Observation of Bs-Bs Oscillations · Historic Review: A 20-Year Effort 1987 ﬁrst evidence of B...

Observation ofBs-Bs Oscillations

Christoph PausMassachusetts Institute of Technology

Wine and Cheese SeminarSeptember 22, 2006

Overview

Theory and some HistoryThe MethodEquipment Used for the MeasurementsOur Samplesb Flavor TaggingResults per SampleMixing Result SummaryConclusions

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 �

�

L

�

cs�

�L

�tb�

�L

Weak interaction through W ± bosons

cs

W+c

d

W+

In general: weak eigenstates ≠ strong eigenstatesmixing between families possiblelower quark doublet components absorb differenceneutrinos also mix

3

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

d �

s�

�

=

�

cos θ sin θ− sin θ cos θ

��

ds

�

rotation matrix

Matrix has to be unitary: V �V = 1

Describe mixing between three quark-pair families��

d �

s�

b�

�� = V ×

��

dsb

�� with V =

��

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

��

V is Cabbibo–Kobayashi–Maskawa matrix

Three families → 4 degrees of freedom3 angles1 complex phase → CP violation

4

CKM MatrixMatrix structure

mostly diagonalcrossing of families suppressedthe further the less probablevalues not predicted

Particles are conserved:V �V = 1

→ unitarity condition

u

d

c

t

s b

Wolfenstein parametrization (λ = 0.2272 ± 0.0010):

V =

��

1 − λ 2/2 λ Aλ 3(ρ − iη)−λ 1 − λ 2/2 Aλ 2

Aλ 3(1 − ρ − iη) −Aλ 2 1

�� + O(λ 4)

Least known parameters: ρ and η5

Unitarity Triangle

Unitarity condition: V �V = 1 V =

��

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

��

→ 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

tdVV

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

�

− i2

�Γ Γ12

Γ∗12 Γ

�

Diagonalizing the Hamiltonian results intwo 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 � mBqBBqf2Bq

��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 2βVub/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

CK 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

Resulttime integratedχ = 0.121 ± 0.047implied 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

1989CLEO confirms Argus result PRL 62 (1989) 2233

1990sinclusive measurements of B0 mixing from LEP establish Bs mixing

1993first 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

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

PRL 82 (1999) 3576

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

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

2006D0 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

Ds

+

+

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 mixingproper decay time ct , B rest frameB flavor at decay, final stateB flavor at production, flavor tagging

13

An Event Display

14

B Mixing Phenomenology

Behavior in proper timeP(t)B0→B0 = 1

2τe−t /τ(1 + cos ∆mt)

P(t)B0→B0 = 1

2τe−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 =

�

nSεD2

2�

nSnS+nB

exp(−(∆msσct)22 )

σct =�

(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, Ameasure ∆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

Unchangedsame data: 1 fb−1

Improvementsflavor tagging

added opposite side kaon taggerapplied NN to combine all opposite side taggersapplied NN to same side tagger

signal yieldsadded partially reconstructed decaysused particle identification in selectionused NN for hadronic selectionadded 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 system3 level, pipelined, flexible systemSilicon Vertex Trigger (SVT) at 2nd level (≈25 kHz)

Charged particle reconstructionredundancy for pattern reco in busy environmentexcellent momentum resolution: R = 1.4m,B = 1.4Texcellent vertex resolution: L00 at 1.5cm

Particle identificationenergy loss in drift chamber (dE /dx)Time-of-Flight system at 1.4 m radiuselectron 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∗−

�

+XBs → J/ψφwith D∗− → D0π−, D0 → K −π+(π+π−), D− → K +π−π−

Signal sampleshadronic: Bs → D−

sπ+(π+π−)semileptonic: Bs → D−

s�

+Xwith 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 resolutionsample is cleansmall 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 �DsXreconstruct: ct∗ = Lxy

mB

p�DT

large branching ratioinferior ct , mass resolutionsample composition issue

29

b Flavor Tagging

30

Flavor Tagging Introduction

L xy

ct = L xymp

B

T

��

��

opposite side

K

K

π

π

0sB

Ds

+

+

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

Crucial parametersefficiency: 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, kaonsame side: pion (B+, B0), kaon (Bs)

Tuning the algorithmbased on huge heavy flavour rich �+track samplefind dependencies and determine parametrizationsfind optimal point for the algorithm

Calibration of the taggerverify algorithms on B0 and B+ semileptonic/hadronic samplesdetermine scale factor S inB+ : p ∼ exp(−t /τ)(1 ± SD)B0 : p ∼ exp(−t /τ)(1 ± SD cos ∆mdt)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 Taggersnew kaon taggernot mutually exclusive → hierarchical schemenew 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 differno direct transfer B+,B0 → Bs

need MC to measure tagger dilution

Strategytune MC with B+ and B0

apply PID to de-weight pionsuse MC to parametrize dilution

ParticleID very importantsignificantly 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 variablesuse 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 protonsdecision: track charge of highest NN tag candidate

Expected improvementMC ≈ 6% relative

Measured improvement0% 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 factoriesapplied in hadronic and semileptonic analysesusing combined Time-of-Flight and dE/dx (see SSKT)

Effectsstrongest in Ds → K ∗0Kno explicit D+ → K −π+π+

rejection (+35%)combinatorial backgrounddominated 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

Depthsets 95% CL interval1σ 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 signatureBs → 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

T/pReconstructedT = pκ

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 semileptoniclarge 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 Idopt. D+ rejectionrelax kinematiccuts

Neural Netlarger signal atsame bgadd new modeBs → 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

plit

ud

e

-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

Noteworld 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

Systematicwell behavedct scale uncertaintyrest: 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

InputsmBdmBs

= 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 oscillationsfound signal consistent with Bs-Bs oscillationssignificance: 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

Observation of Bs-Bs Oscillations · Historic Review: A 20-Year Effort 1987 ﬁrst evidence of B...

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