Use of binned Dalitz plots to measure at LHCb - Physics at LHCb

Physics at LHCb, Bad Honnef, 28 th April 2011Use of binned Dalitz plots to measure γ atLHCbDaniel Johnson, Sneha Malde, Guy WilkinsonUniversity of OxfordPhysics at LHCb, Bad Honnef28 th April 2011D. Johnson γ in binned Dalitz analyses at LHCb 1 / 16

Physics at LHCb, Bad Honnef, 28 th April 2011Outline1 γ determination in B ± → DK ±2 Multibody D 0 final states3 D 0 phase information from CLEO-cSelf-conjugate final statesNon self-conjugate final states4 Status of analyses at LHCbExpected impact on γ precisionD. Johnson γ in binned Dalitz analyses at LHCb 2 / 16

Physics at LHCb, Bad Honnef, 28 th April 2011Measuring γ using B ± → D 0 ( ¯D 0 )K ±Use interference between b → c and b → u processes:(a) B − → D 0 K −(b) B − → ¯D 0 K −Yields for the B − (or B + ) decays sensitive to γ = arg( V ∗ubV ∗ cb)B − D 0r Be i(δB−γ)D 0r D e −iδDFr B e i(δ B−γ) = A B − → ¯D 0 K −A B − →D 0 K −and similarly for D decayparameters, r D and δ DD. Johnson γ in binned Dalitz analyses at LHCb 3 / 16

Physics at LHCb, Bad Honnef, 28 th April 2011Multibody D 0 final statesIncrease statistical power by combining multibody modes with 2-body B → (hh ′ ) D KModeB ± → (K ± π ∓ ) D K ±Self-conjugate multibodyB ± → (K 0 S π± π ∓ ) D K ±B ± → (K 0 S K ± K ∓ ) D K ±ADS-style multibodyB ± → (K ± π ∓ π ± π ∓ ) D K ±B ± → (K ± π ∓ π 0 ) D K ±B ± → (K 0 S K ± π ∓ ) D K ±an extra hurdle in multibody decays:D 0B − r FBe i(δB−γ)r D e −iδDD 0r D and δ D vary over Dalitz spaceRequire either:1 Phase info from amplitude model3 ◦ → 9 ◦ γ uncertainty or2 Determine averages of the varyingparameters using externalinformation from CLEO-c→ model independentD. Johnson γ in binned Dalitz analyses at LHCb 4 / 16

Physics at LHCb, Bad Honnef, 28 th April 2011Measuring D decay parameters at CLEO-cStrong phase differences in Dalitz space bins can be determinedusing quantum correlated (Q.C.) decays:(a) Q.C. samples (CP tags: KK , K 0 Sπ 0 ...) (b) MC: D CP− → K ππ 0Event density in Dalitz plot ∝ |D 0 | 2 + | ¯D 0 | 2 ± 2|D 0 || ¯D 0 |cos δ⇒Accessing strong phase differences a counting experimentD. Johnson γ in binned Dalitz analyses at LHCb 5 / 16

Physics at LHCb, Bad Honnef, 28 th April 2011Binned approach: self-conjugate final statesThe fit for γThe number of B events in bins 1 (N ± i) of the Dalitz space dependson γ and other quantities:N ± i= h(K ±i + r 2 BK ∓i + 2 √ K i K −i [x ± c i ± y ± s i ]K ±i - number of events for flavour tagged D samplex ± = r B cos(δ B ± γ), y ± = r B sin(δ B ± γ)c i and s i are average of cosine/sine of strong phase difference, overthe binMeasuring c i and s i at CLEO-cReconstruct ‘double tags’ (e.g. D 1 → K S ππ and D 2 →CP) then simplycount yields in Dalitz bins.e.g. Yield(bin ±i) ∝ K i ± 2c i√Ki K −i + K −i1 PRD 68 054018 (2003) and EPJ C 55 (2008) 51D. Johnson γ in binned Dalitz analyses at LHCb 6 / 16

Physics at LHCb, Bad Honnef, 28 th April 2011Binned approach: self-conjugate final statesHow to choose the bins?Binning events reduces statistical sensitivity compared tounbinnedIntelligent choice of bins improves the situationOptimally choose bins 2 ...around regions of expected similar strong phase differenceaccounting for expected B statistics distributiongiven LHCb background shapes in Dalitz plot⇒ lose only 10% of statistical sensitivity compared to unbinnedapproach2 PRD 82, 112006 (2010)D. Johnson γ in binned Dalitz analyses at LHCb 7 / 16

Physics at LHCb, Bad Honnef, 28 th April 2011Results: c i , s i for K 0 S ππResults for 〈cos δ D 〉 and 〈sin δ D 〉, different binning choices 3 :Encouraging to see BaBar model agrees with data3 PRD 82, 112006 (2010)D. Johnson γ in binned Dalitz analyses at LHCb 8 / 16

Physics at LHCb, Bad Honnef, 28 th April 2011Results: c i , s i for K 0 S KKResults for 〈cos δ D 〉 and 〈sin δ D 〉, different binning choices 4 :4 PRD 82, 112006 (2010)D. Johnson γ in binned Dalitz analyses at LHCb 9 / 16

Physics at LHCb, Bad Honnef, 28 th April 2011LHCb: Systematic uncertainty on γ from strong phaseBinned approachThe dominant systematic uncertainty in the binned approach comesfrom uncertainties on c i and s i from the CLEO measurement1.7 → 3.9 ◦ for KS 0 ππ (depends on binning choice)3.2 → 3.9 ◦ for KS 0 KK (depends on binning choice)Unbinned approachModelling systematic in the unbinned approach: 3 → 9 ◦Similar uncertainty, but binned approach systematics originatefrom experimentally measured quantities onlyD. Johnson γ in binned Dalitz analyses at LHCb 10 / 16

Physics at LHCb, Bad Honnef, 28 th April 2011LHCb: KS 0ππ/K S 0 KK statusCurrent status at LHCb in 2010 data: clear signals in control modesEvents / ( 20 MeV )Events / ( 20 MeV )180160140120100806040200302520151050B ± ! D 0 (K 0 " ± " # ) " ±SLHCbPreliminarys = 7 TeV Data-1L int = 33.9 ± 3.4 pbN Signal = 443 ± 32m 0 = 5271.8 ± 1.5 MeV! = 23.5 ± 1.6 MeV5200 5400 5600±Bmass (MeV)B ± ! D 0 (K 0 K ± K # ) " ±SLHCbPreliminarys = 7 TeV DataDataReco 06 Stripping 10 (mag down) and Reco 07 Stripping 11 (mag up)‘B2DXWithD2Kshh’ stripping lineSelectionTracksAll 5 tracks: track $ 2 < 5VerticesD: vertex $ 2 /dof 25(LL) >16(DD)D 0 : PT > 1.5 GeVBachelor: PT > 1 GeVB: Lifetime > 0.2 ps: Pointing angle > 0.9998MassK 0 S window: 15 MeV(LL) 21 MeV(DD)D 0 window: 25 MeV(LL) 40 MeV(DD)PID - K 0 KK onlyD 0 SThese are the mostpions: PID (K - ") > 5important cuts-1pb= 33.9 ± 3.4 L intN Signal = 78.4 ± 9.6Fitm 0 = 5270.9 ± 2.1 MeV! = 22.3 ± 2.2 MeVLow mass PDF:K 0 S"" - gaussian tail, floating mean and widthK 0 SKK - exponential, floating coefficientSignal PDF: single gaussian5200 5400 5600 High mass PDF: linear±Bmass (MeV)Daniel Johnson, 25/11/2010D. Johnson γ in binned Dalitz analyses at LHCb 11 / 16

Physics at LHCb, Bad Honnef, 28 th April 2011LHCb: KS 0ππ/K S 0 KK analysisAnalysis methodBin the LHCb data for B + → DK + and B − → DK − in D 0 Dalitz spaceCorrect for LHCb acceptance, PID efficiencies, production/detectionasymmetriesMeasure γ via fit to B + , B − ratios in bins of Dalitz spaceLHCb Acceptance for B ± → DK ±Use B ± → Dπ ± as control mode, since r Dπ ∼ 0.01 so CP violation negligibleCompare to BaBar model 5 (models Dalitz distribution well) to extract efficienciesSystematics: bachelor kinematics, bachelor PID, efficiency variation within bins5 Phys. Rev. Lett. 105, 081803 (2010)D. Johnson γ in binned Dalitz analyses at LHCb 12 / 16

Physics at LHCb, Bad Honnef, 28 th April 2011Binned approach: non self-conjugate final statesThe fit for γF=(2 body), decay rate:D 0B − rBei(δB−γ) rDe −iδDD 0FΓ(B + → (K + π − ) D K + ) ∝ 1 + (r B r D ) 2 + 2r B r D cos(δ B + γ − δ K π )F=Multibody, integrate equivalent expression over the Dalitz spaceΓ(B + → (K + πππ) D K + ) ∝ 1+(r B r D ) 2 +2r B r D R K πππ cos(δ B +γ−δ K πππ )Rwhere R K πππ e iδ dxAD 0 (x)A ¯K πππ = (x) D0A D 0 A ¯ D0(coherence factor and avg. strong phase difference)Measure R F and δ F at CLEO-cAgain, count yields of ‘double tag’ events at CLEO-ceg:CP tag vs F⇒ R F cos(δ F ), F vs F ⇒ R 2 F , (K π) vs F ⇒ R F cos(δ F − δ K π )D. Johnson γ in binned Dalitz analyses at LHCb 13 / 16

Physics at LHCb, Bad Honnef, 28 th April 2011Results: coherence factors/avg strong phase diff’s22K ππ 0 : high coherenceR K ππ 0 = 0.84 ± 0.07δ K ππ 0 = (227 +14−17 )◦⇒Useful for ADS γK πππ: low coherence aR K ππ 0 = 0.33 +0.26−0.23⇒better r B knowledgePRD 80, 031105 (2009)D→ K K - π +S)2(GeVinvar mπ +0K S01.81.61.41.210.80.60.4Bin 10Bin 2Bin 2Entries 14131 1.5 2 2.5 30 -2 2K S K invar m (GeV )20181614121086420)2(GeVinvar mπ -0K S021.81.61.41.210.80.60.40+-D→ K SKπBin 1Bin 2Bin 21 1.5 2 2.5 3Entries 8050 +2 2K S K invar m (GeV )109876543210KS 0 K π: preliminaryFull DalitzR K ππ 0 = 0.73 ± 0.09δ K ππ 0 = (8.2 ± 15.2) ◦Bin 1R K ππ 0 = 0.96 ± 0.17δ K ππ 0 = (25.8 ± 17.3) ◦D. Johnson γ in binned Dalitz analyses at LHCb 14 / 16

Physics at LHCb, Bad Honnef, 28 th April 2011LHCb: K 3π/K 0 S K π/K ππ0 statusSignal (CF) in B → (K πππ) D K in 2010 data:Expected γ precision using ADS modes (excluding K ππ 0 ) in 2 fb −1 :D. Johnson γ in binned Dalitz analyses at LHCb 15 / 16

Physics at LHCb, Bad Honnef, 28 th April 2011ConclusionsSummary:Multi-body LHCb analyses increase statistical power of γ measurementBinning Dalitz space allows model independence with phaseinformation derived from D 0 measurements at CLEO-cself-conjugate: KS 0ππ and K S 0KKADS-style: K πππ, KS 0 K π and K ππ0Limiting systematic originates from experimentally measured quantitiesat CLEO-c (scope to reduce further at BES III)D. Johnson γ in binned Dalitz analyses at LHCb 16 / 16