B Hadron lifetimes using a displaced track trigger

Transcription

1 B Hadron lifetimes using a displaced track trigger Why B Lifetimes are interesting Overview one analysis Results and prospects Sneha Malde University of Oxford 1

2 B Hadrons B Mesons B Baryons Name B + B 0 B s B c Quark Content bu bd bs bc 2

3 Hadron lifetime theory (1) B Hadrons not stable particles decay via weak interaction If the lighter quarks are ignored all B hadrons have the same lifetime Presence of the lighter quarks causes the difference in observed lifetimes 3

4 Hadron lifetime theory (2) Destructive interference in B - decays lengthens the lifetime 4

5 Hadron lifetime theory (3) In weak annihilation the B - decay is Cabbibo suppressed, which also lengthens the lifetime in comparison to the B0 Helicity suppression in mesons not baryons From the phenomenological discussion predict a lifetime hierarchy of τ(b u )> τ (B d ) ~ τ(b s ) > τ(λ b )>> τ(b c ) 5

6 Lifetime predictions 1 " = # = G 2 5, Fm b 192$ V & % 3 cb 2 A 0 + A QCD ). 2 ( + -. ' m b * For numerical prediction use HQE Operator Product Expansion - the calculation is rooted in QCD and gives a prediction of lifetime ratios Lifetimes provide a critical testbed for theoretical framework used to predict heavy quark quantities Currently good agreement between theory and experiment Previously saw some discrepancy on 1-2 σ level 2 & % + A QCD ) 3 ( + ' * m b 6 3 / 1 01

7 Λ b Lifetime Theoretical prediction τ(λ b )/ τ(b 0 )=0.88±0.05 Latest result τ(λ b )/ τ(b 0 )=0.922±0.039 Hadronic channel Λ b Λ c π, Λ c pkπ τ(λ b )/ τ(b 0 )=1.018±0.062 Λ b J/ Psi Λ 7

8 Lifetimes test more than QCD Flavor eigenstates and mass eigenstates are different. B light s and B heavy s => Γ L and Γ H, widths inversely proportional to lifetime Γ s = (Γ L +Γ H )/2, ΔΓ = Γ L -Γ H + φ s ~ 2β s Probe to New Physics : ΔΓ= 2 Γ 12 cos(φ s ) B s J/Ψφ - disentangle eigenstates using angular analysis Meausure ΔΓ and φ s simultaneously 8

9 ΔΓ vs β s =( φ s /2) Confidence Limits drawn in ΔΓ vs β s Ambiguity in fit results - Standard Model probability CDF: 7%, ~1.8σ 9

10 Tevatron Booster CDF Tevatron DØ pp collisions at 1.96 TeV p source Main Injector & Recycler production of all types of B hadrons B 0 B ± B s B c Λ b Σ b Ξ b Ω b Collision rate 1.7MHz Trigger reduces rate to ~ 100 Hz Different triggers can select different B decays 10

11 CDF Detector Drift Chamber (COT) tracks charged particles for momentum σ(1/p T ) 2 ~ 0.15% c/gev Silicon (SVX) tracks charged particles for decay vertex position measurement σ (vertex) ~ 30 µm 11

12 Two Track Trigger Trigger accepts events with pairs of tracks with high impact parameters. Data from trigger rich in B hadrons Data used for many exciting results Observation of Σ b, Σ b * B hh A cp measurements 12

13 Effect on lifetime distribution Trigger preferentially accepts B decays with longer lifetimes Biases the distribution A To use data from the two track trigger for lifetime studies need to find a way to correct for the bias B LHCb has a similar trigger 13

14 Methods of bias correction MC Dependent: Use realistic MC to model the trigger efficiency. cτ = ± 13.8 (stat) ± 8.8(syst) µm Systematic uncertainties dominated by data-mc agreement Trigger Efficiency 14

15 Methods of bias correction MC Dependent: Use realistic MC to model the trigger efficiency. Systematic uncertainties dominated by data-mc agreement MC Independent: Use decay kinematics to calculate acceptance. Smaller systematic errors as no reliance on data-mc agreement The future is high statistics No need for MC generation Today s talk Before using technique on Λ b Test on B ± High yield available, Lifetime well known 15

16 Analysis overview Selection Calculate Acceptance Including Background in likelihood Validate method Fit to data Sources of systematic uncertainty 16

17 Selection L xy Yield: 24,200±200 B+ D(K,pi) Pi ct = ML xy P T Candidates found by TTT Further selection criteria applied to optimise signal 17

18 Analysis overview Selection Calculate Acceptance Including Background in likelihood Validate method Fit to data Sources of systematic uncertainty 18

19 Correcting for the Bias Unbiased trigger could accept the event if it decayed at any time. When can the B + decay and still pass the trigger? Slide the event in the direction of B momentum, check at each point if all trigger cuts are passed. π - π - Prim Vtx B + D 0 K + B direction Prim Vtx B + D 0 K + B direction Acceptance π + π + Only 1 IP in range, event not accepted Acceptance Two tracks pass all cuts Acceptance turns on Does the trigger see all tracks? 19

20 Single Track Finding Efficiency " = N o tracks found by trigger (d 0 ) N o tracks found offline (d 0 ) Fast algorithm for finding tracks - used for trigger decision Beyond max trigger cut More tracks found offline Approximate shape ε= ε s, 120<d 0 <1000 µm ε= 0, otherwise ε s becomes a fit parameter 20

21 Correcting Bias (2) Prim Vtx Acceptance B + D 0 π - K + B direction π + Two possible track pairs: Acceptance increases Prim Vtx Acceptance Trigger not passed. Acceptance returns to 0 B + D 0 π - K + π + When can the B + decay and still pass the trigger, and what s the probability the trigger accepts the event? Acceptance function is different for every event 21

22 Lifetime PDF PDF Pure exponential Normalise over acceptance function Include detector resolution Observables: Proper decay time Acceptance function N 0 tracks actually found by trigger Minimise Likelihood Best fit lifetime Track finding efficiency 22

23 Analysis overview Selection Calculate Acceptance Including Background in likelihood Validate method Fit to data Sources of systematic uncertainty 23

24 Full PDF with background P(lifetime s,acc())xp(mass s)xp(s Acc()) + P(lifetime b,acc())xp(mass b)xp(b Acc()) What s this? If the Acceptance distribution is same for signal and bkg: P(s Acc()) P(s) Acceptance function distributions means not the same Technical difficulty: Acc() is a not a scalar variable but a function How do you deal with a distribution of functions? (Can t even draw the distribution!) 24

25 Fit Procedure PDF: P(lifetime s,acc)xp(mass s)xp(s fish) + P(lifetime b,acc)xp(mass b)xp(b fish) Use fisher discriminants to scalar Fit the variation of signal fraction vs scalar variable Determine a parameterization for the lifetime of background events Established fitting functions for all parts Calculate the likelihood Perform combined lifetime fit to extract τ 25

26 Analysis overview Selection Calculate Acceptance Including Background in likelihood P(lifetime s,acc)xp(mass s)xp(s fish) + P(lifetime b,acc)xp(mass b)xp(b fish) Validate method Fit to data Sources of systematic uncertainty 26

27 Method Validation (Does it work? ) P(lifetime s,acc)xp(mass s)xp(s fish) + P(lifetime b,acc)xp(mass b)xp(b fish) This term corrects the trigger bias Ignoring this term gives another bias Use a custom fast MC simulation Reproduces kinematic distributions observed in data Easy to test various assumptions CDF realistic MC 1CPU day ~ 10 3 events Fast MC 1CPU day ~ 10 6 events 27

28 Validation Studies (2) Generate signal+background samples with observed S/B Ignore the P(s fish) term Full PDF Demonstrates ignoring P(s fish) results in additional bias Full PDF corrects for all biases 28

29 Summary on Fast Simulation Studies Further extensive testing carried out using fast simulation Varying data kinematics, trigger properties, selection criteria Biases consistently correct for Method of lifetime measurement works 29

30 Analysis overview Selection Calculate Acceptance Including Background in likelihood P(lifetime s,acc)xp(mass s)xp(s fish) + P(lifetime b,acc)xp(mass b)xp(b fish) Validate method Fit to data Sources of systematic uncertainty 30

31 Fit to data cτ = ± 6.8 (stat) µm PDG = ± 3.3 µm 31

32 Analysis overview Selection Calculate Acceptance Including Background in likelihood P(lifetime s,acc)xp(mass s)xp(s fish) + P(lifetime b,acc)xp(mass b)xp(b fish) Validate method Fit to data Sources of systematic uncertainty 32

33 Sources of uncertainty Use custom fast simulation to test the assumptions Easy to change detector response e.g: Single track finding efficiency, (3.1 µm) 33

34 Systematic errors summary Systematic source of uncertainty ε s (d 0 ) ε s (P T ) Mass Lifetime Correlation Background parameterisation Alignment Bias due to Fitter Resolution model ε s (η) Total Error (microns) Stat error ~ 6.8 µm 34

35 Results CDF B ± D 0 π (Two Track Trigger) cτ = ±6.8 (stat) ±4.5 (syst) µm NO simulation World Average cτ = ±3.1 µm CDF Λ b Λ c π (Two Track Trigger) cτ = ± 13.8 (stat) ± 8.8(syst) µm Dominated by MC-data agreement Updated measurement with >x4 data would benefit from simulation free measurement 35

36 Prospects At CDF exploring measurement techniques for more precise measurement Precision required to test HQE or look for signs of new physics in B s system Simulation free method for correcting selection biases directly applicable to LHCb Large sample sizes in a range of decays at CDF Other baryon lifetimes Exciting times ahead for lifetimes 36

37 Backup 37

38 Theoretical predictions and experimental comparisons Mode τ(b u )/ τ(b 0 ) τ(b s )/ τ(b 0 ) τ(λ b )/ τ(b 0 ) Theoretical Prediction 1.06± ± ±0.05 Experimental results 1.076±0.008 (2007) 0.961±0.018 (2007) 0.844±0.043 (2006) B s : Since then CDF B s lifetime measurements τ(b s )/ τ(b s )=0.99±

39 Check of lifetime PDF in realistic MC Tested in a variety of modes, with different topologies. Full detector simulation used thousand events used B+ Mode Truth Fit Bu Dπ 496 µm 493 ± 3 µm Bs φφ 438 µm 443 ± 5 µm Λ b Λ c π 323 µm 319 ± 6 µm B0 Dπ 464 µm 468 ± 3 µm Use of event-by-event acceptance function corrects for the trigger induced bias 39

40 Basic Fisher Discriminant Analysis 2 classes of events where each event is described by a set of variables Fisher Discriminant will find the direction that maximises separation. Projection of the vector with the best direction now classified by a single number. Requires a set of variables for each event. Turn the acceptance function into variables Use fisher discriminants Get a number. Single number easy to deal with. 40

41 How to make variables out of Each acceptance function is split into its parts, binned and then the entry in each bin forms a column vector This way for each event get a vector V i Perform fisher discriminant analysis 41

42 Fisher Direction, Fisher Scalar This is the fisher direction, w Usually there is a typical signal and background distribution used Use sideband to represent background sample Use sideband subtraction to represent signal sample Fisher Scalar = V i. w P(s acc) P(s fish) 42

43 Extracting signal fraction as function of fisher scalar signal background fisher scalar From fast simulation fisher scalar Divide signal by total to see the distribution of signal prob as a function of fisher scalar Fit function for P(s fish) is 13th order Lagrange interpolation polynomial. 13 free parameters in fit. Fit uses information from all parts of the fit to determine P(s fish) 43

44 ct Background parameterisation P(lifetime s,acc)xp(mass s)xp(s Acc()) + P(lifetime b,acc)xp(mass b)xp(b Acc()) P(t b) = y(t)dt acc y(t)dt takes into account the acceptance function 10 fit points used (a j ) :10 fit parameters added to fit t j chosen appropriately 44

45 Validation Studies (1) Generate 1000 independent signal samples using custom fast simulation that reproduces kinematic distributions observed in data Similar sample size to that found in data Confirms normalisation over acceptance function corrects for selection 45bias

46 Lifetimes test more than QCD Looking ahead B s J/Ψφ B s φφ, B s KK New Physics more likely to be detected in penguin decays. New CP phases enter through decay amplitudes Difference in τ in B s J/Ψφ (L=0), B s φφ (L=0), B s KK imply new physics Will need precision measurements to detect differences 46