1

3333rdrd International Conference in High Energy Physics

(Jul 26th – Aug 2nd, Moscow, Russia)

Tania Moulik (Kansas University)

presented by Andrei Nomerotski

(Fermilab/Oxford)

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Mass eigenstates are a mixture of flavor eigenstates:

BH and BL have a different mass and may have different decay width.

m = MH – ML = 2|M12| ,

= H - L = 2|12|

B mixingB mixingB mixingB mixing

BpBqB

BpBqB

L

H

(t)B

B(t)

iΓMiΓM

iΓMiΓM

(t)B

B(t)

22222121

12121111

dtd

i

Time evolution follows the Schrodinger equation

Dominant Diagram for the transition :

3

In an Ideal Scenario..In an Ideal Scenario.. In an Ideal Scenario..In an Ideal Scenario..“O

pp

osite

si

gn

”“S

am

e

sig

n”

SSOS

SSOSi NN

NNtA

)(

Oscillations with amplitude = 1.0 andFrequency = ms.

4

DZero DetectorDZero DetectorDZero DetectorDZero DetectorSpectrometer : Fiber and Silicon Trackers in 2 T Solenoid Energy Flow : Fine segmentation liquid Ar Calorimeter and PreshowerMuons : 3 layer system & absorber in Toroidal fieldHermetic : Excellent coverage of Tracking, Calorimeter and Muon Systems

Spectrometer : Fiber and Silicon Trackers in 2 T Solenoid Energy Flow : Fine segmentation liquid Ar Calorimeter and PreshowerMuons : 3 layer system & absorber in Toroidal fieldHermetic : Excellent coverage of Tracking, Calorimeter and Muon Systems

SMT H-disks SMT F-disks SMT barrels

5

Analysis outlineAnalysis outlineAnalysis outlineAnalysis outline

μ+/e+

-

K+K-

φD-

S

μ(e) B

X00ss BB

Signal Selection Look for tracks displaced from primary vertex in same jet as /electron

Two tracks should form a vertex and be consistent with mass ( K K) or K* mass (K*K KK) KK invariant mass should be consistent with Ds mass

Identify e/ PT (e/) > 2.0 | | (e/) < 1.0/2.0

6

Signal SelectionSignal SelectionSignal SelectionSignal Selection

μ (e)+

π -

K+K-

φD-

S

μ(e) B

ν

X

00ss BB

Muons were selected by triggers without lifetime bias

= no online/offline Impact Parameter cuts

Trigger muon can be used as tag muon : gives access to eDs sample with enhanced

tagging purity

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Signal SelectionSignal SelectionSignal SelectionSignal Selection

μ+

π -

K+K-

φ

D-S

μ(e) B

ν

X

PV

LT(DS)

00ss BB

Ds lifetime is used to have non-zero selection efficiency at Interaction Point

Bs can decay at IP and be reconstructed

Eff=30%

8

Effect of NeutrinoEffect of NeutrinoEffect of NeutrinoEffect of NeutrinoNeed to correct Decay Length for relativistic contraction need to know Bs momentum

Can estimate Bs momentum from MC (through so called k-factor) at expense of additional uncertaintyk/k uncertainty causes additional smearing of oscillationsOnly few first periods are useful for semileptonic channels Sensitivity at DL=0 is crucial

All above represents the main difference wrt hadronic channels

Need to correct Decay Length for relativistic contraction need to know Bs momentum

Can estimate Bs momentum from MC (through so called k-factor) at expense of additional uncertaintyk/k uncertainty causes additional smearing of oscillationsOnly few first periods are useful for semileptonic channels Sensitivity at DL=0 is crucial

All above represents the main difference wrt hadronic channels

200 micron

# of periods

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Flavor Tagging and dilution calibrationFlavor Tagging and dilution calibrationFlavor Tagging and dilution calibrationFlavor Tagging and dilution calibration

Identify flavor of reconstructed BS candidate using information from B decay in opposite hemisphere. Identify flavor of reconstructed BS candidate using information from B decay in opposite hemisphere.

a) Lepton Tag : Use semileptonic b decay :Charge of electron/muon identifies b flavor

Ds

cos (l, Bs) < 0.8

Bs

e /

b) Secondary Vertex Tag : Search for secondary vertex on oppositeSide and loop over tracks assoc. to SV.

c) Event charge Tag:All tracks opposide to rec. B

Secondary Vertex

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Dilution in Dilution in ΔΔmmdd measurement measurementDilution in Dilution in ΔΔmmdd measurement measurement

Combine all tagging variables using likelihood ratiosBd oscillation measurement with combined tagger

md= 0.5010.030±0.016ps-1

Combine all tagging variables using likelihood ratiosBd oscillation measurement with combined tagger

md= 0.5010.030±0.016ps-1 Combined dilution: εD2=2.48±0.21±0.08 % Input for Bs

measurement

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Bs decay samples after flavor taggingBs decay samples after flavor taggingBs decay samples after flavor taggingBs decay samples after flavor tagging

NBs( ) = 5601 102 NBs( + e) = 1012 62 (Muon tagged)NBs(K*K + ) = 2997 146

NBs( ) = 5601 102 NBs( + e) = 1012 62 (Muon tagged)NBs(K*K + ) = 2997 146

BsDs e X

Ds

Ds K*K

BsDs X

BsDs XDs

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K*K Fit ComponentsK*K Fit ComponentsK*K Fit ComponentsK*K Fit Components

)(0* signalKKDs

)( 0*0*

KKKD

orKD

)(reflectionPKc )( 0*0* KKKKD

(Cabibbo suppressed)

Difficult mode due to K* natural width and mass resolution – larger errors wrt modeDifficult mode due to K* natural width and mass resolution – larger errors wrt mode

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Results of the Lifetime FitResults of the Lifetime FitResults of the Lifetime FitResults of the Lifetime Fit

cKxΔmec

Kxp s

c

Kx

B

oscnoss

sB

s

/15.0)(/

cos D

From a fit to signal and background region:From a fit to signal and background region:Decay Mode cBs (m) cbkg (m)

BsDs X, Ds 4049 6276

BsDs e X, Ds 44429 64518

BsDs X, Ds K*K 40722 54910

BsDs e X

Ds Ds K*K

BsDs X

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Amplitude MethodAmplitude MethodAmplitude MethodAmplitude Method

tmAsymmetry S cosAmplitude fit = Fourier analysis + Maximum likelihood fit

often used in oscillation measurements

If A=1, the Δm’s is a measurement of Bs oscillation frequency, otherwise A=0

tmDA s cos

Need to know dilution (from Δmd analysis)

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Cross-check on BCross-check on BddXXμμDD±±(())Cross-check on BCross-check on BddXXμμDD±±(())

EXACTLY the same sample & taggerAmplitude Scan shows Bd oscillations

at correct place no lifetime bias with correct amplitude correct dilution calibration

Same results for two other modes

EXACTLY the same sample & taggerAmplitude Scan shows Bd oscillations

at correct place no lifetime bias with correct amplitude correct dilution calibration

Same results for two other modes

Amplitude ScanDØ Run II Preliminary

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Measure Resolution Using DataMeasure Resolution Using DataMeasure Resolution Using DataMeasure Resolution Using Data

Ultimately ms sensitivity is limited by decay length resolution – very important issue Use J/ψ→μμ sample

Fit pull distribution for J/ψ Proper Decay Length with 2 Gaussians Resolution Scale Factor is 1.0 for 72% of the events and 1.8 for the rest

Cross-checked by several other methods

Ultimately ms sensitivity is limited by decay length resolution – very important issue Use J/ψ→μμ sample

Fit pull distribution for J/ψ Proper Decay Length with 2 Gaussians Resolution Scale Factor is 1.0 for 72% of the events and 1.8 for the rest

Cross-checked by several other methods

μ

PVJ/ψ vertex

μ

L±σL

DØ Run II Preliminary

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Amplitude Scan of BAmplitude Scan of BssXXμμDDss(())Amplitude Scan of BAmplitude Scan of BssXXμμDDss(())

Deviation of the amplitude at 19 ps-1 2.5σ from 0 1% probability 1.6σ from 1 10% probability

Deviation of the amplitude at 19 ps-1 2.5σ from 0 1% probability 1.6σ from 1 10% probability

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Log Likelihood ScanLog Likelihood ScanLog Likelihood ScanLog Likelihood Scan

ms < 21 ps-1 @ 90% CL assuming Gaussian errorsMost probable value of ms = 19 ps-1

Systematic

Resolution K-factor variation BR (BsDsX) VPDL model BR (BsDsDs)

In agreement with the amplitude scan

Have no sensitivity above 22 ps-1

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InterpretationInterpretationInterpretationInterpretation

Results of ensemble tests:DZero result :

Combined with World (before CDF measurement):

ms(ps-1)

ms(ps-1)

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Impact on the Unitarity TriangleImpact on the Unitarity TriangleImpact on the Unitarity TriangleImpact on the Unitarity Triangle

BeforeBS mixing

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Impact on the Unitarity TriangleImpact on the Unitarity TriangleImpact on the Unitarity TriangleImpact on the Unitarity Triangle

With D0

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Impact on the Unitarity TriangleImpact on the Unitarity Triangle

With CDF

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““Golden” Events for VisualizationGolden” Events for Visualization““Golden” Events for VisualizationGolden” Events for Visualization

Period of oscillations @ 19ps-1

DØ Run II Preliminary

Weigh events using Weigh events using

210

2

log,

sm

eyMSignif

DF sig

# of periods

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Can We See Bs Oscillations By Eye ?Can We See Bs Oscillations By Eye ?Can We See Bs Oscillations By Eye ?Can We See Bs Oscillations By Eye ?

Weighted asymmetry

This plot does not represent full statistical power of our data

Weighted asymmetry

This plot does not represent full statistical power of our data

# of periods

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More Amplitude ScansMore Amplitude ScansMore Amplitude ScansMore Amplitude Scans

New results : Amplitude scans from two additional modesNew results : Amplitude scans from two additional modes

Ds K*K

BsDs (e XBsDs X

Ds

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CombinationCombinationCombinationCombination

Amplitude is centred at 1 now, smaller errorsLikelihood scan confirms 90% CL ms limits: 17-21 ps-1

Data with randomized tagger : 8% probability to have a fluctuation (5% before for mode)Detailed ensemble tests in progress

Amplitude is centred at 1 now, smaller errorsLikelihood scan confirms 90% CL ms limits: 17-21 ps-1

Data with randomized tagger : 8% probability to have a fluctuation (5% before for mode)Detailed ensemble tests in progress

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Add Same Side TaggingAdd hadronic modes triggering on tag muonAdd more data (4-8 fb-1 in next 3 years) with improved detector – additional layer of silicon between beampipe and Silicon Tracker (Layer0) – better impact parameter resolution

Add Same Side TaggingAdd hadronic modes triggering on tag muonAdd more data (4-8 fb-1 in next 3 years) with improved detector – additional layer of silicon between beampipe and Silicon Tracker (Layer0) – better impact parameter resolution

Layer0 has been successfully installed in April 2006• S/N = 18:1 & no pickup noise • First 50 pb-1 of data on tape, first tracks have been reconstructed

Outlook Outlook Outlook Outlook

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SummarySummarySummarySummary

Established upper and lower limits on ms using Bs Ds X mode

Analysis published in PRL 97 (2006) 021802

Combined with two other channels Bs Ds X Bs Ds e X

considerable improvement in sensitivity 14.1 16.5 ps-1, no improvement for ms interval

Looking forward to a larger dataset with improved vertex detectionIf ms is indeed below 19 ps-1 expect a robust measurement with the extended dataset

Established upper and lower limits on ms using Bs Ds X mode

Analysis published in PRL 97 (2006) 021802

Combined with two other channels Bs Ds X Bs Ds e X

considerable improvement in sensitivity 14.1 16.5 ps-1, no improvement for ms interval

Looking forward to a larger dataset with improved vertex detectionIf ms is indeed below 19 ps-1 expect a robust measurement with the extended dataset

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BACKUP SLIDES

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B MesonsB MesonsB MesonsB Mesons

Bu+ B0 Bs

0 Bc+

b

u

b

d

b

s

b

cMat

ter

b

u

b

c

b

s

b

d

An

ti-M

atte

r

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CKM matrix and B mixingCKM matrix and B mixingCKM matrix and B mixingCKM matrix and B mixing

b

s

d

tbVtsVtdVcbVcsVcdVubVusVudV

b

s

d Wolfenstein parametrisation - expansion in .

1)(

1

)(1

23

22

32

AiA

A

iA

)21(

)21(

801.0

002.02265.0sin

2

2

029.0018.0

A

c

0 tbtdcbcdubud VVVVVV

itdtdiubub eVVeVV ||||

complex 1

cbcd

tbtd

cbcd

ubud

VV

VV

VV

VV

Why are we interested to study B meson oscillations

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B MixingB MixingB MixingB Mixing

In general, probability for unmixed and mixed decays Pu,m(B) Pu,m(B). In limit, 12 << M12 ( << M) (Standard model estimate and confirmed by data), the two are equal.

)cos1(2

)(

)cos1(2

)(

/

/

mte

BBp

mte

BBp

t

t

~ 10-4 for Bs system

~ 10-3 for Bd system

310~

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Constraing the CKM Matrix from Constraing the CKM Matrix from mmss

Constraing the CKM Matrix from Constraing the CKM Matrix from mmss

2*22

22

2

2

6tdtbBQCD

W

ttb

Fd VVfB

m

mFmm

Gm

ddB

cbts VV

from Lattice QCD calculations)

Ratio suffers from lower theoreticalUncertainties – strong constraint Vtd

2

2

2

td

ts

Bd

Bs

Bd

Bs

Bd

Bs

d

s

V

V

B

B

f

f

M

M

m

m

And similar expression for ms

CDF+D0 (2006) ms inputs

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Excellent Tevatron PerformanceExcellent Tevatron PerformanceExcellent Tevatron PerformanceExcellent Tevatron Performance

Data sample corresponding to over 1 fb-1 of the integrated luminosity used for the Bs mixing analysis Full dataset is ready (85-90% DAQ efficiency)

Data sample corresponding to over 1 fb-1 of the integrated luminosity used for the Bs mixing analysis Full dataset is ready (85-90% DAQ efficiency)

Run II Integrated Luminosity

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

Apr-02 Jul-02 Oct-02 Jan-03 Apr-03 Jul-03 Oct-03 Jan-04 Apr-04 Jul-04 Oct-04 Jan-05 Apr-05 Jul-05 Oct-05 Jan-06 Apr-06 Jul-06

Lu

min

osi

ty (

fb-1

)

Delivered

Recorded

19 April 2002 - 22 February 2006

1.19

1.41

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Muon TriggersMuon TriggersMuon TriggersMuon Triggers

Limitation of data recording. Triggers are needed to select useful physics decay modes. 396 ns bunch crossing rate ~ 2.5 MHz ~50 Hz for data to be recorded.

Single inclusive muon Trigger: |η|<2.0, pT > 3,4,5 GeV Muon + track match at Level 1Prescaled or turned off depending on inst. lumi. We have B physics triggers at all lumi’s

Extra tracks at medium lumi’s Impact parameter requirements Associated invariant mass Track selections at Level 3

Dimuon Trigger : other muon for flavor tagging

e.g. at 50·10-30 cm-2s-1, L3 trigger rate : 20 Hz of unbiased single μ 1.5 Hz of IP+μ 2 Hz of di-μ No rate problem at L1/L2

Limitation of data recording. Triggers are needed to select useful physics decay modes. 396 ns bunch crossing rate ~ 2.5 MHz ~50 Hz for data to be recorded.

Single inclusive muon Trigger: |η|<2.0, pT > 3,4,5 GeV Muon + track match at Level 1Prescaled or turned off depending on inst. lumi. We have B physics triggers at all lumi’s

Extra tracks at medium lumi’s Impact parameter requirements Associated invariant mass Track selections at Level 3

Dimuon Trigger : other muon for flavor tagging

e.g. at 50·10-30 cm-2s-1, L3 trigger rate : 20 Hz of unbiased single μ 1.5 Hz of IP+μ 2 Hz of di-μ No rate problem at L1/L2

36

μμ Sample Sampleμμ Sample Sample

μDs: 26,710

Opposite-side flavortagging

Tagging efficiency 21.90.7%

μD±: 7,422

μD±: 1,519

μDs: 5,601±102

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check Using Bcheck Using BddXXμμDD±±(())check Using Bcheck Using BddXXμμDD±±(())

The Amplitude Scan shows Bd oscillations at 0.5 ps-1 no lifetime bias (A=1) : correct dilution calibration

The Amplitude Scan shows Bd oscillations at 0.5 ps-1 no lifetime bias (A=1) : correct dilution calibration

38

BS

Se

S tsm

2

)( 2

1

2D2

Detector EffectsDetector EffectsDetector EffectsDetector Effects

flavor tagging power,background

Decay lengthresolution

momentumresolution

p)/p = ? %l = ?

SM prediction - ms ~ 20 ps-1

Trying to measure : Tosc~0.3 X 10-12 s !

39

Sample CompositionSample CompositionSample CompositionSample Composition

Estimate using MC simulation, PDG Br’s, Evtgen exclusive Br’s

Estimate using MC simulation, PDG Br’s, Evtgen exclusive Br’s

Signal: 85.6%

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Flavor tag Dilution calibrationFlavor tag Dilution calibrationFlavor tag Dilution calibrationFlavor tag Dilution calibration

Bd mixing measurement using Bd D* X, D* D0 ,

D0 , and evaluate dilution in various diution bins. Follows similar analysis outline as Bs mixing.Form measured asymmetry in 7 bins in visible proper decay length (xM) – Count OS and SS events (compare charge of reconstructed muon with tagger decision)

Fit the 2:

Also include B+ D0 X decay asymmetry.

Bd mixing measurement using Bd D* X, D* D0 ,

D0 , and evaluate dilution in various diution bins. Follows similar analysis outline as Bs mixing.Form measured asymmetry in 7 bins in visible proper decay length (xM) – Count OS and SS events (compare charge of reconstructed muon with tagger decision)

Fit the 2:

Also include B+ D0 X decay asymmetry.

7

12

22

)(

)),((),(

i i

eii

A

mAAm

DD

SSOS

SSOSMi NN

NNxA

)(

41

Dilution calibration : ResultsDilution calibration : ResultsDilution calibration : ResultsDilution calibration : ResultsFor final fit, bin the tag variable |d| in 5 bins and do a simultaneuos fit

(i) where i=1,5. Parameters of the fit : m, fcc, 5 Dd, 5 Du = 12

For final fit, bin the tag variable |d| in 5 bins and do a simultaneuos fit

(i) where i=1,5. Parameters of the fit : m, fcc, 5 Dd, 5 Du = 12

mstat.) ps-1

D2 = (2.48 0.21) (%) (stat.)stat.

Incr

easi

ng d

ilutio

n

Incr

easi

ng d

ilutio

n

B0 B+

42

Individual Taggers performanceIndividual Taggers performanceIndividual Taggers performanceIndividual Taggers performance

Tagger D (%) D2 (%)

Muon 6.61 0.12

0.473 0.027

1.48 0.17(stat)

Electron 1.83 0.07

0.341 0.058

0.21 0.07 (stat)

SV 2.77 0.08

0.424 0.048

0.50 0.11 (stat)

Total OST

11.14 0.15 2.19 0.22 (stat)

Note :To evaluate the individual tagger performance |dpr| > 0.3

This cut was not imposed for final combined tagger. Final eD2 is higher.

43

Likelihood minimization to get Likelihood minimization to get msmsLikelihood minimization to get Likelihood minimization to get msms

Form Probability Density Functions (PDF) for each source Form Probability Density Functions (PDF) for each source

sigisigbgisigcandidates

fff ,,1 FF

fln2Minimize

yMdprxM

xi ppppdxpf prMx

M

M 10log,,

dpr

Dilution Calibration (From md measurement)

Signal selection function (y)

44

Bs Signal and backgroundBs Signal and backgroundBs Signal and backgroundBs Signal and background

Signal PDF:

Background PDF composed of long-lived and prompt components – Evaluated from a lifetime fit.

Long Lived Background – Described by exponential convoluted with a gaussian resolution function.

Non-sensitive to the tagging Non-oscillatingOscillating with Δmd frequency

Prompt Background – Gaussian distribution with resolution as fit parameter.

Signal PDF:

Background PDF composed of long-lived and prompt components – Evaluated from a lifetime fit.

Long Lived Background – Described by exponential convoluted with a gaussian resolution function.

Non-sensitive to the tagging Non-oscillatingOscillating with Δmd frequency

Prompt Background – Gaussian distribution with resolution as fit parameter.

)(),,()()(),,( // xgKdxpxKfdKdxp proscnos

sMjjprxMoscnos

j M

45

Combine individual tag informations to tag the event.Get tag on opposite side and construct PDF’s for variables discriminating b () and b (+) (Use B+ D0 X decays in data)

Discriminating variables (xi):

Combine individual tag informations to tag the event.Get tag on opposite side and construct PDF’s for variables discriminating b () and b (+) (Use B+ D0 X decays in data)

Discriminating variables (xi):

Combined flavor tag algorithmCombined flavor tag algorithmCombined flavor tag algorithmCombined flavor tag algorithm

more puremore pure

Electron/Muon SV Tagger

46

Ensemble TestsEnsemble TestsEnsemble TestsEnsemble TestsUsing data

Simulate Δms=∞ by randomizing the sign of flavour tagging Probability to observe Δlog(L)>1.9 (as deep as ours) in the range 16 < Δms < 22 ps-1 is 3.8% 5% using lower edge of syst. uncertainties band

Using MC Probability to observe Δlog(L)>1.9 for the true Δms=19 ps-1 in the range 17 < Δms < 21 ps-1 is 15%

Many more parameterized MC cross-checks performed – all consistent with above

Using data Simulate Δms=∞ by randomizing the sign of flavour tagging Probability to observe Δlog(L)>1.9 (as deep as ours) in the range 16 < Δms < 22 ps-1 is 3.8% 5% using lower edge of syst. uncertainties band

Using MC Probability to observe Δlog(L)>1.9 for the true Δms=19 ps-1 in the range 17 < Δms < 21 ps-1 is 15%

Many more parameterized MC cross-checks performed – all consistent with above