Sinéad M. Farrington

University of Liverpool

MCNet School Durham April 2007

Bs Mixing at CDF:The need for MC

0

2

Observation of Bs Mixing

-Last year the phenomenon of mixing was observed for the first time in the Bs meson system

I shall:

•Explain why Bs mixing is interesting

•Explain briefly the experimental method to measure it

•Show how we relied on MC and, crucially, how we assessed the associated systematic errors

Bs PhysicsBound states:

b

s

b

s

Bs0 Bs

0

MATTER

ANTIM

ATTER

Matterantimatter:

0

• The mass eigenstates (H and L) are superpositions of Bs and Bs

• System characterised by 4 parameters:

masses: mH, mL lifetimes: H, L (=1/)

• Predicted ms around 20ps-1

• No measurements of ms have been made until now:

• B factories do not produce Bs Mesons

• Limits set by LEP, SLD, Tevatron

0 0

b s

s b

u, c, t, ?

u,c,t,?

Bs0 Bs

0W+ W-

NEW PHYSICS?

occurs

via

Vts

Vts*

2*22

2222

6

)/(tbtsBBB

WtWFs VVBfm

mmSmGm

sss

"I have no satisfaction in formulas unless I feel their numerical magnitude." (Kelvin)

from md

from md/ms

Lower limit on ms

4

Why is ms interesting?

1) Probe of New Physics - may enter in box diagrams

2) Measure CKM matrix element:

md known accurately from B factories• Vtd known to 15%• Ratio Vtd/Vts md/ms related by constants:

• (from lattice QCD) known to ~4%

• So: measure ms gives Vts

Standard Model Predicts rate of mixing, m=mH-mL, so Measure rate of mixing Vts (or hints of NEW physics)

2

2

2

td

ts

B

B

d

s

V

V

m

m

m

m

d

s

CKM Fit result: ms: 18.3+6.5 (1) ps-1

5

Measuring ms

mttBBNtBBN

tBBNtBBNtA

ssss

ssss

cos

))(())((

))(())(()(

0000

0000

In principle: Measure asymmetry of number of matter and antimatter decays:

In practice: m is measured by more complex techniques: amplitude scan and likelihood profile

H. G. Moser, A. Roussarie, NIM A384 (1997)

tmADeP

tmADeP

s

t

BB

mix

s

t

BB

unmix

sB

s

s

sB

s

s

cos12

1

cos12

1

Test Case: B0

d mixing

6

Mixing Ingredients

1) Signal samples - semileptonic and hadronic modes

2) Time of Decay - and knowledge of Proper decay time resolution

3) Flavour tagging - had the B mixed when it decayed? - opposite side - same side (this is where the main MC application enters!)

Whichever technique is used, the information we need to extract from the events is:

7

Flavour Tagging

To determine B flavour at production, use tagging techniques:b quarks produced in pairs only need to determine flavour of one of them

jet charge

soft leptonb hadron

fragmentation K

Bs

Ds

Opposite side Same Side

To know whether a B meson “mixed” or not, need to know1) flavour (B or B) when it was produced2) flavour (B or B) when it decayed

SAME SIDESame Side K Tag

D2 = 4.8±0.04 %(semileptonic) 3.5±0.06 % (hadronic)

OPPOSITE SIDESoft Muon Tag semileptonic BR ~10%Soft Electron TagJet charge tag sum of charges in jet D2 = 1.82±0.04 % (semileptonic) 1.81±0.10 % (hadronic)Figure of merit is D2 = efficiency (% events tagger can be applied) D = dilution (% events tagger is correct)

8

Calibrating Flavour Taggers

e-/-

Bd

D- Opposite side

Opposite side: can be calibrated with a sample of any B meson:1) Take sample of B+/Bd (mixing behaviour known) – “same side”2) Calculate how many B’s in that sample mixed3) Look on opposite side for leptons4) How often is there a lepton? (efficiency, )5) How often is it the correct sign? (dilution, D)

b b

c

This is a completely data driven method to obtain the tagger power BUT! We can’t apply this to the same side tagger!

e

Same Side

• This is the first time this type of tagger has been implemented

• Completely different principle from opposite side tags

• charge of B and K correlated

• Use Time Of Flight detector, dE/dx information from tracking detector to select Kaon track

• The kaon is also selected based on its kinematics

• The dilution and efficiency of this tagger cannot be calibrated independently of the B meson type (in Bd case, we would have a pion instead: pion ID different, fragmentation of Bd could be different)

9

Same Side Kaon Tagger

Bs0

s

b

s u u

K+}

b

Entirely new calibration strategy is needed

• If MC reproduces distributions well for B0,B+, then rely on it to predict tagger dilution and efficiency in Bs (with appropriate systematic errors)

• High statistics Bd and B+ samples in which to make data/MC comparisons:

• Compare e.g. transverse momentum distributions

• split into particle content (pions, kaons, protons)10

Same Side Kaon Tagger CD

F P

ublic N

ote

820

6

tagging track tagging track

• Then enhance kaon fraction by making selection on particle ID

• Check still get good comparison within available statistics

• (assign systematic error for this comparison)

11

Same Side Kaon Tagger

Two key points:1) this was not achieved by using “out of the box” Pythia 2) after finding a good comparison, most important to assign

systematic errors

• Each of these modifications is driven by previous measurements, and then associated systematic errors are assigned

• Data and MC are used in tandem (and consultation with theorists on what are “reasonable” variations to assess systematics)

• Multiple proton-antiproton interactions

• Fragmentation Model

• As well as usual GEANT detector simulation, specific response of particle ID systems treated especially for this analysis

• Trigger prescales

12

Modifications to MC

After these modifications we make a comparison of all of the relevant variables between MC and data for all B meson types

will discuss further

• More than one pp pair can interact in a bunch crossing

• Gives rise to additional particles (usually low momentum)

• These could be additional SSKT tagging tracks

• Pythia does have a switch to simulate this

• but in this analysis data is used to simulate additional tracks

1)Calculate how many additional tracks should be added

• do this by looking at the (N+1)th event in our data files

• count how many tagging tracks are present in the signal region

2)Harvest tagging tracks from data (which fail one or more of the real cuts)

3)Embed these tracks in MC according to fraction determined in 1)

13

Multiple p-p interactions

• The Lund string fragmentation model is used throughout

• This has a “z” parameter to define the fraction of energy the B meson takes from the string

• Default z parameterisation is symmetric Lund function

• use tuning to LEP data specifically for B mesons

14

Fragmentation Function

E. Ben-Haim et al. Phys. Lett. B580, 108 (2004)

• After all the modifications we compare all relevant distributions including efficiency and dilution in data and MC for Bd, B+

15

Efficiency and Dilution in Data/MC

So we conclude that for Bd, B+ there is a good match between data and MC. Thus we can move to using MC only for the Bs case.

B+ Bd

(%) Eff Dil Eff Dil

Data 58.4±0.5 25.4±1.4 57.2±0.6 14.2±2.9

MC 55.9 ±0.1 24.5±0.3 56.6±0.1 12.9±0.4

• already showed some comparisons for Bd and B+

• here are comparisons for Bs

16

Comparisons for Bs

Limited statistics statistical error of comparison is included as systematic error

• Statistical errors only:

17

Bs Dilution and Efficiency Results

What about the systematic errors?

Bs

(%) Eff Dil

Data 49.3±2.3 21.8±0.8

MC 52.1±0.3 -

• A reminder of what we’ve done:

• modified MC

• checked that it compares well with data for Bd, B+

• compared efficiency and dilution for Bd, B+ from data and MC

• on the basis that they compare well, we extracted efficiency and dilution for Bs from MC

• To apply these numbers in our analysis we need a good understanding of the systematic errors

• Several sources:

• bb production mechanism

• fragmentation fraction

• particle content around the B

• variation within data statistics

• B** fraction

• particle ID detectors simulation

• pile-up18

Systematic Errors

will discuss further

• Three main methods for producing bb in proton-antiproton collisions

• Flavour Creation, Flavour Excitation, Gluon Splitting (default mix 5:11:4)

• In gluon splitting case, the two b’s are close together – could pick up tagging tracks from the opposite b

• Systematic error obtained by fitting distribution in data and varying MC distribution within the errors

• This results in varying Gluon Splitting [-68%,+46%], Flavour Excitation and Creation [-50%,+50%]

19

bb Production Mechanism

Q

Q

• Track multiplicity, transverse momentum of B meson and fragmentation tracks are sensitive to fragmentation function

• Tuning made at LEP should apply equally at Tevatron

• Variables compare well with data for Bd, B+

• No reason to be suspicious of fragmentation used as a default, but systematic errors assigned to cover the possibility of problems

• Simultaneous fit to these distributions to determine allowed parameters of the symmetric Lund function

• data not sufficient to give a

tight constraint

• reasonable variation can be obtained,

beyond which comparison between

MC and data is degraded

• The variations are used to

assign systematic errors:

20

Fragmentation

• Particle species around the B meson gives insight on fragmentation

• Agrees well between data and MC for Bd, B+

• Slight discrepancy for Bs: (20.2±1.4)% kaons in data, (23.6±0.2)% in MC

• Vary the kaon fraction in the data downwards in two ways:

• reweight all events with a kaon tagging track

• reweight only those events with prompt kaons from b-string21

Particle Content around B Meson

• We claim the comparisons of data and MC are good

• but that is only valid within the errors on our data!

22

Variation within Data Statistics

MC samples varied within ranges allowed by statistical uncertainties

• Including all of the systematic errors we can remake the comparisons of data

and MC

• Note that the MC distributions envelope the data distributions

23

Compare again with data

24

Final SSKT Results

Final Tagger Power: S2<D2>= (4.0+0.9-1.2) %(Notes: <D> is the average dilution over all quantities, in reality we bin dilution in momentum, particle IDvariable to get extra power.S is a scale factor to account for any differences between data and MC in dependency of dilution on variables. )

MC simulations combined with measurements in data make this measurement possible

Dilution and its systematic errors:

25

The Results

• Amplitude scan performed on Bs candidates

• Inputs for each candidate:

• Mass

• Decay time

• Decay time resolution

• Tag decisions

• Predicted dilution

26

Put the 3 Ingredients Together

• All elements are then folded into the amplitude scan

mtADSe Dt cos1

1 /

“With three parameters, I can fit an elephant.” (Kelvin)

Combined Amplitude Scan

Amplitude consistent with 1 • probability of fake from random tags = 8x10-8

• Equivalent to 5.4significance

ms = 17.77±0.10(stat)±0.07(syst) ps-1

Conclusions

• CDF has found a signature consistent with Bs - Bs oscillations

– probability of this being a fluctuation is 8x10-8

• MC enabled the calibration of the most powerful flavour tagger– would not have been possible to such accuracy without experimental data to inform

the use of MC

• In my view the best (safest) possible way to use MC in analysis– use the data to make all possible checks

– use previous measurements, talk to theorists and use data itself to assign systematic errors for all of the unknowns

• Gives confidence in the results

ms = 17.77±0.10(stat)±0.07(syst) ps-1

Vts / Vtd= 0.2060 ± 0.0007 (exp) +0.0081 (theo) -0.0060

Interpretation of ResultsThis measurement decreases uncertainty on CKM triangle apex:

Easter 2006 October 2006

Likelihood Significance

• probability of fake from random tags = 8x10-8 measure ms

• Equivalent to 5.4 significance

ms = 17.77±0.10(stat)±0.07(syst) ps-1

AsymmetryOscillations folded modulo 2/ms

• Can extract Vts value

• compare to Belle bs (hep-ex/050679):

|Vtd| / |Vts| = 0.199 +0.026 (exp) +0.018 (theo)

• our result:

|Vtd| / |Vts| = 0.2060 ± 0.0007 (exp) +0.0081 (theo)

|Vts| / |Vtd|

• inputs:• m(B0)/m(Bs) = 0.9832 (PDG 2006)• = 1.21 +0.05 (Lattice 2005)• md = 0.507±0.005 (PDG 2006)

-0.04

-0.0060

-0.025 -0.016

Interpretation of ResultsMeasurements compared with global fit (CKM fitter group) updated this month

In excellent agreement with expectations

Systematic Uncertainties on ms

• Systematic uncertainties from fit model evaluated on toy Monte Carlo

• Have negligible impact• Relevant systematic

uncertainties are from lifetime scale

Systematic Error

Fitting Model < 0.01ps-1

SVX Alignment 0.04 ps-1

Track Fit Bias 0.05 ps-1

PV bias from tagging

0.02 ps-1

Total 0.07 ps-1

All systematic uncertainties are common between hadronic and semileptonic samples

1) Signal Samples for BsMixing

35

L

Semileptonic: partially reconstructed

These modes are flavour specific: the charges tag the B at decay

Hadronic: fully reconstructed

Crucial: Triggering using displaced track trigger (Silicon Vertex Trigger)

Triggering On Displaced Tracks

• trigger Bs → Ds-, Bs → Ds

- l+

• trigger processes 20 TB /sec• trigger requirement:

• two displaced tracks: (pT > 2 GeV/c, 120 m<|d0|<1mm)• requires precision tracking in silicon vertex detector

Primary Vertex

Secondary Vertex

d0 Onlineaccuracy

signalBs→ Ds, Ds → → K+K-

Example Hadronic Mass Spectrum

partiallyreconstructed

B mesons(satellites)

combinatorialbackground

B0→ D- decays

Previous mixing fit range

Now we use the entire range, capitalising on satellites also

Hadronic Signal Yields

• Neural Network selection used in these modes• Particle ID (dE/dx, Time of Flight) used to suppress backgrounds

Decay Channel

Yield

Bs→ Ds () 2000

Satellites 3100

Bs → Ds (K* K)

1400

Bs → Ds (3) 700

Bs → Ds3 ( )

700

Bs → Ds3 (K*K)

600

Bs → Ds3 (3)

200

Total 8700

Semileptonic Samples: Ds- l+ x

Fully reconstructed Ds mesons: Bs mesons not fully reconstructed:

Particle ID used; new trigger paths added

The candidate’s m(lDs-) is included in the fit: discriminates against

“physics backgrounds” of the type B0/+ → D+Ds

Mixing fit range

61500 semileptonic candidates

Summary of Yield changes since April 2006

1fb-1 of data used in both analyses

What changed?

Hadronic modes:•Added partially reconstructed “satellite” Bs decays•Add Neural Net for candidate selection•Used particle identification to eliminate background

Semileptonic Modes:•Used particle identification to eliminate background•Added new trigger path

Effective increase in statistics x2.5 from these changes

B Physics Program: $12M/year (1/5 per physics group)

41

What do the candidates cost?: FECb

Tevatron Accelerator Value: $7M/year ($741M RPV at 70% spread over 25 years and 3 experiments)

CDF Detector Value: $0.8M/year ($95M total facilities RPV at 70% value)

Tevatron Operation to CDF: $48M/year ($120M/year at 40% of overall facilities)

CDF Operation: $5M/year

Total CDF data $61M/year

The Bsottom Line: $0 850 Per Bs meson

42

• Reconstruct decay length by vertexing• Measure pT of decay products

K

lDp

BmL

Bp

BmL

Lct

T

xy

)()(

)(

2) Time of Decay

%0/

300

p

m

p

ct

2

20

pct p

ctct

%15/

590

p

m

p

ct

osc. period at ms = 18 ps-1

Crucial: Vertex resolution (Silicon Vertex Detector, in particular Layer00 very close to beampipe)

Hadronic:Semileptonic:

Proper time resolution:

Layer 00

• layer of silicon placed directly on beryllium beam pipe• Radius of 1.5 cm• additional impact parameter resolution

I.P resolutionwithout L00

• So-called because we already had layer 0 when this device was designed!• UK designed, built and (mostly) paid for this detector!

Classic B Lifetime Measurement

• reconstruct B meson mass, pT, Lxy

• calculate proper decay time (ct)

• extract c from combined mass+lifetime fit

• signal probability:

psignal(t) = e-t’/ R(t’,t)

● background pbkg(t) modeled from sidebands

pp collision B decays

Hadronic Lifetime Measurement

• Displaced track trigger biases the lifetime distribution

• Correct with an

efficiency function derived from MC:

p = e-t’/ R(t’,t) (t)

0.0 0.2 0.4proper time (cm)

ModeLifetime

(ps)B0 → D- + 1.508± 0.017

B- → D0 - 1.638 ± 0.017

Bs → Ds () 1.538 ± 0.040

World Averages:

B0 : 1.534 ± 0.013 psB- : 1.653 ± 0.014 psBs : 1.469 ± 0.059 ps

Good agreement in all modes

Hadronic Lifetime Measurements

Errors are statistical only

Semileptonic Lifetime Measurement• neutrino momentum missing

• Correct with “K factor” from MC:

• Also correct for displaced track trigger bias as in hadronic case

High m(lD) candidates have narrow K factor distribution: almost fullyreconstructed events!

Capitalise on this by binning K factorin m(lD)

Semileptonic Lifetime Results

• Errors are statistical only• Lifetimes measured on first 355 pb-1 • Compare to World Average: Bs: (1.469±0.059) ps

• All Lifetime results are consistent with world average• Gives confidence in fitters, backgrounds, ct resolution

Lifetime (ps)

Bs:Ds 1.51± 0.04

Bs:Ds K*K 1.38 ± 0.07

Bs:Ds 1.40 ± 0.09

Bs combined

1.48 ± 0.03

49

The CDF Detector and Triggers

• (bb) << (pp) B events are selected with specialised triggers• Displaced vertex trigger exploits long lifetime of B’s• Yields per pb-1 are ~3x those of Run I

p

p

50

The Tevatron

Fermilab, Chicago

-

Currently the world’s highest energy collider

CDF

D0

p

p

1km

Ecom=2TeV

Hadron collisions can produce a wide spectrum of b hadrons (in a challenging environment)

Bs cannot be produced at the B factories since their Centre of Mass energy is below threshold (except for a special run by Belle)

-

Ep=0.96TeV Ep=0.96TeV

ECoM=2TeV

• This analysis: Feb 2002 – Jan 2006: 1 fb-1

Tevatron Integrated LuminosityRun I: 1992-1996 L= 0.1fb-1

Major Upgrades 1996-2001Run II: 2001-2006 L= 1.6 fb-1

• Recorded Luminosity 1.6 fb-1

52

Measuring ms

1: amplitude scan method

•Introduce Amplitude, A, to mixing probability formula

• Evaluate A at each m point• A=1 if evaluated at correct m • This method facilitates limit setting before mixing signal observed

Mixing signal manifests itself as pointsin the plot which are most compatible with A=1

H. G. Moser, A. Roussarie, NIM A384 (1997)

Test Case: B0

d mixing

world average

tmAeP

tmAeP

s

t

BB

mix

s

t

BB

unmix

sB

s

s

sB

s

s

cos12

1

cos12

1

So instead we employ two methods:

53

Measuring ms

2: To establish the value of ms, we evaluate the likelihood profile:

Log L(A=0)-Log L(A=1)

Proper Time Resolution• Displaced track triggers also gather large prompt charm samples• construct “Bs-like” topologies of prompt Ds

- + prompt track• calibrate ct resolution by fitting for “lifetime” of “Bs-like” objects

– expect zero lifetime by construction

trigger tracksprompt track

Ds- vertex

P.V.

“Bs” vertex

Systematic Uncertainties

• related to absolute value of amplitude, relevant only when setting limits – cancel in A/A, folded in to confidence calculation for observation– systematic uncertainties are very small compared to statistical

Semileptonic Decays

Lepton+Ds Lifetime Fits Two cases treated separately:

Lepton is a displaced track: Lepton is not a displaced track:

57

Opposite Side Taggers•Performance studied in high statistics inclusive lepton+SVT trigger

•Enables calibration of taggers•Can also parameterise tagging dilution as function of variables: •Soft Lepton Tag: dilution parameterised as function of likelihood and pt

rel

•Jet Charge Tag: dilution parameterised as function of jet charge for a given jet

Soft Electron Tag Soft Electron Tag Jet Charge Tag

58

Opposite Side Taggers•Performance studied in high statistics inclusive lepton+SVT trigger

•Enables calibration of taggers•Can also parameterise tagging dilution as function of variables: •E.g. Soft Lepton Tag dilution parameterised as function of electron likelihood

Soft Electron Tag

59

Proper Time Resolution

osc. period at ms = 18 ps-1

• event by event determination of primary vertex position used

• average uncertainty

~ 26 m

• this information is used per candidate in the likelihood fit

• utilize large prompt charm cross section

• construct “Bs-like” topologies of prompt Ds- + prompt track

• calibrate ct resolution by fitting for “lifetime” of “Bs-like” objects

%15/

590

p

m

p

ct

%0/

300

p

m

p

ct

semileptonic: hadronic:

Performance of All Taggers

• Errors are statistical only

• use exclusive combination of tags on opposite side

• same side and opposite side taggers are assumed to be independent

D2 Hadronic (%) D2 Semileptonic (%)

Muon 0.48 ± 0.06 0.62 ± 0.03

Electron 0.09 ± 0.03 0.10 ± 0.01

JQ/Vertex 0.30 ± 0.04 0.27 ± 0.02

JQ/Prob. 0.46 ± 0.05 0.34 ± 0.02

JQ/High pT 0.14 ± 0.03 0.11 ± 0.01

Total OST 1.47 ± 0.10 1.44 ± 0.04

SSKT 3.42 ± 0.06 4.00 ± 0.04

61

The Tevatron and CDF

Fermilab, Chicago

-

Currently the world’s highest energy collider

CDF

D0

p

p

1km

Ecom=2TeV

pp collisions can produce a wide spectrum of B hadrons in a challenging environment

Bs cannot be produced at the B factories since Centre of Mass energy is below threshold

p

p

CDF Run I: 1992-1996 L= 0.1fb-1

Major Upgrades 1996-2001CDF Run II: 2001-2006 L= 1fb-1

Real Measurement Layout

momentum resolutiondisplacement resolutionflavor tagging power

UnbinnedLikelihood

Fitter

Data

A(ms=[1…30] ps-1)= ?

ms = ?

scan for signal:

measure frequency:

The CDFII Detector• multi-purpose detector• excellent momentum

resolution (p)/p<0.1%

• Yield:– SVT based triggers

• Tagging power:– TOF, dE/dX in COT

• Proper time resolution:– SVXII, L00

64

Bs – Bs System

tags flavour at decay

narrow mass

Bs: travels ~ 1.0mm

0

Ds: travels ~ 0.5mm

-

‘neighbour’ tags flavour at production

-: opposite charge to l+

0 0

65

-

Ep=0.96TeV Ep=0.96TeV

ECoM=2TeV

b Hadron Production at the Tevatron

66

Semileptonic Decay Fit ModelUnbinned maximum likelihood fit to c(B)

– Background is parameterised by delta function and positive exp convoluted with Gaussian resolution:

Free parameters: D E + f+ G

– Signal: exp convoluted with Gaussian resolution, K factor distribution, P(K), and bias function,

– Maximum likelihood function:

),(exp)(1 GE

Dbkg tGtf

tfF

)(),()(exp KPstGKtKt

cK

NF isig

bkgsig N

j

jbkg

N

i

ibkgbkg

isigbkg FFfFfL 1

67

• Reconstruct decay length by vertexing• Measure pT of decay products

K

lDp

BmL

Bp

BmL

Lct

T

xy

)()(

)(

2) Time of Decay

%0/

300

p

m

p

ct

•Displaced Track Trigger imposes bias correct with efficiency function

2

20

pct p

ctct

%15/

590

p

m

p

ct

osc. period at ms = 18 ps-1

Crucial: Vertex resolution (Silicon Vertex Detector, in particular Layer00 very close to beampipe)

68

Bs – Bs System

Want to understand: - Average lifetime,

- Lifetime difference, - Rate of mixing, m

Current Status: Experiment Theory

<0.29 0.15

m (ps-1) >14.1 20

0 0

2LH

LH

LH mm