observation of bs-bs oscillationshepweb.ucsd.edu/~vsharma/ppt/ringberg06/talks06/cdf/paus... ·...

Observation ofBs-Bs Oscillations

Christoph PausMassachusetts Institute of Technology

Wine and Cheese SeminarSeptember 22, 2006

Overview

☞ Theory and some History☞ The Method☞ Equipment Used for the Measurements☞ Our Samples☞ b Flavor Tagging☞ Results per Sample☞ Mixing Result Summary☞ Conclusions

1

Theory and some History

2

Matter in the Standard ModelMatter build of families of fermion doublets

Leptons

�

νe

e−

�

L

�

νµµ−

�

L

�νττ −

�L

Quarks

�

ud 0 �

L

�

cs0 �

L�

tb0 �

L

Weak interaction through W ± bosons

cs

W+c

d

W+

In general: weak eigenstates ≠ strong eigenstates☞ mixing between families possible☞ lower quark doublet components absorb difference☞ neutrinos also mix

3

Cabibbo–Kobayashi–Maskawa MatrixExample: two families of quark pairs → one mixing angle�

d 0

s0 � =

�

cos θ sin θ−sin θ cos θ

��

ds

�

rotation matrix

Matrix has to be unitary: V yV = 1

Describe mixing between three quark-pair families0B� d 0

s0

b01CA = V ×

0B� dsb

1CA with V =

0B� Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

1CA

V is Cabbibo–Kobayashi–Maskawa matrix

Three families → 4 degrees of freedom☞ 3 angles☞ 1 complex phase → CP violation

4

CKM MatrixMatrix structure

☞ mostly diagonal☞ crossing of families suppressed☞ the further the less probable☞ values not predicted

Particles are conserved:V yV = 1

→ unitarity condition

u

d

c

t

s b

Wolfenstein parametrization (λ = 0.2272 ± 0.0010):

V =

0B� 1 − λ 2/2 λ Aλ 3(ρ − iη )−λ 1 − λ 2/2 Aλ 2

Aλ 3(1 − ρ − iη ) −Aλ 2 1

1CA + O (λ 4)

Least known parameters: ρ and η5

Unitarity Triangle

Unitarity condition: V yV = 1 V =

0B� Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

1CA

→ VudV ∗ub + VcdV ∗

cb + VtdV ∗tb = 0

→ 1 + VudV ∗ub/VcdV ∗

cb + VtdV ∗tb/VcdV ∗

cb = 0

1

η

γ

≅*

*

*

* λ *

*

λ = sin θV V

V V

V

V V

V

ud

cd cb

ubcd cb

tbtd

c

ts

tdV

V

α

βρ

6

Neutral B Meson Mixing

t

t

(c, u)

(c

, u

)

W+ W−

s

b

b

s

Bs Bs

Vts

Vts W+

W−

s

b

b

s

(c

, u

)t

(c, u)tBs Bs

V

Vts

ts

Quark mixing → non diagonal Hamiltonian for ⟨B|H|B⟩

H =

�

M M12

M ∗12 M

�− i

2�

Γ Γ12

Γ ∗12 Γ

�

Diagonalizing the Hamiltonian results in☞ two masses: mH and mL and ∆m = mH − mL

☞ two decay widths: ΓH and ΓL and ∆Γ = ΓH − ΓL

☞ remember: Γ = 1/τ

Mass and decay width (lifetime) are measurable!!7

Theoretical Predictions - ∆mTheory prediction for B0/B0

s mix through box diagram

∆mq / mBqBBqf 2Bq

��VtbV ∗tq

��2 q = s,d

Lattice QCD calculations

BBdf 2Bd

= (246 ± 11 ± 25) MeV2

Hadronic uncertainties limit|Vtd | determination to ≈ 11%

t

t

(c, u)

(c

, u

)

W+ W−

s

b

b

s

Bs Bs

Vts

Vts

In ratio theory uncertainties are reduced∆ms∆md

= mBsmBd

ξ 2 |Vts|2

|Vtd |2 with ξ = 1.21 +0.047−0.035

Determine |Vts||Vtd | to ≈ 3.4%

8

Unitarity Triangle - Status EPS 2005Apex (ρ, η )

Squeezing alongside b

☞ sin 2β☞ Vub/Vcb

Squeezing alongside c

☞ ∆md

☞ ∆ms

☞ γ

CKM fit result:∆ms = 18.3 +6.5

−1.5 ps−1 -1.5

-1

-0.5

0

0.5

1

1.5

-1 -0.5 0 0.5 1 1.5 2

sin 2β

sol. w/ cos 2β < 0(excl. at CL > 0.95)

excluded at CL > 0.95

γ

γ

α

α

∆md

∆ms & ∆md

εK

εK

|Vub/Vcb|

sin 2β

sol. w/ cos 2β < 0(excl. at CL > 0.95)

excluded at CL > 0.95

α

βγ

ρ

η

excluded area has CL > 0.95

C K Mf i t t e r

EPS 2005

cb

9

First Measurement of B Mixing from UA1

Signature: like sign high pT leptons PLB 186 (1987) 247

Result☞ time integrated

χ = 0.121 ± 0.047☞ implied heavy top

For Bs

☞ too fast: χs = 0.5

Later Argus/Cleo/LEP/SLD/Tevatron/BaBar/Belle ....10

Historic Review: A 20-Year Effort1987

☞ first evidence of B mixing from UA1 PLB 186 (1987) 247

☞ Argus observes B0 mixing: UA1 implies large Bs mixing, mt > 50 GeV/c2PLB 192 (1987) 245

1989☞ CLEO confirms Argus result PRL 62 (1989) 2233

1990s☞ inclusive measurements of B0 mixing from LEP establish Bs mixing

1993☞ first time dependent measurement of ∆md from Aleph PLB 313 (1993) 498

☞ first lower limit on ∆ms from Aleph: ∆ms > 12 ⋅ 10−4 eV/c2PLB 322 (1994) 441

1999☞ CDF Run I result on ∆ms: ∆ms > 5.8 ps−1

PRL 82 (1999) 3576

2005☞ DØ first result on ∆ms: ∆ms > 5.0 ps−1

☞ CDF Run II first result on ∆ms: ∆ms > 7.9 ps−1

2006☞ D0 reports interval: ∆ms ∈ [ 17, 21] ps−1 at 90% CL PRL 97 (2006) 021802

☞ CDF Run II first measurement ∆ms = 17.31 +0.33−0.18 ± 0.07 ps−1

PRL 97 (2006) 062003

11

The Method

12

A Picture Book Event

L xy

ct = L xymp

B

T

��

��

opposite side

K

K

π

π

0sB

D s

+

+

K+

same side (vertexing)

opposite

D meson

fragmentationkaon

−l

side lepton

B hadronB jet

Collision Point

Creation of bb

side kaonopposite

K −

typically 1 mm

Ingredients to measure mixing☞ proper decay time ct , B rest frame☞ B flavor at decay, final state☞ B flavor at production, flavor tagging

13

An Event Display

14

B Mixing Phenomenology

Behavior in proper timeP(t)B0→B0 = 1

2τ e−t /τ (1 + cos ∆mt)P(t)

B0→B0 = 12τ e−t /τ (1 − cos ∆mt)

Determine asymmetry

A0(t) = N(t)unmixed−N(t)mixedN(t)unmixed+N(t)mixed

= cos ∆m t

In a perfect world

0

0.2

0.4

0.6

0.8

0 1 2 3proper decay time, t [ps]

prob

abili

ty d

ensi

ty

unmixedmixedtotal

-1

-0.5

0

0.5

1

0 1 2 3 4proper decay time, t [ps]

Mix

ed A

sym

met

ry

Perfect tag D=1

15

What Do We See in the End?

Flavor tagging Vertex Vertex and Momentum

-1

-0.5

0

0.5

1


asym

met

ry

Realistic tag D=0.2

-1

-0.5

0

0.5

1


asym

met

ry

Realistic resolution: vtx: 50 µm

-1

-0.5

0

0.5

1


asym

met

ry

Realistic resolutions: vtx: 50 µm pt: σ(p)/p = 5%

1/σA =

qnSεD2

2q

nSnS+nB

exp(−(∆msσct)22 )

σct =r

(σ0ct)2 +

�

ct σpp

�2

16

Perfect to Realistic

-1

-0.5

0

0.5

1


asym

met

ry

Perfect tag and resolutions

-1

-0.5

0

0.5

1


asym

met

ry

Realistic tag D=0.2Realistic resolutions: vtx: 50 µm pt: σ(p)/p = 5%

Unbinned likelihood fit: p ∼ exp(−t /τ )(1 ± AD cos ∆mt)☞ scan ∆m for signal: determine amplitude, A☞ measure ∆ms with A = 1

17

Status: Scanning for Bs Oscillation SignalBefore this analysis

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 2.5 5 7.5 10 12.5 15 17.5 20 22.5 25

∆ms (ps-1)

Am

plitu

de

data ± 1 σ 95% CL limit 14.4 ps-1

1.645 σ sensitivity 18.2 ps-1

data ± 1.645 σdata ± 1.645 σ (stat only)

Average for PDG 2006

before Spring 2005

]-1 [pssm∆0 5 10 15 20 25

Am

pli

tud

e

-4

-2

0

2

4 (stat.)σ 1.645 ±data

syst.)⊕ (stat. σ 1.645 ±data

σ 1 ±data

-195% CL limit: 14.8ps -1Expected limit: 14.1ps

DØ Run II

-11 fb

recent DØ resultPRL 97 (2006) 21802

17 ps−1 < ∆ms < 21 ps−1 at 90% CL

p-value about 5.0%

18

Last CDF Result PRL 97 (2006) 062003

]-1 [pssm∆0 10 20 30

Am

plitu

de

-2

0

2

σ 1 ± data

σ 1.645

σ 1.645 ± data

(stat. only)σ 1.645 ± data

95% CL limit

sensitivity

-116.7 ps-125.8 ps

-π +π +π _ s D→ 0

s, B+π _ s D→ 0

s X, B_ s D+ l→ 0

sB

CDF Run II -1L = 1.0 fb

A = 1.03 ± 0.28(stat) compatible with 1 for ∆ms ∼ 17.3 ps−1

19

Last CDF Result PRL 97 (2006) 062003

Signature: minimum of log(L (A = 1)) − log(L (A = 0))

)-1

(pssm∆15 16 17 18 19 20

log(

L)∆-

-5

0

5

10

15

20hadronicsemileptoniccombined

CDF Run II Preliminary -11 fb

Minimum: -6.75

p-value: 0.2%

Analysis was blinded

∆ms = 17.31 +0.33−0.18(stat) ± 0.07(syst) ps−1

20

Plan After April

Close box again

Refine analysis methods

Go for 5σ

21

What We Improved

Unchanged☞ same data: 1 fb−1

Improvements☞ flavor tagging

☞ added opposite side kaon tagger☞ applied NN to combine all opposite side taggers☞ applied NN to same side tagger

☞ signal yields☞ added partially reconstructed decays☞ used particle identification in selection☞ used NN for hadronic selection☞ added trigger path in `D−

s

Added effective statistics of factor of 2.522

Equipment Used for theMeasurements

23

CDF II Detector

24

CDF II Detector - Key Features

’Deadtimeless’ trigger system☞ 3 level, pipelined, flexible system☞ Silicon Vertex Trigger (SVT) at 2nd level (≈25 kHz)

Charged particle reconstruction☞ redundancy for pattern reco in busy environment☞ excellent momentum resolution: R = 1.4m,B = 1.4T☞ excellent vertex resolution: L00 at 1.5cm

Particle identification☞ energy loss in drift chamber (dE /dx)☞ Time-of-Flight system at 1.4 m radius☞ electron and muon identification

25

Our Samples

26

Sample Luminosity

Store Number

Tot

al L

umin

osity

(pb

-1)

0

250

500

750

1000

1250

1500

1750

2000

1000 1500 2000 2500 3000 3500 4000 4500

1 4 7 10 1 4 7 101 4 7 1 4 7102002 2003 2004 2005 2006Year

Month

DeliveredTo tape

Bs Mixing Analysis uses: 1 fb−1

now: 1.8 fb−1 delivered, 1.6 fb−1 on tape27

Samples Used in the Analysis

Sample to tune flavor taggers (largest)☞ `+track sample (track is required to be displaced)

Calibration samples (taggers, vertex resolutions)☞ B+ → J/ψK +,D

0π+(π+π−), D0`+X ,

☞ B0 → J/ψK ∗ 0, D−π+(π+π−), D−`+X , D∗− `+X☞ Bs → J/ψφ☞ with D∗− → D0π−, D0 → K −π+(π+π−), D− → K +π−π−

Signal samples☞ hadronic: Bs → D−

sπ+(π+π−)☞ semileptonic: Bs → D−

s`+X☞ with D−

s → φπ−,K ∗ 0K −, π+π−π−

28

Samples - Semileptonic Versus Hadronic

]2

) [GeV/cπ,πφmass(5.2 5.4 5.6 5.8

2ca

ndid

ates

per

10

MeV

/c

0

100

200

300

400

data

fit+/K+π -

s D→ s B

+ρ-s D→ s B

+/K+π*-s D→ s B

X-s D→ b

+π - D→ 0 B-π +

cΛ → bΛ

comb. bkg.

]2

) [GeV/cπ,πφmass(5.2 5.4 5.6 5.8

-1CDF Run II L = 1 fb

Hadronic Dsπ(ππ)☞ reconstruct: ct = Lxy

mB

pBT

☞ great ct , mass resolution☞ sample is clean☞ small branching ratio

]2

mass [GeV/c--l+π φ

3 4 5

2ca

ndid

ates

per

35

MeV

/c

0

500

1000

1500

2000 data

fit

signal0sB

false lepton & physics

comb. bkg.

]2

mass [GeV/c--l+π φ

3 4 5

]2

mass [GeV/c+π φ1.94 1.96 1.98 2.00

2ca

nd. p

er 1

MeV

/c

0

1000

2000

3000

4000

]2

mass [GeV/c+π φ1.94 1.96 1.98 2.00

Semileptonic `DsX☞ reconstruct: ct ∗ = Lxy

mB

p`DT

☞ large branching ratio☞ inferior ct , mass resolution☞ sample composition issue

29

b Flavor Tagging

30

Flavor Tagging Introduction

L xy

ct = L xymp

B

T

��

��

opposite side

K

K

π

π

0sB

D s

+

+

K+


opposite

D meson

fragmentationkaon

−l

side lepton

B hadronB jet

Collision Point

Creation of bb

side kaonopposite

K −

typically 1 mm

Crucial parameters☞ efficiency: ε, dilution: D = 1−2pw (pw prob. for wrong decision)☞ εD2 expresses statistical power

31

Flavor Tagging IntroductionTagging algorithms used

☞ opposite side: electron, muon, jet charge, kaon☞ same side: pion (B+, B0), kaon (Bs)

Tuning the algorithm☞ based on huge heavy flavour rich `+track sample☞ find dependencies and determine parametrizations☞ find optimal point for the algorithm

Calibration of the tagger☞ verify algorithms on B0 and B+ semileptonic/hadronic samples☞ determine scale factor S in

B+ : p ∼ exp(−t /τ )(1 ± SD)B0 : p ∼ exp(−t /τ )(1 ± SD cos ∆md t)

☞ use single scale factor: should be consistent with 1

Scheme for combination of taggers32

OST Flavor TaggersIndividual performance and combination (`+track sample)

tagger [%] efficiency dilution εD2

Muon 4.6 ± 0.0 34.7 ± 0.5 0.58 ± 0.02Electron 3.2 ± 0.0 30.3 ± 0.7 0.29 ± 0.01JQT 95.5 ± 0.1 9.7 ± 0.2 0.90 ± 0.03Kaon 18.1 ± 0.1 11.1 ± 0.9 0.23 ± 0.02OST old 95.6 ± 0.1 11.9 ± 0.1 1.34 ± 0.03OST NN 95.8 ± 0.1 12.7 ± 0.2 1.54 ± 0.04

Opposite Side Taggers☞ new kaon tagger☞ not mutually exclusive → hierarchical scheme☞ new NN combination: tag decisions as input

33

OST Flavor Taggers - Neural Network

predicted dilution0 0.05 0.1 0.15 0.2 0.25 0.3

mea

sure

d di

lutio

n

0

0.05

0.1

0.15

0.2

0.25

0.3

/ ndf 2χ 45.06 / 9S 0.008463± 0.9917

/ ndf 2χ 45.06 / 9S 0.008463± 0.9917 CDF Run II Preliminary

combined OS tagger

0.01±S = 0.99

= 96 %∈

Linear parametrization works wellImprovement of εD2

☞ hadronic 1.81 ± 0.10% from 1.51%☞ semileptonic 1.82 ± 0.04% from 1.54%

34

Same Side Kaon TaggingFragmentation

☞ Bd /u likely accompanied by π+/π−

☞ Bs likely accompanied by a K +

☞ processes differ☞ no direct transfer B+,B0 → Bs

☞ need MC to measure tagger dilution

Strategy☞ tune MC with B+ and B0

☞ apply PID to de-weight pions☞ use MC to parametrize dilution

ParticleID very important☞ significantly improves εD2

☞ reduces systematic uncertainty

→TOF (dE /dx) very important!

+

b b

b b

b b

d

u s

u

s

d s

u d

B0

B0

B

K+

0∗K

K0∗

K

d

u s

d s

u

s

u d

}

}

}

}

}

}

s

π

π

35

Flavor Tagging - SSKT Calibration: B+, B0

max PID dilution D [%]

5 10 15 20 25 30

max PID dilution D [%]

5 10 15 20 25 30

CDF Run II Preliminary -1 355 pb≈L

+ Kψ J/→ +B

+π 0

D → +B

π 30

D → +B

*0 Kψ J/→ 0B

+π - D→ 0B

π 3- D→ 0B

data

MC

syst.

☞ find good agreement: particle Id and kinematic variables☞ use kinematic variables to improve tagger

36

SSKT Particle Id Algorithm

log(LH(PID))

-20 -10 0 10 20

entr

ies

per

bin

0

200

400

Pythia Data MC pions MC kaons MC protons

log(LH(PID))

-20 -10 0 10 20

entr

ies

per

bin

0

200

400

+π -s D→ sB

CDF Run II Preliminary -1 1 fb≈L

[GeV/c]Tp0 1 2 3

entr

ies

per

bin

0

100

200


[GeV/c]Tp0 1 2 3

entr

ies

per

bin

0

100

200

+π -s D→ sB


[GeV/c]Tp0 1 2 3

entr

ies

per

bin

0

10

20


PID > 1 [GeV/c]Tp

0 1 2 3

entr

ies

per

bin

0

10

20

+π -s D→ sB


+πs- -> DsB

log(LH(PID)) of tagging track-20 -10 0 10

dilu

tion

[%] (

agre

emen

t)

-10

0

10

20

30

40

50

60

70

CDF Run II Monte Carlo

Pid algorithm works well

Kinematic of tag track not

used

algorithm)relL [GeV/c] (max pTtagging track p

1 2 3 4 5 6

dilu

tion

(agr

eem

ent)

0.1

0.2

0.3

0.4

0.5

algorithm)relL [GeV/c] (max pTtagging track p

1 2 3 4 5 6

dilu

tion

(agr

eem

ent)

0.1

0.2

0.3

0.4

0.5

(MC)+π -s D→ s B

CDF Run II Monte Carlo

ex.: max. prelL algorithm shows dependencies → use it

37

Neural Network SSKTAlgorithm

☞ variables: pid, ∆R, pT , prelL , prel

T , b (bool tags have same charge)☞ train: signal - RS kaons, bg - WS kaons, pions and protons☞ decision: track charge of highest NN tag candidate

Expected improvement☞ MC ≈ 6% relative

Measured improvement☞ 0% relative hadronic

→ εD2 = 3.5%☞ 8% relative semileptonic

→ now εD2 = 4.8%

Neural Network output0 0.2 0.4 0.6 0.8 1

Dilu

tion

[%] (

agre

emen

t)

0

0.2

0.4

0.6

0.8

1CDF Run II Monte Carlo

)πφ(s D→ sB

38

Results per Sample

39

Samples - Semileptonic SelectionUse of particle identification in selection

☞ standard practice at B factories☞ applied in hadronic and semileptonic analyses☞ using combined Time-of-Flight and dE/dx (see SSKT)

Effects☞ strongest in Ds → K ∗ 0K☞ no explicit D+ → K −π+π+

rejection (+35%)☞ combinatorial background

dominated by π

Yields: 62k (was 37k)☞ S/Bx2 for D−

s → K ∗ 0K −,φπ−

☞ added trigger paths]

2 mass [GeV/c--l+ K*0K

3 4 5

2ca

ndid

ates

per

35

MeV

/c

0

2000

4000

data

fit

signal0sB

false lepton & physics reflection+ D

comb. bkg.

]2

mass [GeV/c--l+ K*0K3 4 5

]2

mass [GeV/c+ K*0K1.95 2.00

2ca

nd. p

er 2

MeV

/c

0

2000

4000

6000

]2

mass [GeV/c+ K*0K1.95 2.00

40

Semileptonic Amplitude Scan

]-1 [pssm∆

0 5 10 15 20 25 30 35

Am

plitu

de

-4

-3

-2

-1

0

1

2

3

4σ 1 ± data

σ 1.645

σ 1.645 ± data


95% CL limit

sensitivity

-116.5 ps-119.3 ps

X_ s D+ l→ 0

sB

A compatible with 1 for ∆ms ∼ 17.75 ps−1

A/σA(∆ms = 17.75 ps−1) ≈ 2, can set two sided 95% CL limit

41

Semileptonic Likelihood Profile

Minimum17.89 ps−1

Depth☞ sets 95% CL interval☞ 1σ equiv. to ± 0.3 ps−1

]-1 [pssm∆15 16 17 18 19 20

-log(

L)

-2

-1

0

1

2

3

4

42

Samples - Hadronic: Bs → D−sπ+(π+π−)

Bs Modes Signal S/B(φπ)π 2000(1600) +13%partial 3100(–) –(K ∗ 0K )π 1400(800) +35%(3π)π 700(600) +22%(φπ)3π 700(500) +92%(K ∗ 0K )3π 600(200) +110%(3π)3π 200(–) –total 8700(3700) –

Golden signature☞ Bs → D−

s(φπ−)π+

]2

) [GeV/cπ,πφmass(5.2 5.4 5.6 5.8

2ca

ndid

ates

per

10

MeV

/c

0

100

200

300

400

data

fit+/K+π -

s D→ s B

+ρ-s D→ s B

+/K+π*-s D→ s B

X-s D→ b

+π - D→ 0 B-π +

cΛ → bΛ

comb. bkg.

]2

) [GeV/cπ,πφmass(5.2 5.4 5.6 5.8

-1CDF Run II L = 1 fb

Improvements:☞ partial reconstruction, particle Id, NN in selection

43

How Good are Partially Reconstructed Decays?

sB

T/pReconstructedT = pκ

0.4 0.6 0.8 1.0

prob

abili

ty d

ensi

ty

5

10

ν l (*)s D→ 0

sBall 2 3.1 GeV/c≤ lsD 2.0 < m2 4.5 GeV/c≤ lsD 4.3 < m2 5.1 GeV/c≤ lsD 4.9 < m

π *s D→ 0

sB

ρ s D→ 0sB

CDF Run II

sB


0.4 0.6 0.8 1.0

Proper decay time [ps]0 1 2 3

Pro

per

deca

y tim

e re

solu

tion

[fs]

0

200

400

600

800

-1Osc. / 18 ps

π s D→ 0sB

ρ s / Dπ *s D→ 0

sB

2 5.1 GeV/c≤ lsD, 4.9 < mν l (*)s D→ 0

sB

2 4.5 GeV/c≤ lsD, 4.3 < mν l (*)s D→ 0

sB

2 3.1 GeV/c≤ lsD, 2.0 < mν l (*)s D→ 0

sB

CDF Run II

Decay modes: Bs → D∗−s (Dsγ(π0))π+, Bs → D−

sρ+(π0π−)☞ need to correct for missing momentum, as semileptonic☞ large reconstructed mass → missing momentum small

Partial reco almost as good as full reco44

Amplitude Scan Partial Reconstruction Only

]-1 [pssm∆0 10 20 30

Am

plitu

de

-4

-2

0

2

4 σ 1 ± data

σ 1.645

σ 1.645 ± data


95% CL limit

sensitivity

-117.0 ps-118.3 ps

+π_*

s,D+ρ_ s D→ 0

sB

CDF Run II Preliminary -1L = fb

A = 1.02 ± 0.57(stat)consistent with 1 for ∆ms ∼ 17.75 ps−1

45

Amplitude Scan Golden Mode Only

]-1 [pssm∆0 10 20 30

Am

plitu

de

-4

-2

0

2

4 σ 1 ± data

σ 1.645

σ 1.645 ± data


95% CL limit

sensitivity

-117.0 ps-122.7 ps

+π_*

s,D+ρ_ s,D+π

_ s D→ 0

sB

CDF Run II Preliminary -1L = fb


46

Likelihood Curves - Golden Channel Only

Golden LikelihoodMinimum: −7.4p-value: 0.15%

→ 3.2σ

Spring analysisMinimum: −6.4p-value: 0.2%

Golden sample

∆ms = 18.01 +0.17−0.18 ps−1

]-1 [pssm∆16 18 20

-ln(L

)

-8

-6

-4

-20

2

4

6

8

10

12

14Total golden

Part.Reco’d

Full.Reco’d

Consistent results: full and partial reconstruction47

Non-Golden Channels, Bs → Dsπ

Particle Id☞ opt. D+ rejection☞ relax kinematic

cuts

Neural Net☞ larger signal at

same bg☞ add new mode

Bs → Ds(3π)3π

]2 mass [GeV/cBπ -) K-π +(K*K

5.4 5.6 5.82

Can

dida

tes

per

5 M

eV/c

0

50

100

150

data

fit+π -

s D→ s B

background

π - D→ 0 B

π cΛ → bΛ

]2 mass [GeV/cBπ -) K-π +(K*K

5.4 5.6 5.8

/ NDF = 83.54 / 60, Prob = 2.40%2χ

]2 mass [GeV/cBπ -π -π +π5.4 5.6 5.8

2C

andi

date

s pe

r 5

MeV

/c

0

50

100 data

fit

+π -s D→ s B

background

π cΛ → bΛ

]2 mass [GeV/cBπ -π -π +π5.4 5.6 5.8

/ NDF = 71.40 / 64, Prob = 24.55%2χ

proper time [cm]0 0.2 0.4

mµC

andi

date

s pe

r 50

1

10

210

data

fit+π -

s D→ s B

background

π - D→ 0 Bπ cΛ → bΛ


/ NDF = 46.61 / 29, Prob = 2.04%2χ


mµC

andi

date

s pe

r 50

1

10

210

data

fit+π -

s D→ s B

backgroundπ cΛ → bΛ


/ NDF = 35.48 / 25, Prob = 7.99%2χ

48

Non-Golden Channels, Bs → Ds3π

]2 mass [GeV/cBπ 3-π) - K+

(Kφ5.4 5.6 5.8

2C

andi

date

s pe

r 5

MeV

/c

0

50

100

data

fitπ 3s D→ s B

background

π 3- D→ 0 Bπ 3cΛ → bΛ

satellites

]2 mass [GeV/cBπ 3-π) - K+

(Kφ5.4 5.6 5.8

/ NDF = 41.73 / 45, Prob = 61.14%2χ

]2 mass [GeV/cBπ 3-

) K-π +(K*K

5.4 5.6 5.82

Can

dida

tes

per

5 M

eV/c

0

50

100 data

fitπ 3s D→ s B

background

π 3- D→ 0 Bπ 3cΛ → bΛ

satellites

]2 mass [GeV/cBπ 3-

) K-π +(K*K

5.4 5.6 5.8

/ NDF = 41.67 / 39, Prob = 35.54%2χ

]2

mass [GeV/c-π +π + π) π (3sD5.4 5.6 5.8

2C

andi

date

s pe

r 5

MeV

/c

0

10

20

30

data

fitπ 3s D→ s B

backgroundπ 3cΛ → bΛ

satellites

]2

mass [GeV/c-π +π + π) π (3sD5.4 5.6 5.8

/ NDF = 24.54 / 24, Prob = 43.13%2χ


mµC

andi

date

s pe

r 50

1

10

210 data

fitπ 3s D→ s B

background

π 3- D→ 0 Bπ 3cΛ → bΛ


/ NDF = 28.01 / 26, Prob = 35.82%2χ


mµC

andi

date

s pe

r 50

1

10

210 data

fitπ 3s D→ s B

background

π 3- D→ 0 Bπ 3cΛ → bΛ


/ NDF = 40.82 / 24, Prob = 1.74%2χ


mµC

andi

date

s pe

r 50

1

10

data

fitπ 3s D→ s B

backgroundπ 3cΛ → bΛ


/ NDF = 19.38 / 18, Prob = 36.86%2χ

49

Performance of Neural Network Selection

2ca

ndid

ates

per

20.

0 M

eV/c

500

1000

1500

2000

2500

3000

CDF Run II Preliminary

Neural Network

-1L = 1.0 fb

Cut Based

]2candidate mass [GeV/c4.8 5 5.2 5.4 5.6 5.8 6

2ca

ndid

ates

per

20.

0 M

eV/c

0

500

1000

1500

2000

2500

3000


2ca

ndid

ates

per

20.

0 M

eV/c

0

500

1000

1500

2000

2500

3000 Neural Network, butnot Cut Based


Cut Based, butnot Neural Network

50

Amplitude Scan Non-Golden Modes

]-1 [pssm∆

0 5 10 15 20 25 30 35

Am

plitu

de

-3

-2

-1

0

1

2

3σ 1 ± data

σ 1.645

σ 1.645 ± data


95% CL limit

sensitivity

-117.1 ps-128.3 ps


51

Likelihood Curves - Non-Golden Channels

Non-Golden LikelihoodMinimum: −9.6

Spring analysisMinimum: −6.4p-value: 0.2%

Non-Golden sample

∆ms = 17.66 ± 0.11 ps−1

]-1 [pssm∆15 16 17 18 19 20

log(

L)∆

-10

-5

0

5

10

15

CDF Run II Preliminary -1L = 1.0 fb

Consistent result with Golden Only

52

Combined Amplitude ScansSemileptonic Hadronic

]-1 [pssm∆

0 5 10 15 20 25 30 35

Am

plitu

de

-4

-3

-2

-1

0

1

2

3

4σ 1 ± data

σ 1.645

σ 1.645 ± data


95% CL limit

sensitivity

-116.5 ps-119.3 ps

X_ s D+ l→ 0

sB

]-1 [pssm∆

0 5 10 15 20 25 30 35

Am

plitu

de

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2σ 1 ± data

σ 1.645

σ 1.645 ± data


95% CL limit

sensitivity

-117.1 ps-130.7 ps

Signal at ≈ 17.75 in hadronic analysis

Note☞ world best semileptonic analysis: 19.3 ps−1

☞ hadronic analysis in different league: 30.7 ps−1

53

Combined Amplitude Scan

]-1 [pssm∆

0 5 10 15 20 25 30 35

Am

plitu

de

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2σ 1 ± data

σ 1.645

σ 1.645 ± data


95% CL limit

sensitivity

-117.2 ps-131.3 ps

A = 1.21 ± 0.20(stat) compatible with 1 for ∆ms ∼ 17.75 ps−1

A/σA(∆ms = 17.75 ps−1) = 6.05, but what is the p-value?

54

Likelihood Profile

Difference, −∆ log(L)

log(L (A = 1)) − log(L (A = 0))

Minimum: −17.26

]-1 [pssm∆0 5 10 15 20 25 30 35

log(

L)∆

-30

-20

-10

0

10

20

30 data

expected no signal

expected signal

Key question:How often can random tags produce a minimum at least as deep?

55

Likelihood Significance

min log(L)∆

-30 -25 -20 -15 -10 -5 00

2

4

6

8

10

12

14

610×

observed

randomly tagged

=17.77sm∆signal

min log(L)∆-20 -15 -10 -5 0p-

valu

e

-910

-810

-710

-610

-510

-410

-310

-210

-110

1

σ5

28 trials out of 350 millionp-value ≈ 8 × 10−8 corresponding to 5.4σ

(5 standard deviations is = 5.7 × 10−7)→ passed observation criterion

56

∆ms Measurement∆ms = 17.77 ± 0.10(stat) ± 0.07(syst) ps−1

was submitted to PRL on Monday

]-1 [pssm∆15 16 17 18 19 20

log(

L)∆

-10

0

10

20

30combinedhadronic

semileptonic

Systematic☞ well behaved☞ ct scale uncertainty☞ rest: small

Agrees with SM18.3 +6.5

−1.5 ps−1EPS 2005

Agrees with 1st result17.31 +0.33

−0.18(stat) ± 0.07(syst) ps−1

PRL 97 (2006) 62003

57

Visualizing the Result

∆ms = 17.77 ± 0.10(stat) ± 0.07(syst) ps−1

[ps]sm∆/πDecay Time Modulo 20 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Fitt

ed A

mpl

itude

-2

-1

0

1

2

data

cosine with A=1.28

CDF Run II Preliminary -1L = 1.0 fb

Proper decay time folded onto a 2π interval

58

Direct Measure of |Vtd /Vts|Relation between ∆mq and Vtq

∆ms∆md

= mBsmBd

ξ 2|VtsVtd

|2

Inputs☞

mBdmBs

= 0.98390 PRL 96 (2006) 202001

☞ ξ = 1.21 +0.047−0.035 M.Okamoto hep-lat/0510113

☞ ∆md = 0.507 ± 0.005 PDG 2006

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

−0.0060(theo)

Best so far Belle: PRL 96 221601 (2006)

|Vtd ||Vts| = 0.199 +0.026

−0.025(exp) +0.018−0.016(theo)

59

ConclusionsLong journey ended☞ 19 years of search to see Bs-Bs oscillations☞ found signal consistent with Bs-Bs oscillations☞ significance: 5.4σ corresponding to p = 8 × 10−8

]-1 [pssm∆

0 5 10 15 20 25 30 35

Am

plitu

de

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2σ 1 ± data

σ 1.645

σ 1.645 ± data


95% CL limit

sensitivity

-117.2 ps-131.3 ps

∆ms = 17.77 ± 0.10(stat) ± 0.07(syst)60

Accomplishments in the Course of the AnalysisPhD Theses

C.Chen UPenn Charm Cross Section MeasurementI.Furic MIT Reconstruction of Bs → D−

sπ+

A.Bolshov MIT Reconstruction of Bs → D−s3π

S.DaRonco Padova Lifetimes from Exclusive ReconstructionJ.Piedra Cantabria B0 Mixing and Tagger CalibrationG.Giurgu CMU Muon TaggingV.Tiwari CMU Electron TaggingD.Usynin UPenn Charged Particle Composition Around B MesonsG.Salamanna Rome I Opposite Side Kaon TaggingA.Belloni MIT SSKT and Neural Network for Hadronic DecaysN.Leonardo MIT Likelihood FrameworkJ.Miles MIT Proper Time Resolution and Partial DecaysG.Di Giovanni Paris Same Side Kaon Tagging (next gen. analysis)B.Casal Cantabria Neural Network (next gen. analysis)

2006 Tollestrup AwardG.Ceballos (Cantabria), I.Furic (Chicago), S.Menzemer (MIT/Cantabria)

61

The End

62

New Physics in Loops?from Murayama et al. hep-ph/0212180

bR

g~g~

bR

sR

sR

bR~

bR~

sR~

sR~

(δ23)RRd

(δ23)RRd

b

b

L

L

g~g~

sR

sR

b

b

R

R

~

~

b

b

L

L

~

~

s

s

R

R

~

~

δd23( )

RRtanβµmb

tanβµmb δd23( )

RR

Supersymmetry model☞ gluino in loop☞ squarks in loop☞ describes all data☞ allows very high ∆ms

☞ ∆ms excludes models→ ∆ms sensitive to

New Physics0

50

100

150

200

250

300

350

400

450

500

−1 −0.5 0 0.5 1

κ= −1.1

0

50

100

150

200

250

300

350

400

450

500

−1 −0.5 0 0.5 1

κ= −1.5

0

50

100

150

200

250

300

350

400

450

500

−1 −0.5 0 0.5 1

κ= −2.0

0

50

100

150

200

250

300

350

400

450

500

−1 −0.5 0 0.5 10

50

100

150

200

250

300

350

400

450

500

−1 −0.5 0 0.5 1

κ= −0.7

∆ Βs

∆ Βs

M vs. SφΚ

M

−1(ps )

SφΚ

m

[1/p

s]∆

s400

500

300

200

100

0SM Expectation

63

Observables: Neutral B Meson Mixing

For Bs no imaginary matrix element involved|Bs,H ⟩ = 1p

2(|Bs⟩ + |Bs⟩) CP odd |Bs,L⟩ = 1p

2(|Bs⟩ − |Bs⟩) CP even

Initial particles and anti-particles|Bs⟩ = 1p

2(|Bs,H⟩ + |Bs,L⟩) |Bs⟩ = 1p

2(|Bs,H ⟩ − |Bs,L⟩)

Behavior in proper timeP(t)B0→B0 = 1

2τ e−t /τ (1 + cos ∆mt)P(t)

B0→B0 = 12τ e−t /τ (1 − cos ∆mt)

Determine asymmetry

A0(t) = N(t)unmixed−N(t)mixedN(t)unmixed+N(t)mixed

= cos(∆m t)0

0.2

0.4

0.6

0.8


prob

abili

ty d

ensi

ty

unmixedmixedtotal

64

Accelerator Setup at FermilabComplex accelerator system

C D F D0

Tevatron Collider☞ Tevatron 1 km ring radius, CM energy

p

s = 1.96 TeV☞ 36x36 colliding p, p bunches, 1011(1010) p(p) per bunch

65

CDF Detector – Opened Up

66

b Production: Tevatron versus B FactoriesDisadvantages

☞ nqq = 1000 x nbb

☞ hostile environment☞ second b often outside fiducial

Advantages☞ larger cross section x105

☞ larger boost x10☞ b hadrons: B+, B0, Bs, Bc, Λb, ..

Conclusion☞ fast event selection necessary, we call this trigger☞ typical rejection factors are 1/50,000

67

Upgrades: Displaced Track Trigger

Decay PointB

Sketch of a B Decay

p

B Production Point

d0 − impact parameter

Challenge:☞ fast readout☞ track above 25 kHz

B Signatures☞ electrons, muons☞ high momentum tracks☞ displaced tracks

−600 −400 −200 0 200 400 6000

2000

4000

6000

8000

10000

12000

14000

16000

18000

m)µ (0SVT d

25≤SVT2χ 2 GeV/c; ≥tP

mIncludes

beamspot33 mµ µ = 47 σ

mµtr

acks

per

10

68

Vertexing - Key Detector

Layer 00☞ innermost silicon layer: mounted on beampipe☞ at distance of about 1.5 cm from the beamline☞ significant boost for vertexing resolution

69

Flavor Tagging - Key Detector

Time-of-Flight Detector☞ distinguish pions/kaons to p ≈ 1.5 GeV/c, 100 ps resolution☞ most important information for same side tagger

70

Unbiased Analysis Upgrade

Upgrade power estimated in an unbiased fashion

Signal Improvements☞ fits of mass spectra provide estimate of S/

pS + B

Flavor tagging☞ OST improvement measured in calibration samples:`+track, B0/B+

☞ SSKT improvement obtained from Monte Carlo

71

Proper Time Resolution

72

Proper Time Resolution - Basics

Significance revisited

1/σ =

q

nSεD2

2

q

nSnS+nB

exp(−(∆msσct)22 )

Reconstructed proper decay timect = LB

xymBpB

Thadronic

ct = L`Dxy

mBp`D

T⋅

�

p`DT

pBT

LBxy

L`Dxy

�

MCsemileptonic

Understanding of resolution☞ irrelevant for lifetime measurements☞ critical piece for Bs oscillations☞ the faster the more important☞ calibration on data needed

-1

-0.5

0

0.5

1


asym

met

ry

Realistic resolution: vtx: 50 µm

-1

-0.5

0

0.5

1


asym

met

ry

Realistic resolutions: vtx: 50 µm pt: σ(p)/p = 5%

73

Proper Decay Time Resolution- CalibrationUse prompt D+ and track

☞ large sample of prompt D+

☞ most tracks from PV☞ same topology as signal☞ measure of ct resolution

proper time [cm]

-0.2 -0.1 0.0 0.1 0.2

mµca

ndid

ates

/ 20

10

210

310

410

data+π - D

fit

+ f

++ f

prompt

proper time [cm]

-0.2 -0.1 0.0 0.1 0.2


Calibrated on our data

74

Proper Decay Time Resolution - Results

m]µproper time resolution [0 20 40 60 80 100

mµP

roba

bilit

y pe

r 5

0.00

0.05

0.10

0.15

0.20

0.25

m]µproper time resolution [0 20 40 60 80 100

mµP

roba

bilit

y pe

r 5

0.00

0.05

0.10

0.15

0.20

0.25+π (3)-

s D→ sB

mµ> = 26.0 ctσ <

-1 1 fb≈CDF Run II Preliminary L

one oscillation at m = 18/ps∆ s

Optimal use of data☞ PV per candidate☞ resolution per candidate

Superior resolution☞ access to high ∆ms

☞ CDF plays in a newleague

75

Proper Decay Time Resolution - Results

sB


0.4 0.6 0.8 1.0

prob

abili

ty d

ensi

ty

5

10

ν l (*)s D→ 0

sBall 2 3.1 GeV/c≤ lsD 2.0 < m2 4.5 GeV/c≤ lsD 4.3 < m2 5.1 GeV/c≤ lsD 4.9 < m

π *s D→ 0

sB

ρ s D→ 0sB

sB


0.4 0.6 0.8 1.0

Proper decay time [ps]0 1 2 3

Pro

per

deca

y tim

e re

solu

tion

[fs]

0

200

400

600

800

π s D→ 0sB

ρ s / Dπ *s D→ 0

sB

2 5.1 GeV/c≤ lsD, 4.9 < mν l (*)s D→ 0

sB

2 4.5 GeV/c≤ lsD, 4.3 < mν l (*)s D→ 0

sB

2 3.1 GeV/c≤ lsD, 2.0 < mν l (*)s D→ 0

sB

Hadronic Bs → Ds(3)π☞ σ0

ct ∼ 26 µm, 87 fs; σp/p < 1%Semileptonic Bs → `DsX

☞ σ0ct ∼ 30-70 µm, 100-230 fs; σp/p ∼ 3-20%

76

Flavor Taggers - Overview

L xy

ct = L xymp

B

T

��

��

opposite side

K

K

π

π

0sB

D s

+

+

K+


opposite

D meson

fragmentationkaon

−l

side lepton

B hadronB jet

Collision Point

Creation of bb

side kaonopposite

K −

typically 1 mm

Production flavor tagging☞ combine same side and opposite side tags☞ opposite side: muon, electron, kaon and jet charge taggers

jet selection algorithms: vertex, jet probability and highest pT

☞ same side: particle ID based Kaon Tagger77

Flavor Taggers - Maximize PerformanceParametrize tagger performance in dependent variables:here muon tagger and prel

T

Tune on large B+, B0 samples: transfers directly to Bs

→ each event has predicted dilution

78

Flavor Taggers - Fit for Tagger Performance

Fit B+ and B0

☞ `D and Dπ(ππ) are fitseparately

☞ parameters: D and ∆md

☞ depicted: combined `Dsamples with combinedlepton tags

proper decay-length [cm]

0.05 0.1 0.15 0.2

asym

met

ry

-0.3

-0.2

-0.1

0

0.1

0.2

0.3


D Xµ e/→B

Soft Lepton Taggers

-1 355 pb≈L

proper decay-length [cm]

0.05 0.1 0.15 0.2

asym

met

ry

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

data

fit projection

contribution0 B contribution+ B

B0 Mixing Result☞ 0.536 ± 0.028(stat) ± 0.006(syst) ps−1 hadronic

☞ 0.509 ± 0.010(stat) ± 0.016(syst) ps−1 semileptonic

☞ 0.507 ± 0.005 ps−1 PDG 2006

79

Flavor Taggers - ResultsUsage of flavor taggers

☞ OST: selection of best available OS tag☞ OST and SST use disjunct input information☞ simple uncorrelated OST/SST combination algorithm

εD2[%] Hadronic SemileptonicMuon 0.48 ± 0.06 0.62 ± 0.03Electron 0.09 ± 0.03 0.09 ± 0.01JQ/Vertex 0.30 ± 0.04 0.28 ± 0.02JQ/JetCharge 0.46 ± 0.05 0.34 ± 0.02JQ/highPt 0.14 ± 0.03 0.11 ± 0.01OST 1.47 ± 0.10 1.44 ± 0.04SSKT 3.42 ± 0.96 4.00 ± 1.12

SSKT improves tagging by factor of 380

Unbinned Likelihood Fit Overview

For each sample component and event

L = Lm ⋅ Lt ⋅ Lσt ⋅ LD

Most complex is proper decay time description

Lt =1N

κe−κ t 0

τ

τ1 ± ASDD cos(∆msκ t 0)

2⊗ R(t − t 0; Sσtσt) ⋅ ε(t)⊗ F (κ )

81

Amplitude Scan Method - Using B0

]-1

[psdm∆0 10 20 30

Am

plitu

de

-1

0

1

2σ 1 ± data

σ 1.645


95% CL limit

sensitivity

-10.4 ps-127.5 ps


]-1

[psdm∆0 0.5 1 1.5 2

Am

plitu

de

-1

0

1

2

σ 1 ± data

σ 1.645

(stat. only)σ 1.645 ± data σ 1 ± dm∆

95% CL limit

sensitivity

-10.3 ps-1> 2.0 ps


Unbinned likelihood fit☞ p ∼ ( 1 ± AD cos(∆mt))☞ scan fixed values of ∆m☞ record A and σ(A)

Signal ≡ unit amplitude☞ else A consistent with 0☞ exclude ∆m @95%CL for

(1 − A) > 1.645σ(A)

82

Systematic Uncertainties on Amplitude

Hadronic Semileptonic

]-1

[pss m∆

0 5 10 15 20 25 300

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45Total

ctσNon-Gaus Cabibbo DConSSTOST+SST Corr

ctσSΓ / Γ ∆

]-1 [pssm∆0 10 20 30 40

syst

.Aσ

0.05

0.1

0.15

0.2

physics bkg.

ctS

DS

prompt dil.

promptf tailsctσ

total

Systematic uncertainties ∼ 0.15-0.20 at high ∆ms:→ analysis is statistically limited

83

Probabilities of Uncertainties

]-1 [pssm∆Uncertainty on 0 0.2 0.4

-1E

xper

imen

ts p

er 1

0 fs

1

10

210

Positive Unc. Golden Mode

Prob: 43%

]-1 [pssm∆Uncertainty on 0 0.1 0.2 0.3 0.4 0.5

-1E

xper

imen

ts p

er 1

0 fs

1

10

210

Positive Unc. Other Hadronic

Prob: 38%

]-1 [pssm∆Uncertainty on 0 0.05 0.1 0.15 0.2

-1E

xper

imen

ts p

er 4

fs

1

10

210

Positive Unc. Hadronic + Golden

Prob: 37%


-1E

xper

imen

ts p

er 1

0 fs

1

10

210

Negative Unc. Golden Mode

Prob: 37%


-1E

xper

imen

ts p

er 1

0 fs

1

10

210

Negative Unc. Other Hadronic

Prob: 38%

]-1 [pssm∆Uncertainty on 0 0.05 0.1 0.15 0.2

-1E

xper

imen

ts p

er 4

fs

1

10

210

Negative Unc. Hadronic + Golden

Prob: 18%

Uncertainties as expected for this sample84

Systematic on ∆ms

Relevant systematic uncertainties☞ all related to ct scale☞ common for hadronic and semileptonic samples

Source Value [ps−1]SVX alignment 0.04Track fit bias 0.05P.V. bias from tagging 0.02Others < 0.01Total 0.07

85

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