Hadronic Moments in Semileptonic B Decays from CDFII

Transcription

1 Hadronic Moments in Semileptonic B Decays from CDFII Alessandro Cerri Hep-ph/ Accepted for publication in PRDRC

2 Analysis Strategy Typical mass spectrum M(X 0 c ) (Monte Carlo): D 0 and D* 0 well-known measure only f** only shape needed 1) Measure f**(s H ) 2) Correct for background, acceptances, bias moments of D** 3) Add D and D* M 1,M 2 4) Extract L, l 1 3/15/05 Alessandro Cerri CKM Workshop 2

3 Channels Possible D D ( * ) ππ contributions neglected: No B ld experimental evidence so far DELPHI limit: BR BR + + ( b D π π l ν ) * + + ( b D π π l ν ) < 90% CL < 90% CL We assume no D contribution in our sample Must reconstruct all channels to get all the D ** states. However CDF has limited capability for neutrals B 0 D **- l + ν always leads to neutral particles ignore it B - D **0 l - ν better, use isospin for missing channels: - D **0 D + π - OK D **0 D 0 π 0 Not reconstructed. Half the rate of D + π - D **0 D *+ π - D *+ D 0 π + OK D *+ D + π 0 Not reconstructed. Feed-down to D + π - D **0 D *0 π 0 Not reconstructed. Half the rate of D *+ π - 3/15/05 Alessandro Cerri CKM Workshop 3

4 Event Topology D **0 D + π **- K - π + π + (Br=9.2%) Exclusive reconstruction of D ** : D + D* + D **0 D *+ π **- D 0 π *+ K - π + K - π + π - π + K - π + π 0 (Br=67.7%) (Br=3.8%) (Br=7.5%) (Br=13.0%) 3/15/05 Alessandro Cerri CKM Workshop 4

5 Backgrounds Physics background: B D ( * )+ D s-, D (s) Xlν MC, subtracted Combinatorial background under the D ( * ) peaks: sideband subtraction Prompt pions faking π**: fragmentation underlying event separate B and primary vertices (kills also prompt charm) use impact parameters to discriminate model: wrong-sign π** + l - combinations Feed-down in signal: D** 0 D* + ( D + π 0 )π - irreducible background to D** 0 D + π -. subtracted using data: shape from D 0 π - in D** 0 D* + ( D 0 π + )π - rate: ½ (isospin) x eff. x BR 3/15/05 Alessandro Cerri CKM Workshop 5

6 Data Sample: e/µ + displaced track ~ 180 pb -1 ( Sept 2003) Lepton + D Reconstruction Total: ~ events Track Selection: 2 GeV track (SVT leg) e/µ: p T > 4 GeV other: p T > 0.4 GeV Lepton + D ( * )+ : D vertex: 3D l+d(+π * ) vertex ( B ): 3D L xy (B) > 500 µm m(b) < 5.3 GeV 3/15/05 Alessandro Cerri CKM Workshop 6

7 Raw m** Distributions Measured in m**, shifted by M(D ( * )+ ), side-band subtracted. D 1,D 1 *,D 2 * Feed-down D 2 *,D 0 * 3/15/05 Alessandro Cerri CKM Workshop 7

8 Efficiency Corrections 1) Correct the raw mass for any dependence of ε reco on M(D**): Possible dependence on the D** species (spin). Monte-Carlo for all D** (Goity-Roberts for non-resonant), cross-checked with pure phase space decays. Detector simulation shortcomings cause residual data/mc discrepancy: derive corrections from control samples (D* and D daughters) 2) Cut on lepton energy in B rest frame: Theoretical predictions need well-defined p l * cut. We can t measure p l *, but we can correct our measurement to a given cut: p l * > 700 MeV/c. 3/15/05 Alessandro Cerri CKM Workshop 8

9 Corrected Mass and D** Moments Procedure: Results (in paper): Unbinned procedure using weighted events. Assign negative weights to background samples. Propagate efficiency corrections to weights. Take care of the D + / D* + relative normalization. Compute mean and sigma of distribution. m m 1 2 = = m 2 D** ( 5.83± 0.16 ) ( 2 ) 2 4 m m = ( 1.30 ± 0.69 ) GeV D** = 1 stat GeV 2 stat No Fit!!! 3/15/05 Alessandro Cerri CKM Workshop 9

10 Final Results ρ(m 1,m 2 )=0.61 ρ(m 1,M 2 )=0.69 Pole mass scheme 1S mass scheme 3/15/05 Alessandro Cerri CKM Workshop 10

11 Stat. Systematic Errors (from the paper) m 1 (GeV 2 ) 0.16 m 2 (GeV 4 ) 0.69 M 1 (GeV 2 ) M 2 (GeV 4 ) 0.26 Λ (GeV) λ 1 (GeV 2 ) Syst. Mass resolution Eff. Corr. (data) Eff. Corr. (MC) Bkgd. (scale) Bkgd. (opt. Bias) Physics bkgd. D + / D *+ BR D + / D *+ Eff. Choice of p l * cut /15/05 Alessandro Cerri CKM Workshop Semileptonic BRs ρ T i α s m b, m c

12 Comparison with Other Measurements Pole mass scheme 3/15/05 Alessandro Cerri CKM Workshop 12

13 Summary First measurement at hadron machines: different environment and experimental techniques. Competitive with other experiments. Little model dependency. No assumptions on shape or rate of D** components. Through integration with other experiments and other moments we can seriously probe HQET/QHD Let s do it! 3/15/05 Alessandro Cerri CKM Workshop 13

14 BACK-UP SLIDES

15 Motivation (I) Most precise determination of V cb comes from Γ sl ( inclusive determination): Γ sl BR ( b cl ν ) ( b cl l 2 ν ) = = Vcb τ b F theory Υ(4S), LEP/SLD, CDF measurements. Experimental V cb ~1% Theory with pert. and non-pert. corrections. V cb ~2.5% F theory evaluated using OPE in HQET: expansion in α s and 1/m B powers: O(1/m B ) 1 parameter: Λ (Bauer et al., PRD 67 (2003) ) O(1/m B2 ) 2 more parameters: λ 1, λ 2 O(1/m B3 ) 6 more parameters: ρ 1, ρ 2, T 1-4 Constrained from pseudoscalar/vector B and D mass differences G sl GFVcb 5 a s c3 a s c5 2 1 as = mb c1{ 1 c2 +? (1 c4 ) + (? + c6? 1 + c7? 2) + O( ) + O( ) p p m p m m p B B B } 3/15/05 Alessandro Cerri CKM Workshop 15

16 Motivation (II) Many inclusive observables can be written using the same expansion (same non-perturbative parameters). The spectral moments: Photonic moments: Photon energy in b s γ (CLEO) Leptonic moments: B X c lν, lepton E in B rest frame (CLEO, DELPHI, BABAR) Hadronic moments: B X c lν, recoil mass M(X c ) (CLEO, DELPHI, BABAR, CDFII) Constrain the unknown non-pert. parameters and reduce V cb uncertainty. With enough measurements: test of underlying assumptions (duality ). 3/15/05 Alessandro Cerri CKM Workshop 16

17 What is X c? Semi-leptonic widths (PDG 04): Higher mass states: D** Br (%) B + X c l n B + D* l n B + D l n ± ± ± 0.15 (PDG b/b + /B 0 combination, b u subtracted) ~25% of semi-leptonic width is poorly known Possible D D ( * ) ππ contributions neglected: No B ld experimental evidence so far DELPHI limit: BR b BR b + + ( D π π l ν ) * + + ( D π π l ν ) < 90% CL < 90% CL We assume no D contribution in our sample 3/15/05 Alessandro Cerri CKM Workshop 17

18 Combination with D 0, D* 0 Take M(D 0 ), M(D* 0 ), Γ sl, Γ 0, Γ * from PDG 2004 : - Γ sl, Γ 0, Γ * are obtained combining BR s for B -, B 0 and admixture, assuming the widths are identical (not the BR s themselves), and using Average: f - /f 0 = ± 0.05 τ(b - )/τ(b 0 ) = ± BR(B + fi X 0 c l+ ν l ) = ± BR(B + fi D 0 l + ν l ) = ± BR(B + fi D* 0 l + ν l ) = ± /15/05 Alessandro Cerri CKM Workshop 18

19 MC vs. semileptonic sample: Monte-Carlo Validation (I) Kππ, e Kπππ, e Kπ, µ Kππ 0, e Kπππ, µ Kππ, e Matching c 2 probability for those plots: 67% 74% 23% 43% 69% 87% 3/15/05 Alessandro Cerri CKM Workshop 19

20 p** Selection Based on topology: impact parameter significances w.r.t. primary, B and D vertices π** 2D IP signif. wrt PV π** 3D IP signif. wrt BV Cuts are optimized using MC and background (WS) data: Additional cuts only for D + : p T > 0.4 GeV R < 1.0 d 0 PV /σ > 3.0 d 0 BV /σ < 2.5 d 0 DV /σ > 0.8 L xy B D > 500µm 3/15/05 Alessandro Cerri CKM Workshop 20

21 P l * Theory prediction depends on P l * cuts. We cannot do much but: see how our efficiency as a function of P l* looks like Use a threshold-like correction Evaluate systematics for different threshold values 3/15/05 Alessandro Cerri CKM Workshop 21

22 V cb measurements V cb from exclusive B decays Large statistics on B d0 D (*) l - ν available and new measurements are coming Present precision (5%) is systematics limited: Experiments: D** states, D s BR Theory: form factor extrapolation, corrections to F(1)=1 can be reduced in the future V cb excl =(42.1 ±1.1 exp ±1.9 theo ) 10-3 (PDG 2002, Vcb review) V cb from inclusive B decays Experiment: large statistics on BR(B X c l - ν) and t B and small systematics V cb incl = (40.4 ± 0.5 exp ± 0.5 Λ,λ ± 0.8 theo ) 10-3 (PDG 2002, V cb review) 3/15/05 Alessandro Cerri CKM Workshop 22

23 D* + Reconstruction and Yields D* + channels: Dm* M(D 0 π * ) M(D 0 ) D ( * )+ l - (+cc) yields: ~ events 3/15/05 Alessandro Cerri CKM Workshop 23

24 MC validation: quantitative Matching-c 2 Kπ Kπ(π 0 ) Kπππ Kππ prob (%) e µ e µ e µ e µ p T (l) p T (D) p T (l-d) d 0 (l) m(l-d) L XY (l-d) L XY (D) L XY (B to D) p T (π*) >0.4 GeV d o (K) R(l-D) R(l-K) p T (K) p T (π) p T (2π) /15/05 Alessandro Cerri CKM Workshop 24

25 Impact Parameters in MC Comparison data/mc for IP: (worst case) Kp Kp π** 2D IP signif. wrt PV π** 3D IP signif. wrt BV Residual corrections: derived from data: p * non-svt D daughters (p T > 1.5 GeV) corrections from double ratios in p T in m** 3/15/05 Alessandro Cerri CKM Workshop 25

26 Computing the X c Moments The D 0 and D* 0 pieces have to be added to the D** 0 moments, according to f where the f i are the fractions of D i l events above the p l *cut. Only ratios of f i s enter the final result. 3/15/05 Alessandro Cerri CKM Workshop 26

27 P l * Theory prediction depends on P l * cuts. We cannot do much but: see how our efficiency as a function of P l* looks like Use a threshold-like correction Evaluate systematics for different threshold values 3/15/05 Alessandro Cerri CKM Workshop 27

28 Lepton momentum cut-off We are not literally cutting on Pl* (it is not accessible, experimentally) Detector implicitly cuts on it Assume a baseline cut-off Vary in a reasonable range to evaluate systematics We use f to derive f**, given f 0, f* f=f(λ,λ 1 ) We use experimental prior knowledge on Λ,λ 1 to evaluate systematics Effect is negligible 3/15/05 Alessandro Cerri CKM Workshop 28

29 Efficiency vs m** 3/15/05 Alessandro Cerri CKM Workshop 29

30 MC/Data corrections Dominant source of systematics! π* reproduces π** topology but statistics too low: Use all D* candidates Cross check on non-triggering D 0 daughters (helps for p T ) 3/15/05 Alessandro Cerri CKM Workshop 30

31 Background Subtraction Use mass side-bands to subtract combinatorial background. Use D* + [fid 0 π + ] π - to subtract feed-down from D* + [fid + π 0 ] π - to D + π -. Use wrong-sign π** + l - combinations to subtract prompt background to π**. Possible charge asymmetry of prompt background studied with fully reconstructed B s: 4% contribution at most. 3/15/05 Alessandro Cerri CKM Workshop 31

32 BACK-UP: details on systematics

33 Input parameters Systematics D ( * )+ Masses, in combining D ( * ) with D** m M [PDG errors] BR (B D + /D* + m M) [PDG errors] Experimental Detector resolution [re-smear satellite sample by full resolution: ±60MeV] Data/MC Efficiency discrepancies [measure P t and m dependency on control sample, probe different fit models] Decay models in MC [full kinematic description vs pure phase space] P l * cut correction [repeat measurement at various P l * thresholds] Backgrounds Scale [charge correlation WS/RS from fully reconstructed B: ±4%] Optimization Bias [repeat optimization procedure on bootstrap copies of the sample] Physics background [vary ±100%] B X c τν [estimate τ/µ yield and kinematic differences using MC] Fake leptons [no evidence in WS D + l +, charge-correlated negligible] 3/15/05 Alessandro Cerri CKM Workshop 33

34 Data-based study 1. Extract a bootstrap sample a of the data 2. Optimize get new set of cuts 3. Evaluate bias with respect to the parent distribution (initial data) with new cuts We can repeat this 50 times and obtain 50 independent estimates of the bias(es) CPU intensive [~5 hours/(bootstrap+optimization+ fit )] Mean of those estimates is an unbiased estimator of the bias (as long as the data is a good representation of the ideal distribution) σ is a convolution of: 1) Intrinsic fluctuation of bias 2) Statistical fluctuation of a after cuts µ=bias Bootstrap 3/15/05 Alessandro Cerri CKM Workshop 34 a Optimize Selection m 1a,m 2 a σ=(bias fluctuation) (statistical uncertainty) Data Cuts! - Bias! Selection m 1 unb,m 2 unb

35 Physics Background Physics background studied with B D ( * )+ D s - Size wrt signal: ε BR ~7% (*) + BR ( ) ( B DsD ) D lx s ~7% BR ( B signal) ~1 100% uncertainty 1.5 Other modes 3/15/05 Alessandro Cerri CKM Workshop 35

36 τ Background A problem if observed m** distributions are different! Two possible sources of difference: Kinematics: different m** distribution to begin with because m(τ)/m(b) >> m(e/µ)/m(b) Different reconstruction efficiency Study with generator-level MC + smearing + trigger & reco. parameterization Conclusion: [B ld**τ]/[b ld**µ] 2% Difference in m** acceptance is ~10% and mass-independent irrelevant m(τ)/m(b) matters only for the nonresonant component which is in MC 13% of the overall distribution I.e. 13%x2% small [( m 1, m 2 ) (0.01 GeV 2,0.065 GeV 4 )] is evaluated on the above montecarlo, the overall BKG systematics is (0.02,0.1)) BfilD**t Not a Significant Source of Systematics 3/15/05 Alessandro Cerri CKM Workshop 36

37 Fake Correlated Leptons For background which is sign correlated the nastiest source is D** (-) π + X where we mismatch π + as a fake lepton: C=D 0 C=D *0 C=D 1 *0 Clν 2.2% 6.5% 0.56% Cπ Cρ 0.5% 1.3% 0.5% 1% 0.15% <0.14% Decreasing efficiency AND BR Assuming: An average efficiency equal to the one for signal Overall BR(B D** (-) π + X) is at most 3xBR(B D** (-) l + X) From Run I + Run II studies from Masa, e+µ fakes are about 1.6% in total for this trigger We get a fake count of ~2.4% the signal Kinematic m** bias much smaller than for the τ background case Similar fake rate As negligible (or more favorable) than t 3/15/05 Alessandro Cerri CKM Workshop 37

38 One fit to combine them all, one fit to find them! (Λ λ) Fit based on Bauer et al. (hep-ph/ ) Fit (Λ,λ 1 ) in the pole scheme to moments vs p l * cut Not including all the CLEO points Including BELLE s (thanks to the BELLE folks for privately providing the correlations) 3/15/05 Alessandro Cerri CKM Workshop 38

39 Statistical Weight All All but BABAR All but BELLE All but CDF All but CLEO All but DELPHI 3/15/05 Alessandro Cerri CKM Workshop 39

40 Statistical Weight All All but BABAR All but CDF Same fit as previous page, but excluding single experiments CDF contribution is significant Only BABAR Only CDF 3/15/05 Alessandro Cerri CKM Workshop 40