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Model independent determination of γ from B ± →D(K 0 S π + π − )K ±

Model independent determination of γ from B ± →D(K 0 S π + π − )K ±. Jim Libby (University of Oxford). Outline. Current e + e − B-factory and LHCb status Explanation of the model independent method Implementation to LHCb environment and results Background Acceptance

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Model independent determination of γ from B ± →D(K 0 S π + π − )K ±

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  1. Model independent determination of γ from B±→D(K0Sπ+π−)K± Jim Libby (University of Oxford) CPWG

  2. Outline • Current e+e−B-factory and LHCb status • Explanation of the model independent method • Implementation to LHCb environment and results • Background • Acceptance • Experimental systematic uncertainties • Conclusions CPWG

  3. Current status of this measurement of γ • Decays of D0or D0 to common final state gives sensitivity to γ • For B+→D(K0π+π-)K+ • Assume model for amplitudes • Fit D-Dalitz plots from B-decay to extractγ, rB and δB CPWG

  4. Current results • Current measurements: • BABAR and Belle use large samples of flavour tagged D*+D0π+events to find parameters of the isobar model • Model uncertainties from assumptions about the resonance structure in the model • NB scaled to the BELLE value of rB BABAR model error is ~6° • Recent studies for LHCb showed that the model-dependent fit would yield an uncertainty onγbetween 7-12° for an rB=0.1 • Range represents differing assumptions about the background • Uncertainties 1/rB • However, the best current model uncertainty is 10° with an rB=0.1 • Without improvements LHCb sensitivity will be dominated by model assumptions within 1 or 2 years of data taking CPWG

  5. Pincer movement • The largest and most challenging aspects of the model uncertainty come from KπandππS-wave • Lauren Martin (CPWG 24/05/07) investigating these issues in the model-dependent fit • A model-independent method that relies on a binned analysis of the Dalitz plot • Obvious problem is that information is lost via binning • Rest of this talk will discuss this method and its first implementation at LHCb CPWG

  6. 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, Eur. Phys. J. C47, 347 (2006) • BP, hep-ph/0703267 • If one bins the Dalitz plot symmetrically about m−2= m+2 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 CPWG

  7. Binned method continued • The original GGSZ paper concentrated on trying to determine si and ci at the same time as extracting γ, rB and δB from B data • 3 + 2×Nbins free parameters (ci =c-i and si =−s-i) • Huge loss in γsensitivity and not practical until you have O(106) events (cf 2500/fb-1 @ LHCb) • However, CP-correlated e+e−→ ψ″→D0D0datawhere onedecay is to KSππand the other decays to a CP eigenstate or KSππallowssi and ci to be determined • KL ππ equally sensitive • CLEO-c are collecting a ~750 pb-1 sample ofψ″data at the moment – running atψ″will finish later this year • Analyses underway to measure ci and si • Bondar and Poluektov estimate that the uncertainties on ci and si from this data set will lead to 3° uncertainty on γin a model dependent fit CPWG

  8. Implementation to LHCb 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 • 8 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 CPWG

  9. 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 • Bin Ki,ci and si amplitudes calculated from model • In reality from flavour tagged samples and CLEO-c • No attempt to add this uncertainty yet in detail • take the BP 3° CPWG

  10. No background with predicted 2 fb-1 yield 5000 experiments γ=60°, rB=0.1 and δB=130° The four Cartesian coordinates and normalization are free parameters All pulls are normal therefore calculate γ, rBandδB with propagated Cartesian uncertainties CPWG

  11. No background with predicted 2 fb-1 yield Model independent average uncertainty 7.7° (c.f. Model dependent 5.9°) CPWG

  12. Acceptance • Acceptance in each bin calculated as a weighted average of the acceptance function used for model dependent studies • I will come back to the use of D amplitudes rather than B amplitudes for this • relative differences in weighted efficiency below 3×10-3 in every bin • Modifies the fit function: • Average γuncertainty increases to 8.1° CPWG

  13. Background • 3 types of background to consider • B→D(KSππ)π(DC04 B/S = 0.24) • rB O(10-3) so Dalitz plots are likeD0andD0forB−andB+, respectively • Combinatoric (DC04 B/S<0.7) • Admixtures of two types considered • DKcomb: real D→ D(KSππ) combined with a bachelor K • Dalitz plot a even sum of D0andD0decays • PScomb:combinatoric D with a bachelor K • Follows phase space • Integrate background PDFs used in model-dependent analysis over each bin, then scaled to background level assumed: fractional area of Dalitz space covered by bin CPWG

  14. γ uncertainties with 5000 toy experiments CPWG

  15. Systematic related to acceptance • The acceptance varies over the Dalitz plane • The relative acceptance in each bin can be measured using the B→Dπcontrol sample with DK selection applied without bachelor K PID • With the DC04 selection expect 60k events/2 fb-1 • Relative relative-efficiency uncertainty 1-3%/ΔδD bin with 2 fb-1 • Increased statistics reduces error • Toy MC study smearing bin efficiencies in event generation by this amount leads to an additional 1° uncertainty without background and 2.5° uncertainty with DKcomb B/S=0.7 • Small effect compared to statistical uncertainty • NB: the efficiency related to the PID of the bachelor π/K can be factored out and will be determined from the D*→D(Kπ)π data to better than one percent-ignore at present CPWG

  16. Asymmetry in efficiency in Dalitz space • Concern was raised a while ago about asymmetries in the efficiency across the Dalitz plane i.e. ε(m2+, m2 −)≠ε(m2−, m2 +) • Generated with the efficiency biased relative to one another by up to 10% depending on whether the event had m2+>m2 − or m2+<m2 − • Significant biases on x±and y±but they effectively cancel in determination ofγ • Maximum bias onγinduced was 0.5° for 10% relative effect and full background CPWG

  17. Resolution • ΔδD binning has some narrow regions in Dalitz space • Preliminary investigation of how resolution on the Dalitz variables might affected the extraction of γ • Assumed a 10 MeV2/c4 resolution on Dalitz variables and generated toy experiments with this smearing • Found that this led to a few bins with largest (red) and smallest (dark blue) phase difference having a 2-3% relative changes in expected yields due to resolution induced migration • Fit results on toy experiments where resolution included in generation but ignored in fit found no significant bias (<0.5°) on γ • Cartesian coordinates exhibit bias but cancels in extraction of γ CPWG

  18. Background fractions • Combinatoric background rate will be determined from B and D mass sidebands which will cover at least 2-3 times the area of the signal region • Use 10× in DC04 background studies but this will probably be unrealistic with data • If background distributions relatively flat in masses one can estimate that this leads to B/S will be determined absolutely to around 0.01 or better • Toy studies suggest that there is no impact on γprecision with this kind of uncertainty • Maybe complications depending on Dalitz space distribution of the PS background but can only speculate until we have the data in hand CPWG

  19. Conclusion Model independent Model dependent σ(model)=10° σ(model)=5° • Implemented 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 • Such a measurement will be better than model dependent method after one year of data taking if we can not improve the model error • 10 fb-1 statistical uncertainty 4-6° depending on background assumptions • Experimental systematic uncertainties considered can be controlled from data • Acceptance determined from B→Dπ sample will contribute ~2.5° with 2 fb-1 • Liaison required with CLEO-c to get common binning and to best understand all uncertainties related to the ψ″data • Some further scope to optimise binning for combined statistical sensitivity CPWG

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