Measurement of the Measurement of the

Lifetime in the Decay ModeLifetime in the Decay Mode

Robyn MadrakRobyn Madrak

Harvard UniversityHarvard University

Ëb

Ëb ! J = Ë

LEPP Journal ClubLEPP Journal Club

January 22, 2004January 22, 2004

2

• First seen First seen unambiguously at CDF in unambiguously at CDF in – Only measured massOnly measured mass

Decay ModesDecay Modes

• Lifetimes measured at Lifetimes measured at – CDF/LEP inCDF/LEP in– LEP in baryon decays tagged by LEP in baryon decays tagged by

Ëb ! J = Ë

Ëb ! Ëcl÷ö

Ël

3

Why measure the Lifetime ?

• Test theoretical models used in predictions of Test theoretical models used in predictions of heavy quark quantitiesheavy quark quantitiesNot only interesting in themselves - need to extract Not only interesting in themselves - need to extract

weak interaction quantities from measureablesweak interaction quantities from measureables

• Currently, experiment and theory disagreeCurrently, experiment and theory disagree

• Besides this measurement, lifetime measured Besides this measurement, lifetime measured only in semileptonic decay modesonly in semileptonic decay modes

• Initially expected to have huge amount of data Initially expected to have huge amount of data by now by now very competitive measurement very competitive measurement

Ëb

4

• Theory predictions work well for Theory predictions work well for • But not (though others claim 0.85 could be But not (though others claim 0.85 could be

accommodated)accommodated)

Discrepancy:Discrepancy:

Bà ;Bs

Ëb

5Ëb

Measurements up to NowMeasurements up to Now

all semileptonicall semileptonicmeasurementsmeasurements average b-baryonaverage b-baryon

lifetimelifetime

6

Sources of Lifetime DifferencesSources of Lifetime Differences

In the simple spectator model, same lifetime for In the simple spectator model, same lifetime for all hadrons with same heavy quarkall hadrons with same heavy quark

• The heavier the quark, the more valid the The heavier the quark, the more valid the approximationapproximation

• With more sophisticated theory, lifetimes are With more sophisticated theory, lifetimes are different, due todifferent, due to

Pauli InterferencePauli Interference Weak Annihilation (for mesons)Weak Annihilation (for mesons) Weak Exchange, or scattering (for baryons)Weak Exchange, or scattering (for baryons)

È(b) = 192ù3

9V2cbG

2FM

5b

7

Sources of Lifetime Differences:Sources of Lifetime Differences:1.) Pauli Interference1.) Pauli Interference

Same final state=>interference

Different finalstates

8

• Only in mesonsOnly in mesons• In B but not B

Sources of Lifetime Differences:Sources of Lifetime Differences:

2.) Weak Annihilation2.) Weak Annihilation

-- 00

9

Sources of Lifetime Differences:Sources of Lifetime Differences:

3.) Weak Exchange: Main source of lifetime 3.) Weak Exchange: Main source of lifetime difference for difference for

• Helicity suppressed in mesons, but not Helicity suppressed in mesons, but not baryons (no antiquarks)baryons (no antiquarks)

B 0=(Ë b)

10

• Upgraded for Upgraded for Run IIRun II

• cm energy of 1.96 TeV (was 1.8)

• 36p on 36pbar bunches (was 6X6)

• 396 ns bunch crossing time: required many detector upgrades (was 3.5 us)

The Fermilab p pbar Accelerators

11

The CDFII DetectorThe CDFII Detector

Time of FlightCentral Calorimeter

Plug Upgrade Calorimeter

Beamline

Silicon Vertex Detector(SVXII)

Drift Chamber(COT)

Solenoid

CMU CMP

CMX

Muon Chambers

12

The CDFII DetectorThe CDFII Detector

13

The COTThe COT

•End view: Fraction of the endplateEnd view: Fraction of the endplate

Closeup of cell layoutCloseup of cell layout

in 1 superlayerin 1 superlayer

•8 “superlayers8 “superlayers” ” • alternating planes of sense alternating planes of sense wires (readout) and field wires (readout) and field sheets(ground)sheets(ground)• alternating axial and stereo alternating axial and stereo (2 °) superlayers(2 °) superlayers

field

shee

t

sense

plane

1 cell

14

The COTThe COT

SegmentsSegments

(in 8 layers)(in 8 layers)

field

sh

eet

field

sh

eet trac

trac

kk

sense wiressense wires

field sheet

Tracking in a Nutshell:Tracking in a Nutshell:•Form line segments in 4 axial layersForm line segments in 4 axial layers•Do axial fit, connecting segmentsDo axial fit, connecting segments•Form segments in stereo layersForm segments in stereo layers•Add stereo segments to fitAdd stereo segments to fit•Final fitFinal fit

15

This measurement: Full ReconstructionThis measurement: Full Reconstruction

•• ReconstructReconstruct

Cons:Cons:• Fewer events - larger statistical errorFewer events - larger statistical error

Pros:Pros:• Potentially smaller systematic errorPotentially smaller systematic error• Less background due to full recoLess background due to full reco• Have a signal invariant mass peak Have a signal invariant mass peak signal and signal and

background regions well definedbackground regions well defined• Good vertex for decay length (use multiple tracks)Good vertex for decay length (use multiple tracks)• Do not rely on MC as in semileptonic case (can’t Do not rely on MC as in semileptonic case (can’t

measure momentum of measure momentum of boost(boost() is unknown) is unknown

Ë B ! J = Ë :

Ë ! pù J = ! ö+öà

p+;ùà ;ö+öà

baryon equiv. of golden baryon equiv. of golden modemode J = K 0

s

16

Data SampleData Sample

Muon stubsMuon stubs(J(J

Pion trackPion trackProton Proton tracktrack

MC event

• 65 pb^-1 with SVX fully 65 pb^-1 with SVX fully functionalfunctional

• J/J/sample: from sample: from dedicated J/dedicated J/triggertrigger

Level 1: Two online, opp. Q Level 1: Two online, opp. Q tracks, pT>1.5 GeV, good tracks, pT>1.5 GeV, good track-stub match (CMU or CMX)track-stub match (CMU or CMX)

Level 2: AutoLevel 2: Auto Level 3: Full tracking, cut on Level 3: Full tracking, cut on

mmtrack-stub matchingtrack-stub matching

• ReconstructingReconstructing pp:: compute invariant mass of all compute invariant mass of all

opp. Q tracksopp. Q tracks use p/use p/mass hypothesis for mass hypothesis for

higher/lower momentum higher/lower momentum particle (Need maximal particle (Need maximal efficiency: efficiency: No dE/dx or TOFNo dE/dx or TOF))

17

Scheme for Measuring the LifetimeScheme for Measuring the Lifetime

• Use control Use control sample:sample:

• kinematically kinematically similarsimilar

• well-known well-known lifetime:lifetime:

B 0 ! J = K 0s

462æ5öm

same cuts except for a few cases (msame cuts except for a few cases (mnot m(Ks))not m(Ks)) 4 track kinematic fit: vertex constrain J/4 track kinematic fit: vertex constrain J/and and or Ks (Vor Ks (V00’s)’s) Mass constrain MMass constrain Mto world average m(Jto world average m(J(better mass resolution)(better mass resolution) Constrain Ks to “point” back to J/Constrain Ks to “point” back to J/

• Measure control sample lifetime Measure control sample lifetime agrees with world average? If so, measure agrees with world average? If so, measure b b lifetimelifetime

cc= 2.7 = 2.7 cm cc= 7.9 7.9 cm

18

Analysis CutsAnalysis CutsQuantity Value Purpose

Tracks N(COT axial) > 20 well -measured momenta

N(COT stereo) > 16

Muons > 2 r SVX hits well -measured Lxy

pT()>1.5 GeV reinf orce trigger

J / prob() > 0.1% quality vertex

3.01 < m() < 3.17 GeV

V0 prob() > 0.1% quality vertex

Lxy > 0.25 cm bg rejection

Ks 0.477 < m() < 0.517

pT() > 0.4 GeV

1.104 < m(p) < 1.128

! 0.48 < m() < 0.513 Ks veto

B/ b prob() > 0.1% good 4-track vertex

cos > 0.9999 pointing

•No dE/dx cutNo dE/dx cut•No TOFNo TOF

use in future use in future with more with more statisticsstatistics

bb: Need max : Need max efficiency nowefficiency now•pt cut only for pt cut only for ’s ’s from Kfrom Kss, not , not efficient for efficient for •get rid of Bget rid of B•remove pairs of remove pairs of real J/real J/ and and or K or Kss that are not B, that are not B, bb

00

00

19

J/ Candidates

• ~600k candidates ~600k candidates with 3 or more with 3 or more r-r- SVX hitsSVX hits

• S/B = 5.1S/B = 5.1• width = 17.6 MeVwidth = 17.6 MeV

20

•Very clean Very clean Most B/ Most B/bb background comes from pairs background comes from pairs of real J/of real J/ and real K and real Kss, ,

Ks and Candidates After Cuts

0

0

21

Event Yields: B control sampleEvent Yields: B control sample00

22

Event Yields: Event Yields: bb

Same cuts as for

Same cuts as for B 00

•J/J/ K Kss background: expect 1 event at <= 5.5 GeV background: expect 1 event at <= 5.5 GeV

23

A A b b candidate event in datacandidate event in data

muon tracksmuon tracks

protonproton

pionpion

24

Proper Decay TimeProper Decay Time

• Need proper decay Need proper decay

time ct for each eventtime ct for each event primary vertexprimary vertex secondary vertexsecondary vertex

• Need pNeed pTTbb ct = L áì í1 = L ápB

mB = L xy ápBT

mB

500 500 mm

10 cm10 cm

25

Unbinned Maximimum Likelihood FitUnbinned Maximimum Likelihood Fit

• Fit mass histogram to determine Fit mass histogram to determine signal/background regions, and signal/background regions, and background fraction fbackground fraction fbb

• Functional for for ct in signal Functional for for ct in signal region:region:

GG::detector resolution smearingdetector resolution smearing

Exp: real long lived distributionExp: real long lived distribution

• And in background region:And in background region:

• Fit signal and background simultaneouslyFit signal and background simultaneously

F isig(cüB) =

Exp(cti;cüB) ê G(cti;ûict;sct)

F ibgr = (1à f à à f +) áG(cti;ûi

ct;sct)õà

f à áe(ct) i=õà; (ct)i < 0õ+

f + áe(àct) i=õ+; (ct)i > 0++{

26

Control Sample MysteryControl Sample Mystery

• The control sample The control sample lifetime came out low!lifetime came out low!

ct=363 ct=363 27 27 m m

PDG = 462 PDG = 462 mm

significance = 3.7significance = 3.7

Why???Why???

• Measured the correct Measured the correct lifetime with 5k B lifetime with 5k B events with full events with full simulation simulation

• Checked for fitter Checked for fitter bias/bugs using Toy MC bias/bugs using Toy MC (next)(next)

00

27

• Want to check fit for any possible bias, bugsWant to check fit for any possible bias, bugs Generate 5k “fake” experiments (Toy MC)Generate 5k “fake” experiments (Toy MC)

these have:these have:

Fitter Checks with Toy MC

° same number of events as in data, same S/Bsame number of events as in data, same S/Bº distributions functional forms same as in datadistributions functional forms same as in dataº errors on cerrors on c drawn from a histogram (of data drawn from a histogram (of data

errors)errors)B toy MC B toy MC

generated cgenerated c= 414 = 414 mm

ave fit cave fit c = 413 = 4130.450.45

B toy MC - cB toy MC - cPULLPULL

fit mean = 4 fit mean = 4 2 2 mm

width = 1.05 width = 1.05 0.02 0.02

28

Answer: COT Tracking AlgorithmsAnswer: COT Tracking Algorithms

00

• Two algorithms:Two algorithms:1 SL (from Run I) links full line SL (from Run I) links full line

segments (in each of 8 layers)segments (in each of 8 layers)2 HL (new) for high pT efficiency HL (new) for high pT efficiency - looks for looks for hits along a line to hits along a line to

the beamlinethe beamline after finding an after finding an outer layer segment outer layer segment

- easy to believe it would be easy to believe it would be biasedbiased - - ISIS biased for Kbiased for Kss

Use ONLY HL:Use ONLY HL:

cc= =

3383383636mm

Use ONLY SL:Use ONLY SL:

cc= =

4144143131mm

•ALSO:ALSO:•by dropping by dropping “supplementary“supplementary” algorithm, we ” algorithm, we lose NO eventslose NO events

For this For this analysis analysis

we use SL we use SL onlyonly

SegmentsSegments

(in 8 layers(in 8 layers))

29

Fit for B Control SampleFit for B Control Sample00

within 1.5 within 1.5 of of PDG world ave of PDG world ave of

462462 mm

(tails)

-

+(tails + real long-lived bg)

G (prompt bg)

F = (1à f b)F s + f bF b

F s = G ê Exp(cü)F b = (1à f + à f à ) â G

(f +=õ+) áe(ct=õ+) ct < 0(f +=õ+) áe(à ct=õ+) ct > 0+{Fit Results

fit quantity value error

c 414um 31

sct 1.26 0.05

f - 0.029 0.009

- 499um 139

f + 0.13 0.02

+ 307um 43

f b 0.571 0.028

30

Fit for Fit for b b LifetimeLifetime

cü(Ë B = 374æ78 öm) = 1:25æ0:26 ps

31

Cross Checks and SystematicsCross Checks and Systematics

•Cross Checks:Cross Checks:•Fitting MethodFitting Method•Splitting of data into separate samplesSplitting of data into separate samples•Treatment of long-lived particles (VTreatment of long-lived particles (V00’s)’s)

•SystematicsSystematics•SVX AlignmentSVX Alignment•Fitting ModelFitting Model•Gaussian resolution functionGaussian resolution function•““Careful Systematics” (from cross checks)Careful Systematics” (from cross checks)

32

• Fit mass and ct distributions simultaneously:Fit mass and ct distributions simultaneously:

• gaussian: gaussian:

• linear:linear:

• Fit parameters:Fit parameters:

Alternative Fitting MethodAlternative Fitting Method:2d Simultaneous :2d Simultaneous Mass and Lifetime FitMass and Lifetime Fit

F ilik = (1à fB) áF i

sig áM isig + fbgr áF i

bgr áM ibgr

M isig

M ibgr

f cü;sct;fB;f+;fà ;õ+õà ;

mB;ûmB;C 0g

33

Cross Check #1: Results with 2d Simult. FitCross Check #1: Results with 2d Simult. Fit

• With this fit:With this fit:

• With separate fit:With separate fit:

B B 00 bb

• With this fit:With this fit:

• With separate fit:With separate fit:

420æ42öm

414æ31öm

351æ69öm

374æ78öm

34

Cross Check #2: Luminosity Effect in Control Sample

•Observed B mass width larger in later data than in earlierObserved B mass width larger in later data than in earlier•Could not find specific change in detector configuration as causeCould not find specific change in detector configuration as causeDivide data into bins of instantaneous luminosityDivide data into bins of instantaneous luminosity

Low Low lumilumi

hi lumihi lumimid mid lumilumi

L < 1:17 cmà 2sà 1

1:17< L < 1:7 cmà 2sà 1

L > 1:7 cmà 2sà 1

35

Cross Check #2: Luminosity Effect in B Cross Check #2: Luminosity Effect in B Control SampleControl Sample

Standard (separate) fit:Standard (separate) fit:•low lum:low lum:

4384383939mm

00

OKOK ( (only 0.8 only 0.8 differencedifference) )

Standard (separate) fit:Standard (separate) fit:•hi lum:hi lum:

3833835555mm

36

Cross Check #3:Treatment of VCross Check #3:Treatment of V0 0 ‘s‘s

•KKss and and are long-lived (c are long-lived (c=2.7 cm and 7.9 cm)=2.7 cm and 7.9 cm)•Many decay outside of SVXMany decay outside of SVX•We use only SVX hits consistent with being on tracksWe use only SVX hits consistent with being on tracks

(based on COT-only info)(based on COT-only info)

•A reasonable analysis may have rejected all SVX hits for A reasonable analysis may have rejected all SVX hits for VV00’s’s

37

VV00 Tracking: Cross Check Results for B Tracking: Cross Check Results for B

•With COT-only tracks With COT-only tracks for Ks, lifetime is for Ks, lifetime is smaller:smaller:

Compare to 414 Compare to 414 31 31 mm

• But in that case, the But in that case, the sample changes, and sample changes, and the difference is still < the difference is still < 1 1

OKOK

00

38

Getting the systematic:Getting the systematic:

Use higher statistics Use higher statistics

B B J/ J/KK Try a series of “inferior” Try a series of “inferior” alignment tablesalignment tables Also try alignment where Also try alignment where SVX wafers are “bowed” out SVX wafers are “bowed” out systematically by 100systematically by 100mm Quantify variation in Quantify variation in lifetime: lifetime: 5 5 mm

Systematic #1: SVX AlignmentSystematic #1: SVX Alignment

Barrel Barrel 11

Barrel Barrel 33

Barrel 2Barrel 2

Projection: Projection: RMS = 7 RMS = 7

mm

80 80 mm

d vs. d vs. : : 3 3

barrels:barrels:

++++

39

Systematic #2: Fitting ModelSystematic #2: Fitting Model

•Current model is well motivated, but can imagine Current model is well motivated, but can imagine others:others:

> Convolute background exponentials with gaussian resolutionConvolute background exponentials with gaussian resolution

(instead of adding)(instead of adding)

B lifetime is 11 B lifetime is 11 m lowerm lower > Add an additional positive going tail in background functionAdd an additional positive going tail in background function

no changeno change> Use mass Use mass errorserrors and fit for scale factor on mass errors and fit for scale factor on mass errors

instead of B widthinstead of B widthB lifetime is 22 B lifetime is 22 m higherm higher

> Separately fit sidebands and signal regionSeparately fit sidebands and signal regionB lifetime is 2 B lifetime is 2 m higherm higher

•Take largest variation as sytematic: 22 Take largest variation as sytematic: 22 mm

40

Systematic #3: Resolution FunctionSystematic #3: Resolution Function

1 ) Fit for s) Fit for sctct: scale : scale factor for resolution - factor for resolution - 1.26 1.26 0.05 0.052) Other studies with ) Other studies with inclusive J/inclusive J/’s (not ’s (not specifically B’s):specifically B’s):

3) Fit those results to a ) Fit those results to a functionfunction

4) Scale our errors by function and ) Scale our errors by function and fix sfix sctct to 1.0 in lifetime fit to 1.0 in lifetime fit

5) Remeasure B lifetime: ) Remeasure B lifetime: 11m m smallersmaller

f 1:075 9ô pT(J = ) ô 101:036 pT(J = ) > 10

0:950+ 0:0308ã(pT(J = ) à 2:86) pT(J = ) < 9

41

Luminosity Effect in B Control Sample Luminosity Effect in B Control Sample Revisited: Cross Check of a Cross CheckRevisited: Cross Check of a Cross Check

•BUT with BUT with 2-d simultaneous2-d simultaneous fitfit::

•low lumi: low lumi: 45545540 40 mm, hi lumi: , hi lumi: 32432450 50 mm: : 22 difference difference•STILL USE SEPARATE FIT FOR CENTRAL VALUE, THOUGHSTILL USE SEPARATE FIT FOR CENTRAL VALUE, THOUGHAssign systematic for Assign systematic for bb as as = 25 = 25mm

where cwhere chhii L) L) is from the separate fit is from the separate fit

•Separate fit:Separate fit:•low lum:low lum:

4384383939mm•high lum:high lum:

3833835555mm

•All OKAll OK

((only 0.8 only 0.8 differencedifference))

00

N s(total)N s(hi L) â (cüpdg à cü(hi L))

42

VV00 Tracking: Results for B Tracking: Results for B

•The worry here: Very small lifetime for COT-only in The worry here: Very small lifetime for COT-only in smallest bin of Lsmallest bin of Lxyxy(K(Kss))

00

• Looked into treatment of Ks before… Looked into treatment of Ks before… now we look a little deeper…now we look a little deeper…•Divide into bins of Lxy(Ks):Divide into bins of Lxy(Ks):

Cross check Cross check from before:from before:

this was OKthis was OK

43

VV00 Tracking: Another Effect Tracking: Another Effect

• Given this and the previous effectGiven this and the previous effect, Assign systematic , Assign systematic as:as:cü(B o)(our method) à cü(B 0)(COT à only K 0

s) = 26öm

Allows SVX hits when appropriateAllows SVX hits when appropriate

44

SummarySummary

*From Bs lifetime control sampleFrom Bs lifetime control sample

(world average = 1.229 (world average = 1.229 0.080 ps0.080 ps ))

cü(Ëb) = 374æ78(stat:) æ43(syst:)öm

Source Value(m)

ct Resolution function 1

SVX Alignment * 5

Occupancy 25

Fitting Model 22

V0 Tracking 26

Total 43

•Systematics:Systematics:

ü(Ëb) = 1:25æ0:26(stat:) æ0:14(syst:)ps

45

ImplicationsImplications

withwith

•cc((bb) = 374 ) = 374 89 89 mm (this measurement)(this measurement)

•cc(B) = 462 (B) = 462 5 5 mm

ü(B0)ü(Ëb) = 0:81æ0:19

46

More Data: PredictionsMore Data: Predictions

< 10% error < 10% error with 3X more datawith 3X more dataAlready on tape!Already on tape!

47

ConclusionsConclusions

We’ve measured the We’ve measured the bb lifetime in lifetime in bbJ/J/

From this we extract a lifetime ratio which is From this we extract a lifetime ratio which is consistent both with theory and the current world consistent both with theory and the current world averageaverage

(Though the two of those disagree)(Though the two of those disagree)

This result will be much more interesting with 3 This result will be much more interesting with 3 times the datatimes the data (The data are available now! Work in progress...)(The data are available now! Work in progress...)

ü(Ëb) = 1:25æ0:26(stat:) æ0:14(syst:)ps

48

Operator Product ExpansionOperator Product Expansion

• Coefficients cCoefficients cii calculable calculable within perturbation theorywithin perturbation theory

•Matrix elements contain Matrix elements contain long-distance physicslong-distance physics

•Terms 1 and 2 calculable Terms 1 and 2 calculable both for mesons and both for mesons and baryonsbaryons•Term 3 is for PI, WA, and Term 3 is for PI, WA, and WS, harder for baryonsWS, harder for baryons

•lifetime differences lifetime differences between mesons begin in between mesons begin in term 3, between baryons term 3, between baryons and mesons in term 2 and mesons in term 2