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Determination of γ from B ± →DK ± : Input from CLEOc

Determination of γ from B ± →DK ± : Input from CLEOc. Jim Libby (University of Oxford). Outline. Measuring γ with B ± →DK ± Complementary measurements of D decay at CLEO-c K 0 ππ K ± X (X= π , ππ or πππ ) Other modes will be discussed later today. Searching for new physics. TREE.

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Determination of γ from B ± →DK ± : Input from CLEOc

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  1. Determination of γfrom B±→DK±: Input from CLEOc Jim Libby (University of Oxford)

  2. Outline • Measuring γwith B±→DK± • Complementary measurements of D decay at CLEO-c • K0ππ • K±X (X=π,ππ or πππ) • Other modes will be discussed later today

  3. Searching for new physics TREE LOOP • Non Standard Model particles contribute within the virtual loops • Differences between tree-level and loop-level triangles • Signature of new physics • Complements direct searches

  4. Introduction B±→DK± Strong phase difference • B→DK decays involve b→c and b→u transitions • Access g via interference if D0 and D0 decay to the same final state • These measurements are theoretically clean • No penguin CKM standard candle • largest correction is sub-degree from D-mixing • LHCb looking at a number of strategies to study such decays • B+: Atwood-Dunietz-Soni ('ADS'), 3 and 4 body Dalitz Plot Anal. Ratio of absolute amplitudes of colour/CKM suppressed to favoured (~0.1)

  5. B±→D(K0Sπ+π−)K± • For B+→D(K0π+π−)K+ • Assume isobar model (sum of Breit-Wigners) • Fit D-Dalitz plots from B-decay to extractγ, rB and δB (770) Number of resonances Rel. BW K*(892) Amplitude and phase extracted from D*+→D0π+sample at B-factories Non-resonant

  6. B±→D(K0Sπ+π−)K± Absence of CP violation: distributions would be identical B+ B− Simulated LHCb data

  7. Current e+e− results PRD 73, 112009 (2006) hep-ex/0607104 • Current best direct constraints on γ: • Based on ~300 events each (~1/3 of final data set) • However, large error from isobar model assumptions • BABAR and Belle use large samples of flavour tagged D*+D0π+events to find parameters of the isobar model • Excellent knowledge of |f|2 but phases less well known • Model uncertainties from assumptions about the resonance structures in the model

  8. K*0(1430) Isobar model uncertainty • Most challenging aspects of the model uncertainty come from Kπand ππS-wave BABAR (PRL 95 121802,2005) Fit to flavour tag sample

  9. Model uncertainty impact at LHCb • The model-dependent likelihood fit yields an uncertainty onγbetween 7-12° for an rB=0.1 • One year of data • Range represents differing assumptions about the background • However, the current model uncertainty is 10-15° with an rB=0.1 • Uncertainties 1/rB • Without improvements LHCb sensitivity (and e+e−)will be dominatedby model assumptions within 1 year of data taking • Motivates a model-independent method that relies on a binned analysis of the Dalitz plot • Disadvantage is that information is lost via binning

  10. Binned method • Proposed in the original paper by Giri, Grossman, Soffer and Zupan and since been extended significantly by Bondar and Poluektov • GGSZ, PRD 68, 054018 (2003) • BP, most recently arXiv:0711.1509v1 [hep-ph] • Bin the Dalitz plot symmetrically about m−2= m+2 then number of entries in B− decay given by:  # events in bin of flavour tagged D0 decays Average cosine and sine of strong phase difference between D0 and D0 decay amplitudes (ΔδD) in this bin

  11. CLEO-c measurement status 1/3 of total data (<1/2 the CP tags) Studies not complete but projected uncertainties on c and s will lead to 3-5 degree uncertainty on γ

  12. Inkblot test Absolute value of strong phase diff. (BABAR model used in LHCb-48-2007) • Bondar and Poluektov show that the rectangular binning is far from optimal for both CLEOc and γanalyses • 16 uniform bins has only 60% of the B statistical sensitivity • c and s errors would be 3 times larger from the ψ″ • Best B-data sensitivity when cos(ΔδD) and sin(ΔδD) are as uniform as possible within a bin Good approximation and the binning that yields smallest s and c errors is equal ΔδD bins-80% of the unbinned precision

  13. Implementation at LHCb (γ=60°, rB=0.1 and δB=130°) • Generate samples of B±→D(K0Sππ)K±with a mean of 5000 events split between the charges • Bin according to strong phase difference, ΔδD • Minimise χ2 • Ki, ci and si amplitudes calculated from model • In reality from flavour tagged samples and CLEO-c

  14. γ uncertainties with 5000 toy experiments

  15. B±→D(K0Sπ+π−)K± at LHCb Model independent Model dependent • Model independent fit with binning that yields smallest error from exploiting CLEO-c data • Binning depends on model - only consequence of incorrect model is non-optimal binning and a loss of sensitivity • Measurement has no troublesome and hard-to-quantify systematic and outperforms model-dependent approach with full LHCb dataset with currently assigned model error • 10 fb-1 statistical uncertainty 4-6°depending on background • CLEO-c measurements essential to validation of assumptions in model dependent measurement • LHCb-2007-141 – Available via CERN document server σ(model)=10° σ(model)=5°

  16. ADS

  17. ADS method • Look at DCS and CF decays of D to obtain rates that have enhanced interference terms • Unknowns : rB~0.1, dB, dDKp, g, NKp, Nhh (rD=0.06 well measured) • With knowledge of the relevant efficiencies and BRs, the normalisation constants (NKp, Nhh) can be related to one another • Important constraint from CLEOc σ(cos dDKp)=0.1-0.2 • Overconstrained: 6 observables and 5 unknowns h=π or K

  18. Four-body ADS • B→D(K πππ)K can also be used for ADS style analysis • Also Kππ0 • However, need to account for the resonant substructure in D→Kπππ • made up of D→K*ρ, K−a1(1260)+,.,… • in principle each point in the phase space has a different strong phase associated with it - 3 and 4 body Dalitz plot analyses exploit this very fact to extract γfrom amplitude fits • Atwood and Soni (hep-ph/0304085) show how to modify the usual ADS equations for this case • Introduce coherence parameter RK3πwhich dilutes interference term sensitive to γ • RK3πranges from • 1=coherent (dominated by a single mode) to • 0=incoherent (several significant components) Integrating over phase space

  19. Determining the coherence factor • Measurements of the rate of K3πversus different tags at CLEO-c allows direct access to RK3πandδK3π • Normalisation from CF K−π+π+π− vs. K+π−π−π+ and K−π+π+π− vs. K+π− • CP eigenstates: • K−π+π+π− vs. K−π+π+π−: • K−π+π+π− vs. K−π+:

  20. Amplitude models • To fully exploit D→K3πinB-decay an unbinned fit to the data maybe optimal • However, need model of DCS decays • Accessible from CP-tagged data at CLEO-c • Furthermore, model can guide division of phase space into coherent regions for binned RK3π analysis

  21. Conclusion • Focussed on the things that are being done and how they impact γ • Apology 1: examples drawn from LHCb because that is what I know best • Rest of the meeting in three parts: • status of the UK work on the ADS and four body fits • extensions to the current work • beer • Apology 2: to those on the phone

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