Measurement of the B-Bs Oscillation Frequencyhome.fnal.gov/~leonardo/docs/seminar_anl.pdfMeasurement of the Bs-Bs Oscillation Frequency Nuno Leonardo Massachusetts Institute of Technology

Measurement of the Bs-Bs Oscillation Frequency

Nuno Leonardo Massachusetts Institute of Technology

for the CDF Collaboration

Argonne National Laboratory, June14th 2006

0 0

N. Leonardo, MIT ANL Seminar, June 2006

History a 20 year quest

-6 -4 -2 0 2 4

amplitude at !ms = 15.0 ps-1

Average for PDG 2006 0.48 ± 0.43

amplitude

(18.2 ps-1)

(sensitivity)

CDF1 l"/l(92-95)

-0.14 ± 2.00 ± 0.51 ( 5.1 ps-1)

SLD dipole(96-98)

0.44 ± 1.00 + 0.44 0.44 ± 1.00 - 0.28 ( 8.7 ps-1)

SLD Ds(96-98) 1.03 ± 1.36 + 0.31 1.03 ± 1.36 - 0.31 ( 3.3 ps-1)

OPAL Dsl(91-95)-3.63 ± 3.05 + 0.40-3.63 ± 3.05 - 0.42 ( 4.2 ps-1)

OPAL l(91-95)

-1.25 ± 2.34 ± 1.91 ( 7.2 ps-1)

DELPHI l(92-00)

-0.96 ± 1.35 ± 0.71 ( 9.1 ps-1)

DELPHI vtx(92-00)

-0.23 ± 3.04 ± 0.56 ( 6.9 ps-1)

DELPHI Dsl+"l(92-95)

1.25 ± 1.37 ± 0.31 ( 8.6 ps-1)

DELPHI Bs+Dsh(92-95) 0.45 ± 3.58 ± 1.93 ( 3.2 ps-1)

ALEPH Bs(91-00)-0.47 ± 1.15 ± 0.47 ( 0.4 ps-1)

ALEPH Dsl(91-95) 3.83 ± 1.49 ± 0.32 ( 7.5 ps-1)

ALEPH l(91-95, no Dsl, adjusted)

0.50 ± 0.79 ± 0.16 (13.1 ps-1)

Heavy FlavourAveraging Group

results from LEP, SLD, CDF I

Δms>14.4 ps-1 @ 95%CL ↔ sensitivity 18.2 ps-1

[PDG 2006]

1987first B0 mixing measurements: UA1 and ArgusCLEO confirms results 2 years after1990’sinclusive B mixing measurements from LEP establish Bs mixing1993First time dependent measurements of Δmd and lower limit on Δms by ALEPH1999CDF Run I result: Δms>5.8 ps-1, sens. 5.1 ps-1

2000’sD∅ recently reports direct bound

Δms ∈ [17, 21]ps-1 at 90% CL, sens. 14.1 ps-1

CDF Run II February 2005: sens. 8.4 ps-1 (limit 7.9 ps-1) October 2005: sens.13.0 ps-1 (limit 8.6 ps-1) Now: sensitivity 25.8 ps-1 !


Flavor Oscillations• neutral mesons undergo particle-antiparticle oscillations

• two-state system

• two mass eigenstates

‣ separately evolve in time

• mass difference

determines oscillation frequency of the system

0

0.2

0.4

0.6

0.8

0 1 2 3 4 5proper decay time, t [ps]

Prob

abilit

y De

nsity

unmixedmixedtotal

P(B → B̄) ∼e−t/τ

2τ(1 − cos ∆m t)

{|B(b̄s)〉, |B̄(bs̄)〉}

{|BH〉, |BL〉}

∆m = MH − ML


In the Standard Model• Mixing occurs via 2nd order flavor changing weak transitions

• Ratio of Bs0 and Bd0 oscillation frequencies

allows precise determination of CKM elements‣ Δmd measured to high precision‣ Δms not been measured until now

∆ms

∆md

=mBs

mB0

ξ2|Vts|2

|Vtd|2

t!

t(c, u)

(c!, u!)W+ W"

s!

b

b!

s

Bs Bs

Vts

Vts

∆mq ∝ |Vtq|2

➠


η̄ = (1 − λ2/2) ηρ̄ = (1 − λ2/2) ρ

Flavor Parameters CKM Matrix

• CKM Matrix unitarity condition

may be represented as a triangle in complex plane

‣ in terms of re-scaled ρ and η parameters

0*** =++ tbtdcbcdubud VVVVVV

CKM Matrix Wolfenstein parameterization

V =

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

=

1 − λ2/2 λ Aλ3(ρ − iη)

−λ 1 − λ2/2 Aλ2

Aλ3(1 − ρ − iη) −Aλ2 1

+O(λ4)


!

0 0.5 1

"

0

0.5

Δmd

!

0 0.5 1

"

0

0.5

The Beauty Unitarity Triangle

!

0 0.5 1

"

0

0.5

/ ΔmsΔmd


Full UT/CKM Fit

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

-0.4 -0.2 0 0.2 0.4 0.6 0.8 1

!

"md

#K

$ "ms & "md

|Vub/Vcb|

sin 2%

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

!

%$

&

'

excl

uded

are

a ha

s C

L > 0.

95 C K Mf i t t e r

EPS 2005

CKM Fit before Δms direct measurement


Probe of New Physics

• Additional virtual particles change Δms from SM expected value

• Measured value can be used to restrict model parameters

∝ tanβ4

[Phys. Rev. D 69 0904024 (2004)] [hep-ph/0605177 (2006)] [Eur. Phys. J. C 24 275 (2002)]

Examples:


Scope & Overview

pp collisionsTevatron

DetectorCDF

Data Analysis

Amplitude ScanΔmS

CKM Fit

Standard ModelFlavor Models

-

Trigger

σpp→bX

Unbinned Likelihood

Fitter

B flavor tagging

B proper decay timeB mass

B lifetime τB0 mixing Δmd

tag calibration

likelihood model

MCsimulation


Final State Reconstructionb-flavor at decay

Proper Decay TimeIn B rest frame

Trigger SideOpposite Side

Analysis Ingredients

b-Flavor Taggingb-flavor at production

/ l+


Realistic Effects oscillation dampening

resolution of a mixing signal determined by

• signal yield, S

• purity, S/B

• flavor tagging power, εD2

• proper decay time uncertainty, σt

‣ decay-length resolution‣ effective momentum resolution

σA =

√2

εD2

√B + S

Se(∆m σt)

2/2

Getting the Bs samples


The CDF DetectorKey features for Δms

• excellent momentum and vertexing resolution

‣ drift chamber, silicon

• particle identification

‣ lepton id in calorimeters and muon chambers

‣ time of flight

‣ dE/dx in drift chamber

• ‘deadtimeless’ trigger system


Triggering on Displaced Tracks

• Heavy flavor decays displaced from the primary vertex

‣ daughter tracks tend to have large impact parameter

• trigger on displaced tracks‣ pT>2GeV/c, 120μm<|d0|<1mm

• requires precision tracking in silicon detector (SVT)

!600 !400 !200 0 200 400 6000

2000

4000

6000

8000

10000

12000

14000

16000

18000

m)µ (0SVT d

25!SVT2" 2 GeV/c; #tP

m Includes

beamspot33 mµ µ = 47 $

mµ

track

s pe

r 10

Secondary VertexPrimay Vertex B

.impactparameter

d0


Fully Reconstructed Decays

• relatively small BR’s• all daughters reconstructed

‣momentum completely contained in tracker‣superior sensitivity at higher Δms

• signal yield: 3,600

HadronicBs→Ds(3)π

]2) [GeV/c+!,-!)-K+(K"Mass(5.0 5.5 6.0

2Ca

ndid

ates

per

20

MeV

/c

0

200

400

600

data

fit+! -

s D# s B

satellites

combi bkg

! - D# 0 B! c$ # b$

]2) [GeV/c+!,-!)-K+(K"Mass(5.0 5.5 6.0

-1 1 fb%CDF Run II Preliminary L

Bs → Ds(ππ)π, Ds → φπ/K∗K/πππ

0sB

−sD

+π+W

b cd

s

u

s

N. Leonardo, MIT ANL Seminar, June 2006]2lepton-D mass [GeV/c3 4 5

2Ca

ndid

ates

per

18

MeV

/c

0

1000

2000

3000

4000

Xs l D! sB

Data Fit

Signals B Physics Background Combinatorial + False Lepton

]2lepton-D mass [GeV/c3 4 5

CDF Run II Preliminary -1 1 fb"L

• large branching ratios• missing neutrino and neutrals

‣need to correct for missing momentum on average‣superior sensitivity in lower Δms range

• signal yield: 37,000

Partially Reconstructed Decays SemileptonicBs→DslX

]2D mass [GeV/c1.94 1.96 1.98 2

2Ca

ndid

ates

per

1 M

eV/c

0

5000

10000

Xs l D! sB

Data Fit

Signals B

Combinatorial + False Lepton

]2D mass [GeV/c1.94 1.96 1.98 2


0sB

−sD

+W

b clν

s

+l

s

Bs → DslX, Ds → φπ/K∗K/πππ

Proper Decay Time B Lifetime measurement


Proper Decay Time

Life

time

effic

ienc

y

0

0.5

1

1.5

21!1f1"

2!2f2"3!3f3"

4!4f4"

0.00179 0.00150 0.06806 0.01322 0.08388 0.02725 0.01218 0.68894 0.00757 0.00755 0.22568 0.00839

/ NDF = 105.02 / 107, Prob = 56.34%2#

Proper decay length [cm]0 0.1 0.2 0.3 0.4

$(d

ata

- fit)

/

-2

0

20.20 0.4

proper decay distance [cm]

Decay time in B rest frame: t = L m/p

t-distribution determined by

• B meson lifetime

• decay distance resolution

• trigger/selection sculpting

‣ trigger (SVT) requirements on |d0| and event selection criteria on LT

modify PDF shape‣ described by t-efficiency function

from Monte Carlo, εt(t)

production vertex

B decay position

t-efficiency ε(t)

L

P(t) ∝ e−t′/τ ⊗ R(t − t

′;σt) · E(t)


proper time [cm]-0.2 -0.1 0.0 0.1 0.2

mµ

cand

idat

es /

20

10

210

310

410 data+! - D

fit+ f

++ f prompt

proper time [cm]-0.2 -0.1 0.0 0.1 0.2

CDF Run II Preliminary

proper time, ct [cm]

Calibrating Resolution in Data

• use large prompt D meson sample to construct B-like topologies of prompt D+track

• compare reconstructed decay point to interaction point• calibrate t-resolution by fitting prompt t-distribution

prompt track

Ds- vertex

P.V.“Bs” vertex


Bs Decay Time Resolution

• candidate specific decay time resolution used in likelihood fit

• average uncertainty ~26 μm or 87 fs about 1/4 oscillation period at Δms=18ps-1 for hadronic decays

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

mµPr

obab

ility

per 5

0.00

0.05

0.10

0.15

0.20

0.25

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

mµPr

obab

ility

per 5

0.00

0.05

0.10

0.15

0.20

0.25 +! (3)-s D" sB

mµ> = 26.0 ct# <

-1 1 fb$CDF Run II Preliminary L

one oscillation at m = 18/ps% s

Superior decay time resolution gives CDF sensitivity at much higher frequencies than previous experiments


• correct for missing momentum

with κ-factor distribution (MC)

• explore dependence on lepton-D invariant mass

• effectively worsens t-resolution

‣ limits semileptonics sensitivity at high Δms

κinematics correction in Semileptonics

Proper decay time [ps]0 1 2 3 4

Prop

er d

ecay

tim

e re

solu

tion

[ps]

0.0

0.2

0.4

0.6

0.8

1.0

! s D" sB2 5.1 GeV/c#

slD X, 4.9 < ms l D" sB2 4.5 GeV/c#

slD X, 4.3 < ms l D" sB2 3.1 GeV/c#

slD X, 2.0 < ms l D" sB

k-factor0.4 0.6 0.8 1.0

prob

abilit

y de

nsity

0.1

0.2

0.3

0.4 all

2 5.1 GeV/c! slD 4.9 < m

2 4.5 GeV/c! slD 4.3 < m

2 3.1 GeV/c! slD 2.9 < m

CDF Run II Monte Carlo s l D"B

k-factor0.4 0.6 0.8 1.0

σt !→ σ0

t ⊕ tσp

p

κ ≡

LB

LDl

pDl

pB

t !→ t κ


proper decay-length [cm]0.1 0.2 0.3

mµ

Cand

idat

es p

er 2

0 0

2000

4000

Xs l D! sB

Data Fit

Signals B Physics Background Combinatorial + False Lepton

proper decay-length [cm]0.1 0.2 0.3


Bs → lDsX


Lifetime Fits

Good agreement with World Average 1.469±0.059 ps-1

Hadronic 1.54±0.04 ps-1(stat)

Semileptonic (355pb-1) 1.48±0.03 ps-1 (stat)

proper time [cm]0.0 0.2 0.4

mµ

cand

idat

es p

er 3

0

1

10

210

310 data

fit+! (3)-

s D" s B

random bkg.+! (3)- D" 0 B-! (3)+

c# " b#


CDF Run II Preliminary -1 1 fb$L


b Flavor Tagging Δmd measurement


Tagging B Production Flavor

• produced B(b) or B(b)?

• use combined flavor taggers

‣ Opposite-side

‣ Same-side

• quantify performance with‣ efficiency, ε ≡ fraction of tagged events‣ dilution, D ≡ 1 - 2 × mistag probability‣ effective statistics for mixing becomes

N ➟ N εD2

• for limit on Δms must know D

K!

Bs

SST

OSTa l!

b K+


Opposite-Side Tagging

µptrel

• soft leptonfrom semileptonic decay of opposite b

• jet chargemomentum-weighted charge average of tracks in opposite side b jet

• use event specific dilution ‣ dependence on ptrel, jet charge

• other b not always in the acceptance

• independent of B species‣ performance calibrated in high

statistics samples of B+ and B0

‣ results applicable directly to Bs

jet axis

]2 [GeV/crelTP

-0.5 0 0.5 1 1.5 2 2.5 3Di

lutio

n [%

]-10

0

10

20

30

40

50

Isolated tracks

CMUP


b →c →μcontamination

μ from b-decay

soft lepton


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 Fit Δmd

• Hadronic: Δmd = 0.536 ± 0.028 (stat) ± 0.006 (syst) ps-1

• Semileptonic: Δmd = 0.509 ± 0.010 (stat) ± 0.016 (syst) ps-1

• World average: Δmd = 0.505 ± 0.005 ps-1

P ∼e−t/τ

2τ(1 − SD · D · cos ∆md t)

OST tagging power εD2 [%]

1.47 ± 0.10 (hadronic modes)

1.44 ± 0.04 (semileptonic modes)


Same-Side Tagging

• exploit b quark fragmentation‣ B0 / B+ likely accompanied by π+ / π-

‣ Bs likely accompanied by K+

➥ identify charge of leading track

• particle ID improves performance‣ separate kaons from pions‣ time-of-flight (TOF) & dE/dx

• dependent on B species‣ results in B0/B+ not applicable to Bs

• dilution for Bs needs to be estimated from Monte Carlo

+

b b

b b

b b

d

u s

u

s

d s

u d

B0

B0

B

!+

0"!

!0"

!

d

u s

d s

u

s

u d

}}

}}

}}

s

#

#


SS(K)T Performance

3.42 ± 0.96 % (Hadronic) Tagging power for Bs, εD2 ⎨

4.00 ± 1.12 % (Semileptonic)

✓ overall tagging performance enlarged by x3-4!

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 + K" J/# +B

+$ 0D # +B

$ 30D # +B

*0 K" J/# 0B

+$ - D# 0B

$ 3- D# 0B

data MC syst.

+!s- -> DsB

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

dilu

tion

[%] (

agre

emen

t)

-100

10203040506070

CDF Run II Monte Carlo

π K

Bs

B0

B+

Fit Procedure


Likelihood putting it all together

1

NLt =

SD D′

′

⊗R(t − t′;Sσt

σt) · E(t)κ

κ

κ

⊗F (κ)

L = Lmass · Lt · Lσt· LD

Δms1 ± cos( t )

2A

[for each sample component & event]

analytical computation

k-factor0.4 0.6 0.8 1.0

prob

abilit

y de

nsity

0.1

0.2

0.3

0.4 all

2 5.1 GeV/c! slD 4.9 < m

2 4.5 GeV/c! slD 4.3 < m

2 3.1 GeV/c! slD 2.9 < m

CDF Run II Monte Carlo s l D"B

k-factor0.4 0.6 0.8 1.0

Life

time

effic

ienc

y

0

0.5

1

1.5

21!1f1"

2!2f2"3!3f3"

4!4f4"

0.00179 0.00150 0.06806 0.01322 0.08388 0.02725 0.01218 0.68894 0.00757 0.00755 0.22568 0.00839

/ NDF = 105.02 / 107, Prob = 56.34%2#

Proper decay length [cm]0 0.1 0.2 0.3 0.4

$(d

ata

- fit)

/

-2

0

2

proper time [cm]proper time [cm]-0.2 -0.1 0.0 0.1 0.2

mµ

cand

idat

es /

20

10

210

310

410 data+! - D

fit+ f

++ f prompt

proper time [cm]-0.2 -0.1 0.0 0.1 0.2


+!s- -> DsB

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

dilu

tion

[%] (

agre

emen

t)

-100

10203040506070

CDF Run II Monte Carlo

e−

t

τ

τ


mµ

cand

idat

es p

er 3

0

1

10

210

310 data

fit+! (3)-

s D" s B

random bkg.+! (3)- D" 0 B-! (3)+

c# " b#


CDF Run II Preliminary -1 1 fb$L

]2) [GeV/c+!,-!)-K+(K"Mass(5.0 5.5 6.0

2Ca

ndid

ates

per

20

MeV

/c

0

200

400

600

data

fit+! -

s D# s B

satellites

combi bkg

! - D# 0 B! c$ # b$

]2) [GeV/c+!,-!)-K+(K"Mass(5.0 5.5 6.0

-1 1 fb%CDF Run II Preliminary L

Frequency Δms

Amplitude (A,σA) for fixed Δms

or


decay time, ps0.0 0.5 1.0 1.5 2.0

prob

abili

ty d

ensi

ty

0.00.1

0.20.30.4

0.50.6

0.70.8

time domain analysis

totalunmixedmixed

Fit Strategy frequency/amplitude

Time domain

P(t) ~ 1± D cos Δmst

Frequency domain

P(t) ~ 1± A D cos Δmst


Amplitude Scan Notation•procedure: repeat Amplitude fit for different Δms probe values

‣A~1 ⇐ true Δms value‣A~0 ⇐ frequencies away from the true value

• frequency values where A + 1.645 σA < 1 are excluded at 95% CL• sensitive in Δms range where 1.645 σA < 1

‣ examples: ☛ recent DØ result: 14.1 ps-1 ☛ average PDG 2006: 18.6 ps-1

-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)

Ampli

tude

data ± 1 " 95% CL limit 14.4 ps-1

1.645 " sensitivity 18.2 ps-1

data ± 1.645 "data ± 1.645 " (stat only)

Average for PDG 2006Example: World Average Δms scanExample: CDF Δmd scan

The Δms Results


]-1 [pssm!0 10 20 30

Ampl

itude

-2

0

2

" 1 ± data " 1.645

" 1.645 ± data (stat. only)" 1.645 ± data

95% CL limitsensitivity

-116.7 ps-125.4 ps

-# +# +# _ s D$ 0

s, B+# _ s D$ 0

sB

CDF Run II Preliminary -1L = 1.0 fb

Amplitude Scan: Hadronic Decays


]-1 [pssm!0 10 20 30

Ampl

itude

-2

0

2

" 1 ± data " 1.645



-115.9 ps-117.3 ps

X_ s D+ l# 0

sB


Amplitude Scan: Semileptonic Decays


]-1 [pssm!0 10 20 30

Ampl

itude

-2

0

2

" 1 ± data " 1.645



-116.7 ps-125.8 ps

-# +# +# _ s D$ 0

s, B+# _ s D$ 0

s X, B_ s D+ l$ 0

sB


Combined Amplitude Scan


Results: Amplitude Scan

]-1 [pssm!0 10 20 30

Ampl

itude

-2

-1

0

1

2" 1 ± data

-# +# +# _ s D$ 0

s, B+# _ s D$ 0

s X, B_ s D+ l$ 0

sB


A/σA=3.7

[1 fb-1]Sensitivity 25.8 ps-1


Measured Value of Δms

)-1 (pssm!15 16 17 18 19 20

log(

L)!-

-5

0

5

10

15

20hadronicsemileptoniccombined

CDF Run II Preliminary -11 fb

"190% CL

confidence intervals

90% CL[17.01, 17.84] ps-1

95% CL[16.96, 17.91] ps-1

Δms = 17.31 (stat) ± 0.07(syst) ps-1- 0.18+0.33


maxlog(L)!0 2 4 6 8 10 12 140

500

1000

1500

2000

2500

observedvalue

CDF Run II Preliminary -11 fb

randomized tags

-1=18 pssm!expected for

Significance Probability of Fluctuation

• probability of random fluctuation determined from data

‣ randomize tags many times

‣ find how often max-Δlog(L) is larger than observed maximum for signal

⇒ 0.2% (3.7σ)

Impact on CKMmatrix elements determination


!

0 0.5 1

"

0

0.5

EPS’05EPS’05 + CDF measurement

!

0 0.5 1

"

0

0.5

Determination of |Vtd/Vts|

∆ms

∆md

=mBs

mB0

ξ2|Vts|2

|Vtd|2

∆md = 0.505 ± 0.005 ps−1

mB0/mBs= 0.983

ξ2= 1.21

+0.047−0.035

∣∣∣∣

Vtd

Vts

∣∣∣∣ = 0.208+0.001

−0.002 (exp) +0.008−0.006(theo)

[from M.Okamoto, hep-lat/0510113]

[from PDG]

[from PDG]

other inputs:

previous best result:

[Belle Collaboration, hep-ex/0506079]

|Vtd/Vts| = 0.199+0.026−0.025(exp)+0.018

−0.015(th)


CKM Fit, without CDF measurement

!-1 -0.5 0 0.5 1

"-1

-0.5

0

0.5

1#

$

%

dm&

K'

cbVubV

!-1 -0.5 0 0.5 1

"-1

-0.5

0

0.5

1

UT Fit, without Δms constraint

beforeafter

!-1 -0.5 0 0.5 1

"-1

-0.5

0

0.5

1#

$

%

sm&dm& dm&

K'

cbVubV

!-1 -0.5 0 0.5 1

"-1

-0.5

0

0.5

1

UT Fit, with CDF measurement

-1.5

-1

-0.5

0

0.5

1

1.5

-1 -0.5 0 0.5 1 1.5 2

sin 2!

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

excluded at CL > 0.95

"

"

#

#

$md

$ms & $md% = 1.21 +0.047

– 0.035 (hep-lat/0510113)

&K

&K

|Vub/Vcb|

sin 2!

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

excluded at CL > 0.95

#

!"

'

(

excluded area has CL > 0.95

C K Mf i t t e r

EPS05+CDF

CKM Fit, with CDF measurement

Impact on Unitarity Triangle Fit


Measurement vs SM Expectation

]-1[pss m!0 10 20 30 40

Prob

abili

ty d

ensi

ty

0

0.0005

0.001

0.0015

]-1[pss m!0 10 20 30 40

Prob

abili

ty d

ensi

ty

0

0.0005

0.001

0.0015

]-1[pss m!0 10 20 30 40

Prob

abili

ty d

ensi

ty

0

0.0005

0.001

0.0015

CKM/UT Fit (SM) without Δms constraint&

CDF Δms Measurement

0

0.2

0.4

0.6

0.8

1

1.2

12.5 15 17.5 20 22.5 25 27.5 30 32.5 35

CKM fit w/o !msCDF measurement

!ms

1 –

CL

CK Mf i t t e r

FPCP 06


Summary

• first direct measurement of Δms

‣ precision: 2% level‣ probability of random fluctuation: 0.2%

• impact on CKM fit‣ most precise measurement of |Vtd|/|Vts|

• publication just submitted

‣ to Physical Review Letters | hep-ex/0606027

Δms = 17.31 (stat) ± 0.07(syst) ps-1- 0.18+0.33

]-1 [pssm!0 10 20 30

Ampl

itude

-2

-1

0

1

2" 1 ± data

-# +# +# _ s D$ 0

s, B+# _ s D$ 0

s X, B_ s D+ l$ 0

sB


Ampl

itude

-2

-1

0

1

! 1 ± data ! 1.645 ± data

(stat. only)! 1.645 ± data !1.645

-1sensitivity: 25.8 ps

CDF Run II -1L = 1.0 fb

)-1 (pssm"0 5 10 15 20 25 30

#

0102030 data

significance=1%

Additional Slides for Reference


Systematic Uncertainties Amplitude

• evaluated on toy MC• total systematic uncertainites very small compared to statistical• relevant only for exclusion limits (cancel in ratio A/σA)

]-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

ct"Non-Gaus Cabibbo DConSSTOST+SST Corr

ct"S# / # !

]-1 [pssm!0 10 20 30 40

syst

.A

"

0.05

0.1

0.15

0.2

physics bkg.

ctS

DS

prompt dil.

promptf tailsct"

total

Hadronic Semileptonic


Systematic Uncertainties Δms

• evaluated on toy MC• common between hadronic and semileptonic• have negligible impact

‣ relevant systematic uncertainties from proper time scale

syst. unc.

Silicon alignment 0.04 ps-1

track fit bias 0.05 ps-1

primary vertex 0.02 ps-1

all other syst. <0.01 ps-1

total 0.07 ps-1


Tevatron Luminosity Data Taking Periods

Store Number

Tot

al L

umin

osity

(pb-1

)

0

200

400

600

800

1000

1200

1400

1600

1000 1500 2000 2500 3000 3500 4000 4500

1 4 7 10 1 4 7 10 1 4 7 1 4 7 102002 2003 2004 2005 2006Year

Month

DeliveredTo tape

“Data Taking Period 1” “2” “3”


Amplitude Scans Data Taking Periods

]-1 [pssm!0 10 20 30

Ampl

itude

-2

0

2

" 1 ± data " 1.645



-13.7 ps-114.9 ps

-# +# +# _ s D$ 0

s, B+# _ s D$ 0

sB


]-1 [pssm!0 10 20 30

Ampl

itude

-2

0

2

" 1 ± data " 1.645



-116.7 ps-120.2 ps

-# +# +# _ s D$ 0

s, B+# _ s D$ 0

sB


]-1 [pssm!0 10 20 30

Ampl

itude

-2

0

2

" 1 ± data " 1.645



-15.5 ps-118.5 ps

-# +# +# _ s D$ 0

s, B+# _ s D$ 0

sB


Had

roni

c

]-1 [pssm!0 10 20 30

Ampl

itude

-4

-2

0

2

4 " 1 ± data " 1.645



-112.0 ps-112.7 ps

-1 230 pb#L CDF Run II Preliminary

X+ l-s D$ 0

sB

]-1 [pssm!0 10 20

Ampl

itude

-4

-2

0

2

4 " 1 ± data " 1.645



-114.4 ps-112.8 ps


X+ l-s D$ 0

sB

]-1 [pssm!0 10 20 30

Ampl

itude

-4

-2

0

2

4 " 1 ± data " 1.645



-118.5 ps-114.2 ps


X+ l-s D$ 0

sBSem

ilept

onic


log(LH(PID))-20 -10 0 10 20

entri

es p

er b

in0

50

100

150 Pythia Data

log(LH(PID))-20 -10 0 10 20

entri

es p

er b

in0

50

100

150

CDF Run II Preliminary -1 355 pb!L

Same Side Tagging simulation validation

• systematic variations covered‣ fragmentation model‣ bb production mechanisms‣ B** content‣ detector/PID resolution‣ multiple interactions‣ PID content around the B‣ Data/MC agreement

• select most likely kaon track as tag track‣ use combined PID: TOF & dE/dx

• SST performance estimated from MC‣ εD2(Bs→Ds(ϕπ)π) = 4.0 %

small discrepancies covered by systematic variations


Fourier Transform amplitude peak shape

proper decay time, t [ps]0 1 2 3 4 5 6 7 8-1

-0.8-0.6-0.4-0.2

00.20.40.60.8

1

]-1ms[ps!10 12 14 16 18 20

0

0.5

1

unbiased proper time

using simplest toy model for illustration purposes

FT

Breit-WignerA(t;w) =1

τe−

t

τ cos(wt) θ(t)


A(t;w) =1

τe−

t

τ cos(wt) θ(t − ζ)

]-1ms[ps!10 12 14 16 18 20

0

0.5

1

proper decay time, t [ps]0 1 2 3 4 5 6 7 8

-0.4

-0.2

0

0.2

0.4

Fourier Transform amplitude peak shape

using simplest toy model for illustration purposes

FT

undershootings expected

unbiased proper time

Documents

Measurement of the B-Bs Oscillation Frequencyhome.fnal.gov/~leonardo/docs/seminar_anl.pdfMeasurement of the Bs-Bs Oscillation Frequency Nuno Leonardo Massachusetts Institute of Technology