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Andrew Powell Oxford Graduate Symposium - Wednesday, 14 th March 2007

Measuring g with B ® D(4h)K Decays at LHCb. LHCb Physics Aims and Objectives . g from B ® DK GLW + ADS Method Dalitz Amplitude Analysis. Selection & Sensitivity Signal Yields & B/S Estimates Toy MC Studies. *Courtesy of. Andrew Powell

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Andrew Powell Oxford Graduate Symposium - Wednesday, 14 th March 2007

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  1. Measuring g with B ®D(4h)K Decays at LHCb • LHCb Physics • Aims and Objectives • gfromB ® DK • GLW + ADS Method • Dalitz Amplitude Analysis • Selection & Sensitivity • Signal Yields & B/S Estimates • Toy MC Studies *Courtesy of Andrew Powell Oxford Graduate Symposium - Wednesday, 14th March 2007

  2. 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!

  3. The Angle g in the SM Unitarity Condition: • 9 orthogonality equations (3 purely real – No CP dependance) • 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

  4. gfrom B±® DK ± • Extraction through interference between b c and b u transitions ColourSuppressed Common starting point for a variety of methods to extract g • Particularly suitable at LHCb:Utilise K-p separation of RICH • Counting experiments:No need for tagging or Proper Time determination • Good target for LHCb to make a measurement from early data

  5. GLW(Gronau, London, Wyler)Method f(D) = CP Eigenstate (e.g. K+K-) Due to rB suppression, the interference is small and thus so is the CP asymmetry ADS(Atwood, Dunietz, Soni) Method Alternative:Rebalance Amplitudes using DCS Decays f(D) = non-CP Eigenstate (e.g. K+p-) Interference is now large when looking at ‘wrong sign’ decays

  6. 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

  7. 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 via Dalitz 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 a value for rB,g, dB

  8. Dalitz Plot Analysis • Should also work for 4-Body decays as well • Never done before - NEW! 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:

  9. SELECTION & SENSITIVITY @ LHCb B ®D(4h)K

  10. 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°

  11. 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

  12. ADS Sensitivity at LHCb • Combine both ADS modes decays into a global analysis • 2-body selection results similar to those shown for 4-body: • - 60,000 Kppp (S/B ~ 1.5) • 60,000 Kp (S/B ~1.7) dKp = 25° dK3p = -120° s(g) ~ 5° • 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 :

  13. The Dalitz Mode: KKpp Signal Evaluation Yield per 2fb-1 = 1.7k events • Only one rate to consider; no right/wrong sign • Additional Kaon reduces combinatoric background in selection [MeV/c2] Background Evaluation • Again, the danger is: • Contribution at B/S = 0.24 ± 0.08 • This can be controlled using RICH PID • Combinatoric then dominant • (Where does this lie in phase-space?) 6 S/B = 1.1 ± 0.5

  14. 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

  15. Fit Results I • So far, only incorporated the Dp bkg, • Now simulate and fit 1,700 events as predicted per 2fb-1. Input values: • g= 60°, dB= 130°,rB= 0.10 • Results from 61 ‘Toy’ experiments: • Mean error on g~ 12° • Unbiased • Pull Width 1.2 ± 0.2

  16. Fit Results II rB (x100) (x100) dB • Results, so far, are pleasing but this is far from finished • Both D + Combin. Kaon, and Combin. D backgrounds to include…

  17. 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 • Utilising an ADS method at LHCb predicts s(g)~ 5-15° for 2fb-1 • Incorporating just the D0p background into a sample of 1700 single events achieves s(g)~ 12° • It is estimated that with a combined analysis incorporating all modes, LHCb will achieve s(g)~ 5° for 2fb-1 • At sucha precision, this will be a starting point to test for contributions from new physics

  18. 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

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