Andrew Powell IOP Nuclear & Particle Physics Conference 2007

1. Measuring g with B ®D(4h)K Decays at LHCb • Standard Model CKM • Weak phase g • gfromB ® DK • Dalitz Amplitude Analysis • Selection & Sensitivity • Signal Yields & B/S Estimates • Toy MC Study Results *Courtesy of Andrew Powell IOP Nuclear & Particle Physics Conference 2007

2. The Angle g in the SM Unitarity Condition: • 9 orthogonality equations (3 purely real – No CP dependence) • Remaining 6 can be drawn as triangles, • e.g. • The angle g is the least well known: An accurate measurement of g is arguably the most important measurement for LHCb and future CP-violation experiments *CKM Fitter 06

3. gfrom B±® DK ± • Extraction through interference between b c and b u transitions ColourSuppressed • Require and to decay to a common final state, f(D) Common starting point for a variety of methods to extract g • Particularly suitable at LHCb:Utilise excellent K-p separation of RICH • Counting experiments:No need for tagging or Proper Time determination

4. GLW(Gronau, London, Wyler)Method f(D) = CP Eigenstate (e.g. K+K-) Due to rBsuppression, the interference is small and thus so is sensitivity to ADS(Atwood, Dunietz, Soni) Method f(D) = non-CP Eigenstate (e.g. K+p-) Use Doubly Cabbibo Suppressed (DCS) of the D0 to ‘rebalance’ amplitude Interference is now large when looking at ‘wrong sign’ decays Experimental Status: No observation yet of wrong sign modes at B-factories This exhausts methods using 2-body final states of the D0 decay rB < (at 90% C.L.) Experiment What about multi-bodied final states (ND-daughters³3)? BaBar 0.23 Belle 0.18

5. Strategies using Only Multibody D0 Decays • Greatest sensitivity to g comes with maximal interference between and and • The presence of large strong phases, both , can greatly enhance the interference terms • For a multibody D decay, each resonance mode has its own strong phase and some are expected to be large Enhanced sensitivity to g With a single rate, how can we extract g? Only viaDalitz Analysis Conventional Strategy: Utilise 3-Body Cabibbo allowed decays of D0, e.g. Resonance decays of D0 allow the Dalitz plot to be fitted to a sum of Breit-Wigner functions, extracting values for rB,g, dB

6. 4 Body Dalitz Analysis • Should also work for 4-Body decays as well • Never done before - NEW! [Phys. Lett. B 647 (2007) 400] f(D) = Singly Cabibbo Suppressed • No suppression in D decay, but it is now many body via resonances • A ‘model’ of the resonances and their amplitudes/phases is needed • 5 variables required to describe kin. • (cp. only 2 for 3-body) • Amplitudes, , and phases, , are inputs to model for each resonance • These values will be extracted from Dalitz fits to decays of D*®Dp data at LHCb Example of resonances included:

7. SELECTION & SENSITIVITY @ LHCb B ®D(KKpp)K

8. B ®D(KKpp)K Selection Use full LHCb Monte Carlo simulation to estimate signal selection efficiency and background: Signal Evaluation Yield per 2fb-1 = 1.7k events • Prompt charged tracks • Multiple kaons [MeV/c2] Background Evaluation Analysis of events selected from sample of ~40x106 bb MC events (º13 minutes of LHCb running!) • Danger is: • Can be controlled using RICH PID • Contribution at B/S = 0.24 ± 0.08 • Combinatoric events then dominant 10xBR(B ® DK) 6 S/B = 1.1 ± 0.5

9. Dalitz KKpp Sensitivity Study 1) Signal Acceptance • Assessment of the MC selected signal suggests that the acceptance is flat: • Kolmogorov ‘similarity’ test • No need for acceptance function P 2) Background in Phase Space Where do the background events lie in phase-space? How to model in fit? • 3 Types of Background: • D0p • D0 + fake Kaon • Fake D + real/fake Kaon Genuine ‘D0’ Particle Signal PDFs ‘phase-space’ Incorporating into RooFit Model and • Framework written by J. Rademacker using FOCUS data to fix • Original study with NO background founds(g)~ 10° • Now adding the background described above to determine realistic sensitivity

10. KKpp Fit Results Example:Accumulated plots for fits combining ALL 3 Bkg Types For each background, perform 100 toy MC experiments with 1,700 signal events. Input values: g= 60°, dB= 130°,rB= 0.10 • D0pBkg Inc. (B/S = 0.24) • D0 + fakeKaon Bkg Inc. (B/S = 0.32) • FakeD0 + fakeKaon Bkg Inc. (B/S = 0.32) • Including ALL 3 Bkg Types

11. Conclusions • An accurate measurement of the CKM angle g is a key goal for the LHCb experiment • Interference of simple tree level diagrams can provide access to g through measurable quantities • 4-body Dalitz amplitude fitting is a very promising technique at LHCb • Incorporating background into a sample of 1,700 signal • Method can be extended to the channel • It is estimated that with a combined analysis incorporating all eventsachieves s(g)~ 15-16° modes, LHCb will achieve s(g)~ 5° for 2fb-1 • This plus similar g extraction methods will provide a precise bench mark against which new physics can be tested

12. BACKUP SLIDES

13. The LHCb Experiment Large Hadron Collider Beauty experiment Dedicated to precision measurements of CP violation and rare decays in the B meson sector. Is the SM the only source of CP violation, or is thereNEW PHYSICS? Need to over-constrain the SM CKM matrix parameters and test its unitarity (such as the weak phase g) B-quark sector predicted to be most prominent (B-factories: Babar,Belle) • The LHC will deliver huge amounts of statistics: • Large b cross-section ~ 500 mb • Large luminosity ~ 2 x 1032 1012 bb per 2fb-1 Plus, all flavours of B-hadrons produced (Bu, Bd, Bs) in large quantities Facility Time to gen. 1x106 bb B-factories LHCb ~ 1 day ~ 10 mins!

14. ADS Method II Considering both the B- and B+ decays, we end up with a total of 4 processes (2 wrong-sign + 2 right-sign): Measuring the relative rate of these 4 process leads to 3 observables which depend on 4 unknowns: rB,g, dB,dD Consider a D decay to another final state: Introduces 3 additional observables and one additional unkown: Can now solve for ALL Unknowns dDK3p Current Experimental Status • B-factories: No observation of wrong sign modes, either 2 or 4 body decay • However, upper limits on rB can be made: rB < (at 90% C.L.) Facility BaBar 0.23 Belle 0.18

15. LHCb MC Simulation Software Full LHCb Monte Carlo simulation to estimate signal selection efficiency and background: PYTHIA – Generation of proton-proton interactions at Ös = 14TeV GEANT– Full detector description simulating resulting response Also, some realism: • Pattern recognition, Trigger simulation • Detector inefficiencies, noise hits The ADS Mode: Kppp Signal Evaluation Right Sign Decays: Yield per 2fb-1 = 61k events Wrong Sign Decays: This yield depends on the precise value of the D-strong phase, dDK3p rB = 0.077 rD = 0.068 dB = 130° g = 60°

16. ADS Sensitivity at LHCb • Combine both 2 and 4 body ADS modes into a global analysis • Both 2 and 4 body MC selection results very similar: • ~ 60,000 Right Sign per 2fb-1 • Background controllable: • S/B ~ 1.5 (Right Sign Decays) dKp = 25° dK3p = -120° s(g) ~ 5° • Number of Wrong Sign decays depends on exact value of the CP invariant strong phases • Toy MC to simulate this 2fb-1 data set, with the following input values: • g= 60° • rB= 0.077 • rD= 0.06 • dB= 130° • -180°<dK3p<180° • -25°<dKp<25° • Depending on the values dKp and dK3p :

17. Kppp: Background Evaluation Right Sign Events Development of selection criteria by analysis of bkg selected from sample of ~40x106 bb MC events (º13 minutes of LHCb running!) Right Sign Events • Dominant bkg found to be: • Dangerous since low tail sits in signal window • RICH provides excellent suppression • Considering all bkg sources: 77 10xBR(B ® DK)! S/B = 1.5 ± 0.2 Wrong Sign Events Wrong Sign Events • Only 7 events of this type seen in sample • Pure combinatoric bkg most dominant • Again, S/B depends on value of dK3p 7 As an example, take dK3p = -60° S/B+ = 0.09 ± 0.03 S/B- = 0.47 ±0.14

18. Dalitz KKpp Sensitivity Study J. Rademacker & G. Wilkinson established that for a 1,700 event sample, g can be measured with an error of ~10° (No acceptance or bkg effects included) Signal Acceptance Assessment of the MC selected signal suggests that the acceptance is flat: Background in Phase Space Out of the background identified, where does it lie in phase-space? • 3 Types of Background: • Dp • D + combinatoric Kaon • Pure combinatoric D ‘Signal’ like in Dalitz space ‘phase-space’ PDFs for Fit

19. Wish to fit Dalitz Plot with: rB,g, dB And then extract values for: Approximate AD as a sum of Breit-Wigner functions: Amplitudes, ar, and phases, dr, are inputs to model and are taken from BELLE/BABAR data 3 Body Dalitz fully described with 2 variable:s12, s13 Complication: 4 Body Dalitz requires 5 variables: s234, s12,s23, s34 , s123 Now similarly for 4 Bodies: The corresponding amplitudes and phases for the Breit-Wigner sum are taken from FOCUS data Added benefit of no Ks compared to 3 Body Dalitz