Optimising sensitivity to γ with B 0 DKπ,

Transcription

1 Optimising sensitivity to γ with B DKπ, D K S π + π double Dalitz plot analysis Daniel Craik, Timothy Gershon, Anton Poluektov MIT, University of Warwick July D. Craik, T. Gershon, A. Poluektov Prospects for γ from B DKπ, D K π + π ICHEP, Seoul, South Korea /

2 Introduction: γ from B DK [See previous talk by M. Whitehead for details] γ is measured in the interference of b c and b u transitions, e.g. B D K : Vus s K ū b V cb c + B ū ū D A V cb Vus Aλ B b ū B D K : V ub V cs u c s ū D K A V ub V cs Aλ (ρ iη) If D and D decay into the same final state: D = D + e ±iγ+iδ B D Ratio of two amplitudes: = A(B D K ) A(B D K ) = V ubv cs V cb V [Color supp]. us Useful to have kinematic degrees of freedom (multibody decays). Multibody D decays (e.g. D KS π+ π ), [GGSZ, ; Bondar, ] Multibody B decays (B DKπ) [T.G. 9] GGSZ can be done model-independently (use binned Dalitz plots, quantum correlations from e + e DD for strong phases in bins). Double Dalitz decay B DKπ, D K S π + π : the way to make model-independent measurement with B DKπ D. Craik, T. Gershon, A. Poluektov Prospects for γ from B DKπ, D K π + π ICHEP, Seoul, South Korea /

3 Formalism: B DK, D K S π + π reminder Amplitude for D K S π + π decay from B + DK + (A D, A D, A D Dlz are functions of Dalitz variables m K S π+, m K S π ) A D Dlz = A D + e i(δ B+γ) A D, () After... and binning (i =... N ): N i = h D Dlz [K i + rbk i + ] K i K i (x + c i y + s i ), () where x + = cos(γ + δ B ), y + = sin(γ + δ B ); K i : yields in bins of flavour-specific D K S π + π decays c i, s i : average cos and sin of strong phase difference in bins Similarly fo DK we obtain x, y (with γ γ) and thus can measure γ w/o ambiguities. All parameters can be extracted from experiment model-independent D. Craik, T. Gershon, A. Poluektov Prospects for γ from B DKπ, D K π + π ICHEP, Seoul, South Korea /

4 Model-independent technique fo DK Binning of the D K S π + π phase space. Bin shapes optimised wrt. γ sensitivity Binning is not the only way to obtain model independence, e.g. Fourier transformation of phase difference could be more promising, [A.P, EPJ C7 () ] c i, s i contain D K S π + π strong phase, obtained by CLEO/BES in ψ(77) D D [CLEO, PRD () ] A D AD cos δd dd A D AD sin δd dd D c i = i A D dd D, s i = i AD dd A D dd. AD dd D i D i D i D i () D. Craik, T. Gershon, A. Poluektov Prospects for γ from B DKπ, D K π + π ICHEP, Seoul, South Korea /

5 B DKπ mode for γ B DKπ decay:. fo DK (both amplitudes colour-suppressed) Expect larger magnitude of CP -violation than in B + DK + Fewer events Recent analyses that used this mode in LHCb: B DK, D K Sπ + π [JHEP()7] Model-dep. GGSZ-like, coherence factor to account for non-dk B DK, D K Sπ + π [JHEP()] Model-indep. GGSZ-like, coherence factor to account for non-dk B DKπ, D K π +, K K +, π π + [PRD 9, ()] Based on technique by [T.G. 9]: Model-dependent measurement using D K + as a reference for the phase. D. Craik, T. Gershon, A. Poluektov Prospects for γ from B DKπ, D K π + π ICHEP, Seoul, South Korea /

6 B DKπ mode for γ Technique using B DKπ, D K S π + π, model-independent wrt. both -body amplitudes is available [T.G and A.P. ]. Bin both B DKπ and D K Sπ + π Dalitz plots (correlated) Additionally use B DKπ with D K π + and K + π D K Sπ + π strong phase coeffs. c i and s i: from CLEO/BES B DKπ strong phase coeffs. κ α and σ α: free parameters Study in [T.G and A.P. ] used rather preliminary B DKπ model (not measured at the time), very rough yields estimates and lacked background study. Now we know much more, so want to update. Is it feasible with Run II and LHCb upgrade? [PRD 97, () ] D. Craik, T. Gershon, A. Poluektov Prospects for γ from B DKπ, D K π + π ICHEP, Seoul, South Korea /

7 Formalism: B DKπ, D K S π + π Two amplitudes, A D (m K S π+, m K S π ) and A B (m Dπ +, m K + π ): A dbl Dlz = A B A D + e iγ A B A D, () After... and binning both B and D Dalitz plots (α =... M): N αi = h dbl Dlz {κ α K i + κ α K i () + } κ α K i κ α K i [(κ α c i σ α s i ) cos γ (κ α s i + σ α c i ) sin γ], Strong phase terms fo amplitude: A B A B cos δ B dd A B A B sin δ B dd D κ α = α A B dd D, σ α = α A B dd A B dd. A B dd D α D α D α D α () D. Craik, T. Gershon, A. Poluektov Prospects for γ from B DKπ, D K π + π ICHEP, Seoul, South Korea 7/

8 Formalism: B DKπ, D K S π + π System of equations () fo DKπ, D K S π + π : N αi = h dbl Dlz {κ α K i + κ α K i + κ α K i κ α K i [(κ α c i σ α s i ) cos γ (κ α s i + σ α c i ) sin γ] And similar for c.c. decay (γ γ). Enough constraints to measure γ. Knowns and unknowns: K i : from flavour-tagged D K S π + π c i, s i : from charm factory (or even free parameters) κ α, κ α : from B D K + π (fav) and B D K + π (sup) (D K π + ) κ α, σ α, γ: free parameters }, D. Craik, T. Gershon, A. Poluektov Prospects for γ from B DKπ, D K π + π ICHEP, Seoul, South Korea /

9 Formalism: B DKπ, D K S π + π Originally, planned to use suppressed B D K + π (D Kπ) events hard at LHCb because of huge B s D K π + background where D decay is favoured. In practice, we plan to use the system of equations () N αi = h dbl Dlz {κ α K i + κ α K i + κ α K i κ α K i [(κ α c i σ α s i ) cos γ (κ α s i + σ α c i ) sin γ] for three classes of events: B DKπ, D K π + (α =, c = cos δ Kπ, s = sin δ Kπ, K /K = r Kπ ) B DKπ, D K K +, π π + (α =, c = +, s =, K = K ) B DKπ, D K S π + π The D CP mode is expected to provide information about κ α instead of suppressed D K + π. Will compare this approach with the strategy where suppressed D K + π sample is available. D. Craik, T. Gershon, A. Poluektov Prospects for γ from B DKπ, D K π + π ICHEP, Seoul, South Korea 9/ },

10 B D K + π and B D K + π amplitudes mk π (GeV/ c) mk π (GeV/ c) B D K + π model from [PRD9, ()] B D K + π model from γ analysis [PRD9, ()], but rb is taken the same (baseline rb =., also try. and.) for all Kπ components (K (9), K (), K () and LASS S-wave). mdπ (GeV D KS π + π model from Belle measurement D. Craik, T. Gershon, A. Poluektov mdπ (GeV/ c) / c) [PRD, ()] Prospects for γ from B DKπ, D K π + π ICHEP, Seoul, South Korea /

11 Estimated yields Run toys for expected yields after the end of Run II ( fb ) and fb, which correspond to and Run I yields (taking into account large CS at TeV and trigger efficiency in Run III). D decay mode Run I Run I+II fb K + π 9 K π + 9 K + K 7 7 π + π K S π + π 7 7 Run I yields are taken from corresponding analyses (D Kπ, KK, ππ), for D K S π + π they are extrapolated from B DK, D K S π + π yield using the measured B DKπ model. D. Craik, T. Gershon, A. Poluektov Prospects for γ from B DKπ, D K π + π ICHEP, Seoul, South Korea /

12 B DKπ binning Optimal binning depends on B DKπ model, calculated by maximising Q α = κ α(κα + σ α) α κ. (7) α σ α Start from equal phase-difference binning, stochastic procedure to maximise Q.... Bin number α /c ) (GeV Kπ m κ α m (GeV /c ) κ α, σ α become closer to a unit circle as a result of optimisation maximises interference term γ sensitivity phase-diff D. Craik, T. Gershon, A. Poluektov Prospects for γ from B DKπ, D K π + π ICHEP, Seoul, South Korea / Dπ Bin number

13 B DKπ binning Optimal binning depends on B DKπ model, calculated by maximising Q α = κ α(κα + σ α) α κ. (7) α σ α Start from equal phase-difference binning, stochastic procedure to maximise Q.... Bin number α /c ) (GeV Kπ m κ α m (GeV /c ) κ α, σ α become closer to a unit circle as a result of optimisation maximises interference term γ sensitivity optimal D. Craik, T. Gershon, A. Poluektov Prospects for γ from B DKπ, D K π + π ICHEP, Seoul, South Korea / Dπ Bin number

14 γ residuals Check the fit procedure is unbiased for both strategies, with and w/o suppressed D K + π mode, for both Run I+II and fb. Run I+II: Entries 7 σ(γ) = (.9 ±.9) with D K + π γ residual ( ) fb : Entries 7 σ(γ) = (. ±.) with D K + π γ residual ( ) Entries Entries σ(γ) = (.7 ±.) w/o D K + π γ residual ( ) 7 σ(γ) = (.9 ±.) w/o D K + π γ residual ( ) Initial γ =, =.. toys for each configuration. γ is unbiased for both Run I+II and fb, with or w/o suppressed D K + π mode Removing suppressed D K + π does not drastically affect sensitivity. D. Craik, T. Gershon, A. Poluektov Prospects for γ from B DKπ, D K π + π ICHEP, Seoul, South Korea /

15 Phase-difference vs. optimal binning Compare various B binning strategies: phase-difference or optimal, number of bins from to. D binning is always optimal with bins. c i, s i are fixed to their true values. ) ( ) σ(γ 9 7 Run II Phase-diff. binning Optimal binning Without D K π + channel With D K π + channel Number of B bins ) ( ) σ(γ... fb Phase-diff. binning Optimal binning Without D K π + channel With D K π + channel Number of B bins Optimal B binning does improve sensitivity for M >. Use it for all further studies. D. Craik, T. Gershon, A. Poluektov Prospects for γ from B DKπ, D K π + π ICHEP, Seoul, South Korea /

16 Finite c i, s i precision c i, s i are either fixed to true values, constrained to current CLEO precision, or freely floated. =. σ(γ ) ( ) Run I+II Without D K π + With D K π + Fixed c i, s i Constrained c i, s i Floated c i, s i Number of B bins ) ( ) σ(γ... fb Without D K π + With D K π + Fixed c i, s i Constrained c i, s i Floated c i, s i Number of B bins Even current CLEO precision is sufficient, and with fb we can even measure c i, s i with reasonable precision! Still, CLEO and BES-III measurements are essential for better stability of the fit and to control systematic uncertainties. D. Craik, T. Gershon, A. Poluektov Prospects for γ from B DKπ, D K π + π ICHEP, Seoul, South Korea /

17 c i, s i obtained from the fit Distributions of c i, s i from the fit where they are left floated (but constrained to lie inside the unit c + s circle) fb. =.. s i.... c i 7 Bin number i Statistical precision on c i, s i is.7.7, which is comparable to or somewhat better than current CLEO measurement. Can use this information for other measurements which require c i, s i (γ from B DK, charm mixing) D. Craik, T. Gershon, A. Poluektov Prospects for γ from B DKπ, D K π + π ICHEP, Seoul, South Korea /

18 Bs D K π + background Bs D K π + is unavoidable background for LHCb, dangerous since produces opposite-flavour D (looks like suppressed amplitude from slide 9). Arb. units Arb. units mk π (GeV/ c) Amplitude structure not studied, but can make an educated guess based on Bs DKπ analysis and known D K resonances. Simulated here: (7) π +, nonres D Kπ. (7) π +, Ds D K, Ds () π +, Ds mdk π (GeV/ c) mdπ.... (GeV / c) Cocktail simulated using [RapidSim] and structure for non-scalars) D. Craik, T. Gershon, A. Poluektov... mdπ (GeV/ c) Arb. units Arb. units.. mk π (GeV/ c) [EvtGen] mdk (GeV/ c) (incoherent, but correct helicity Prospects for γ from B DKπ, D K π + π ICHEP, Seoul, South Korea 7/

19 Adding B s D K π + background Expect % background from B s D K π + in the signal B mass window for D hh and D K S π + π. For D K S π + π, take the contribution to be purely b c transition, uncorrelated with B bin. For suppressed D + π, expect S/B., so just forget about this mode. ) ( ) σ(γ Run I+II No background % background =. =. =. Number of B bins ) ( ) σ(γ..... fb No background % background =. =. =. Number of B bins Effect depends quite strongly on, but even in the worst case =. can get a reasonable precision σ(γ) in Run I+II and. with fb D. Craik, T. Gershon, A. Poluektov Prospects for γ from B DKπ, D K π + π ICHEP, Seoul, South Korea /

20 Sensitivity to B DKπ model variations Check what happens if model used for binning optimisation is different: ) ( ) σ(γ Range of S-wave variations (Kπ and Dπ) from B DKπ analysis. Vary value. Remove D s states in suppressed amplitude. Run I+II Baseline model Alternative S-wave =. =. No D* s Number of B bins ) ( ) σ(γ Less than % effect, no major concern.... fb Baseline model Alternative S-wave =. =. No D* s Number of B bins D. Craik, T. Gershon, A. Poluektov Prospects for γ from B DKπ, D K π + π ICHEP, Seoul, South Korea 9/

21 Summary Performed feasibility study for γ measurement with model-independent double Dalitz plot analysis B DKπ, D K S π + π, in a realistic scenario for Run I+II and upgrade ( fb ). Feasibility study published: [PRD 97, () ] Strategy w/o suppressed D K + π mode (which is contaminated by B s D K π + background) and using D CP instead is feasible, even in presence of B s background at the expected level. Sensitivity to γ is estimated to be, depending on value (in range..) for Run I+II.. for fb Formalism allows any other D decay mode (two- or multibody) to be plugged in (with either c i, s i or δ D and coherence factor) Owing to large =., does not depend significantly on precision of charm factory input (c i, s i ), and can be used to constrain c i, s i itself. Next steps: analyse LHCb data! D. Craik, T. Gershon, A. Poluektov Prospects for γ from B DKπ, D K π + π ICHEP, Seoul, South Korea /

22 Backup D. Craik, T. Gershon, A. Poluektov Prospects for γ from B DKπ, D K π + π ICHEP, Seoul, South Korea /

23 B DKπ binning M= M= 7 () Bin number M= Bin number mk π (GeV/ c) Bin number mk π (GeV/ c) mk π (GeV/ c) Optimal binning depends on B DKπ model, calculated by maximising P κα (κ + σα ) Q = α P α. α κα mk π (GeV/ c) mdπ (GeV M = mdπ (GeV/ c) D. Craik, T. Gershon, A. Poluektov / c) mdπ 9 7 (GeV M = / c) mdπ Bin number mk π (GeV/ c) Bin number mk π (GeV/ c) mdπ (GeV/ c) Prospects for γ from B DKπ, D K π + π (GeV / c) phase-diff M = Bin number mdπ (GeV/ c) ICHEP, Seoul, South Korea /

24 Effect of removing πk mode and dependence on value Check how removing ADS mode affects sensitivity for different values. ) ( ) σ(γ Run II =. =. =. Without D K π + channel With D K π + channel Number of B bins ) ( ) σ(γ.... fb =. =. =. Without D K π + channel With D K π + channel Number of B bins Effect is larger for smaller, but nothing critical. D. Craik, T. Gershon, A. Poluektov Prospects for γ from B DKπ, D K π + π ICHEP, Seoul, South Korea /