sordini CKM 2008

3. 3/10/08Prospects for gamma at LHCb3/20 LHCb High statistics —  bb ~ 500  b at 14 TeV — ℒ ~ 2 x 10 32 cm -2 s -1 —10 12 bb per 2 fb -1 (1 year) —All B species (B 0, B s, B c,  b …) Excellent tracking system —VELO and tracking detectors —Mass resolution,  B(D) ~15 (7) MeV —B vertex resolution,  z  ~ 200  m —Proper time resolution,    ~ 40 fs Excellent particle identification —2 RICH detectors —  separation over p ~2  100 GeV Trigger —High p T hadron trigger at L0 VELO First real tracks RICH HPDs

4.  with trees B  DK Strategies Time integrated analyses based on: “ADS”: Atwood, Dunietz, Soni; Phys. Rev. Lett. 78 (1997) 3257; Phys Rev. D63 (2001) 036005. “GLW”: Gronau, London, Wyler; Phys. Lett. B253 (1991) 483; Phys. Lett. B265 (1991)172. “Dalitz” or “GGSZ”: Giri, Grossman, Soffer, Zupan, Phys. Rev. D68 054018 (2003)

5. 3/10/08Prospects for gamma at LHCb5/20 B  DK Strategies Measure  through interference in decays Provided and decay to common final state Common parameters CKM angle  Amplitude ratio, r B Strong phase difference,  B colour-suppressed colour-allowed colour-suppressed

6. 3/10/08Prospects for gamma at LHCb6/20 B   D(hh)K  (ADS+GLW) 6 rates, 5 parameters   r B = 0.10  B = 130 o (PDG) D decay parameters: r  = 0.0616 (PDG)   = -158 o (ADS formalism requires -180 o phase shift w.r.t published result) Constraints from CLEO-c PRL 100(2008) 221801 LHCb-2008-011 LHCb-2008-031 ModeSig. Yield*B/S B +  D   (fav.) 28k0.6 B +  D   (sup.) 6501.2 B +  D(   3k1.2 B +  D(  )K  1k3.6   ( o ) -190-174-158-144-130   ( o ) 12.710.813.812.610.8 ICHEP 2008 Sensitivity 2 fb -1 *All signal yields presented are for 2 fb -1

7. 3/10/08Prospects for gamma at LHCb7/20 B 0  D(hh)K *0 (ADS+GLW) 6 rates, 5 parameters   r B 0 = 0.40  B 0 (scan) D decay parameters: r  = 0.0616 (PDG)   = -158 o (ADS formalism requires -180 o phase shift w.r.t published result) Constraints from CLEO-c PRL 100(2008) 221801 LHCb-2007-050 LHCb-2008-031 ModeSig. YieldB/S B 0  D(   (fav.) 3.4k[0.4,2.0] B 0  D(   (sup.) O(500)[2.0,13.0] B 0  D(   O(500)[0,0.4] B 0  D(   O(100)[0,14.0]  B 0 ( o ) 04590135180   ( o ) 6.210.812.79.55.2 ICHEP 2008 Sensitivity 2 fb -1 68% 95%

8. 3/10/08Prospects for gamma at LHCb8/20 B   D   (ADS) Br(D  K3  ) = 8.1% c.f. Br(D  K  )=3.89% 4 rates Multi-body final state —Integrate over ALL phase space —“Coherence factor” R  r  = 0.0568 (PDG) Constraints ModeSig. YieldB/S B +  D     31k0.7 B +  D     5302.3 LHCb-2007-004 LHCb-2008-031 R K3π  K3π ( o ) Prelim: arXiv:0805.1722 CLEO-c Atwood and Soni, PRD 68 033003(2003) Sensitivity 2 fb -1

9. 3/10/08Prospects for gamma at LHCb9/20 B   D  s       (“Dalitz”)  s     Dalitz plots contain a CP-violating contribution from the B  and B  interference which is sensitive to . Two analysis methods: —Unbinned fit based on amplitude model —Model independent binned fit using results from  (3770) on D decays Giri et. al., PRD 68 (2003) 054018; Bondar and Poluektov, EPJ C47 (2006) 347; hep-ph/0703267;arXiv:0801.0840 LHCb 2 fb -1

10. 3/10/08Prospects for gamma at LHCb10/20 B   D  s       (“Dalitz”) Signal yield ~ 5k (total) per year B   D  s        background suppressed with max. momentum cut (good for RICH pid) Dominant physics background B  D  s      X plus random “  ” ~ 16% prob. of picking up “  ” from underlying event or other B. LHCb-2008-028 Background typeB/S B   D  s       < 0.095 (90% c.l.) B  D*X+K < 0.05 (90% c.l.) DK-signal< 0.09 (90% c.l.) DK-random 0.35  0.03 Loose K pid 2 fb -1

11. 3/10/08Prospects for gamma at LHCb11/20 B   D  s       (“Dalitz”) Amplitude Fit: Generate and fit events assuming isobar model. —Models of BaBar [PRL 95 (2005) 121802] and Belle [hep-ex/0411049] give consistent results. —Total error will include model uncertainty, currently ~ 7 o [BaBar PRD 78 (2008) 034023] Binned Fit: Removes model dependence by relating bins of Dalitz plot to experimental observables —Slight degradation in statistical precision —Residual error on  from CLEO-c statistics ~1-2 o [Asner, ICHEP 08] (o)(o) rBrB (o)(o) Amp. Fit9.80.0189.3 Binned Fit12.80.02012.6 LHCb-2007-048 LHCb-2007-141 Sensitivity 2 fb -1 Amplitude fit, model error 7 o Binned fit, CLEO-c error 2 o Fit assumes pure combinatorial background same level as DK-random

12.  with trees Time Dependent B  Dh  Strategies B s  D s K: Aleskan, Dunietz and Kayser, Z. Phys. C54 (1992) 653. B 0  D  and B s  D s K “Uspin Approach”: Fleischer, Nuc. Phys. B671 (2003) 459.

13. 3/10/08Prospects for gamma at LHCb13/20 BsDsBsDs Measure  s from interference between mixing and decay amplitudes. Large interference effects  s input from B s  J/  (   s ~ 0.03 mrad for 2 fb -1 see A.Satta talk) Include B s  D s  (20x Br) to determine  m s and tagging dilution Simultaneous fit to B s  D s  and B s  D s  decay time distributions (tagged and untagged) B s →D s - K + LHCb-2007-017 LHCb-2007-041 ModeSig. yieldB/S B s  D s  6.2k0.7 B s  D s  140k0.2 Sensitivity2 fb -1 10 fb -1      10.34.6   m s (ps -1 ) 0.0070.003 Input parameters:  ,  m s = 17.5 ps -1

14. 3/10/08Prospects for gamma at LHCb14/20 B 0  D  Measure  d analogous to B s  D s   d input from B 0  J/  s  (   d = 0.02 mrad for 2 fb -1 see ? talk) Problems —Interference small —8 fold ambiguity (  small) Potential solutions —“Conventional approach”: compare with other channels e.g. B 0  D   —“Uspin approach”: B 0  D  and B s  D s  LHCb-2008-035 LHCb-2007-044 ModeSig. yieldB/S B s  D s  6.2k0.7 B  D  1340k0.22 Sensitivity2 fb -1 10 fb -1      for        for   Input :   Uspin approach shows very promising results.  30% Uspin breaking    2 fb -1 (  stat.  30% Upsin breaking)

15. 3/10/08Prospects for gamma at LHCb15/20  with trees : Global Sensitivity Perform global fit to B  DK with common parameters. Include results from B 0 and B s time dependent analyses.  B  ( o ) 04590135180   for 0.5 fb -1 ( o ) 8.110.19.39.57.8   for 2 fb -1 ( o ) 4.15.14.85.13.9   for 10 fb -1 ( o ) 2.02.72.42.61.9 LHCb-2008-031 Input measurements: B   D 0 K  D 0   (LHCb-2008-011) D 0  (LHCb-2007-004) D 0  s   (LHCb-2007-048) B 0  D 0   D 0  (LHCb-2007-050) Time dependent measurements: B 0  D  (LHCb-2008-035) B s  D s  (LHCb-2007-041) Parameters (input value): B   D 0 K   (60 o ) r B – ratio of magnitude of diagrams (0.1)  B – strong phase difference (130  ) B 0  D 0   analogues: r B 0 (0.4),  B 0 (scan) D  decay parameters for ,  : r , r  well known (PDG)   (  158    (144 o ) R  – coherence factor Constrained by CLEO-c “Conventional” approach used for B 0  D  (     with 2 fb -1 ) to avoid large correlations with B s  D s K.

16.  with loops New physics in B  hh and B  hhh modes B 0   and B s  : “Uspin Approach”, Fleischer, Phys. Lett B458 (1999) 306. B          and B    s      : “Dalitz Approach”, Bediaga, Guerrer and Miranda, Phys Rev D76 073011 (2007).

17. 3/10/08Prospects for gamma at LHCb17/20 B 0   and B s   Measure  from interference between mixing and tree and penguin decay diagrams Demonstrates excellence of RICH pid LHCb-2007-059 ModeSig. yield (untagged) B/S (incl. bb) B 0   36k0.5 B s   36k0.15 B 0   140k< 0.06 B s   10k1.9 W  hypothesis m hh (GeV/c 2 )  hypothesis m hh (GeV/c 2 )

18. 3/10/08Prospects for gamma at LHCb18/20 B 0   and B s   Fit CP asymmetries of B 0  and B s  events —4 observables: Parameters —  —penguin to tree amplitude ratio d  e    d  e   —Input  d and  s Weak Uspin constraint —d   d   20%,     indep. Measures  and tests Uspin symmetry Sensitivity2 fb -1 10 fb -1   ( o ) 105  d  0.180.09    ( o ) 95   ( o ) 178 LHCb-2007-059 2 fb -1 B s   (ps)

19. 3/10/08Prospects for gamma at LHCb19/20 B         and B 0   s     Measure  from a Dalitz analysis of B   K      and B 0  K s     decays —K* resonance (dominant contributions) Extract penguin contribution from B   K      —Use Dalitz anistropy to measure CP asymmetry including phase differences Dalitz analysis of B 0 / B 0  K s     —Untagged analysis possible since B 0 and B 0 interference regions do not overlap Promising results:   ~5 o with 2 fb -1 G.Guerrer CKM 2008 ModeSig. yieldB/S B +  K  494k0.3 B 0   s  90kt.b.d. W I II III IV m 2  m 2  I CP III no-CP

20. 3/10/08Prospects for gamma at LHCb20/20 Summary LHCb offers exciting prospects for a precision measurement of   with trees —Standard Model benchmark —External input from CLEO-c of upmost importance —A combined sensitivity of   ~2-3 o is expected with 10 fb -1 of data —Many channels still to be investigated D    D  s  D  s  D (   (   s  D s (     etc  with loops —Sensitive to New Physics —B  hh analysis can measure  (   ~ 5 o with 10 fb -1 ) and test Upsin symmetry —B  hhh very promising first studies —Other channels to investigate: B d  , B s   B s  K    etc First challenge: reconstruct hadronic final states with real data….. coming soon

21. 3/10/08Prospects for gamma at LHCb21/20 Backup Slides

22. 3/10/08Prospects for gamma at LHCb22/20 B Tagging

23. 3/10/08Prospects for gamma at LHCb23/20  with trees : Global Sensitivity Weight (in %) of each contributing analysis with 2 fb -1 for two values of  B 0 Sensitivity of B 0  D 0 K* 0 improves by a factor of two in going from  B 0 =45  180 o. Residual dependence remains in global fit, but diluted due to other measurements. Analysis  B 0    B 0   B   D 0 (hh)K , B   D 0 (  )K  2538 B   D 0 (  s  )K  1225 B 0  D 0 (hh)K *0 448 BsDsKBsDsK 1624 B0DB0D 35 LHCb-2008-031

24. 3/10/08Prospects for gamma at LHCb24/20 B         and B 0   s     G.Guerrer CKM 2008