bs mixing at tevatron - tu dresden main injector and recycler runi: 1992 – 1996 data taking period...

Bs mixing results from Tevatron

Ulrich Kerzel, University of Karlsruhe

Institutsseminar, Dresden, 18th May 2006

18th May 2006 U.Kerzel, Institutsseminar Dresden 2

B mixing overview⎛⎜⎝ d0s0b0

⎞⎟⎠ =⎛⎜⎝ Vud Vus VubVcd Vcs VcbVtd Vts Vtb

⎞⎟⎠ ·⎛⎜⎝ dsb

⎞⎟⎠Mass eigenstates differ from eigenstates of weak interaction ⇒ CKM matrix

¯̄̄B0

E=

1√2(|BHi+ |BLi)¯̄̄

B̄0E=

1√2(|BHi− |BLi)

Neutral B meson system:decaying 2-component system

Small mass difference: Δ m = mH – mL

“heavy”/”light” state evolve differently with time

Mixing via box diagrams:


B mixing overview

Δmq ∝ mBqB̂Bqf2Bq¯̄̄VtbV

∗tq

¯̄̄2From theory:

Uncertainties cancel in ratio: ΔmsΔmd

∝ |Vts|2|Vtd|2

w/o CDF Δ ms measurement

From CKM fit (EPS 2005):

Δms= 18.3+6.5−1.5 ps

−1

measure Δ ms:• determine ratio of CKM elements• probe for new physics


B mixing overviewexperimentally accessible:

need to:• reconstruct Bs

(including decay vertex/lifetime)• tag flavour at production and decay

challenges:• momentum resolution• vertex resolution• tagging power

A(t) =Nmix(t)−Nunmix(t)Nmix(t)+Nunmix(t)

∝ cos(Δmqt)


B mixing overviewFigure of merit: significance of mixing signal Moser, Roussarie (NIMA 384 491)

signi =

rS²D2

2 e−(Δmsσcτ )2

2

rS

S+B

S√S+B

optimise Bs candidate selection

σcτ optimise resolution

ε D2 optimise tagging performance² = NRS+NWS

N

D =NRS−NWSNRS+NWS

efficiency

dilution: Ameas = D Atrue


Δ mq measurement: Amplitude method

assume fixed value of Δmq → fit for Amplituderepeat for different values of Δmq

e.g. B0 → D- π+

A(t) ∝ A × cos(Δ mq t)

A = 1 for correct Δ mqA = 0 else


Δms from combined amplitude

combines:• LEP• CDF RunI• SLD


CDF D0

Tevatron

Main injectorand recycler

RunI: 1992 – 1996data taking period at

RunII: 2001 – 2009major upgrades tocollider anddetectors

√s = 1.8TeV

The Tevatron

√s = 1.96 TeV

pp̄ collisions


Tevatron performance

Running well - both peak luminosity and integrated luminositybefore shutdown: ~15-20 pb-1 / week delivered

1 fb-1 delivered in beginning of June 2005 .

1 fb-1


CDF:• precise tracking:

silicon vertex detector and drift chamber• important for B physics:

direct trigger for displaced vertices

D0:• excellent muon system and coverage• large forward tracking coverage• new in RunII: magnetic field

⇒ D0 has joined the field of B physics


Physics at the Tevatron• large b production rates:

⇒ 103 times bigger than !

• spectrum quickly falling with pt

• Heavy and excited states not produced at B factories:

• enormous inelastic cross-section:

⇒ triggers are essential

• events “polluted” by fragmentation tracks, underlying events

⇒ need precise tracking and good resolution!

Υ(4S)

Bc, Bs, B∗∗,Λb,Σb, . . .

σ(pp̄, |η| < 1.0) ≈ 20μb

`S

Belle engineering run


Trigger in hadronic environment

• Dimuon: “easy” trigger, clean signal• sensitive to J/ ψ→ μ+ μ-

• low branching fraction

• Semi-leptonic B decays CDF: (μ, e) + displaced trackD0 : single (μ, e)

• Fully hadronic B decays (CDF)• BR ≈ 80%• require two displaced tracks• needs high precision tracking

at trigger level !

Primary Vertex

Secondary Vertex

d0 = impact parameter

B

Lxy

require:• pt > 2 GeV/c• 120 μm<|d0|<1mm

(not used for mixing analysis)

almost “offline” resolution


Some sample events

recorded by J/ψ→ μ+ μ- trigger (CDF)

J/ ψ→ μ+ μ-

what all this fuzz about hadronic environment...


Some sample events

recorded by J/ψ→ μ+ μ- trigger (CDF)

... well, usually events are like this...


plot courtesy C. Lecci

B physics at low pt⇒ no “jet” structure

CDF RunII Simulation

Some sample events


Hadronic vs. semi-leptonic B decays

hadronic decaysfully reconstructedhigh cτ resolutionlow candidate yield

semileptonic decayshigh yieldneutrino not reconstructed⇒ worse cτ resolution

Lxy =(~xdecay−~xprim)·~pt

|~pt|decay

PV

cτ = LxyM(B)

pt(B)

= LxyM(`D)

pt(`D)× K

hadronic

semi-leptonic

from simulation


Bs reconstruction

Ds ≈ 26.7k events

D± ≈ 7.4k events

Exploit excellent muon coverage (single μ trigger):Bs → μ+Ds

-X, Ds- → φ π-, φ→ K+ K-


Signal Yield Summary: Semi-leptonic

Bs → l Ds X Yield

Ds → (φπ) 32k

Ds → (K* K) 11k

Ds → (3π) 10k

Total 53k


Signal Yield Summary: Hadronic

Yield

Bs→ Dsπ (φπ) 1600

Bs→ Dsπ (K* K) 800

Bs→ Ds π (3π) 600

Bs→ Ds3π (φ π) 500

Bs→ Ds3π (K*K) 200

Total 3700

oscill. fit range

partially reconstructed Bs


Mixing measurement outline“same side”:(semi) exclusively reconstructed Bs

“opposite side”

1) decay flavour fromdecay products

2) proper time measurement

e, μoppositeside kaon

3) production flavour fromopposite side tag andsame-side Kaon tagger


Flavour tagging methodssame side

oppositeside

opposite side: (CDF and D0)• jet charge

• (soft) lepton ID• flavour from semi-leptonic B decay (BR ≈ 20%)• dilution due to oscillation and cascade decays

(b → c → l X)

same side: (new at CDF)• same side Kaon tagging

kaon is (often) leading fragmentation partner of Bs⇒ particle ID is essential!

Qjet =Pi wiQiPi wi


Flavour taggers at D0Deploy opposite side taggers:• lepton jet charge (in cone around lepton)

Ql = ∑i qi pti / ∑i pt

i

• secondary vertex jet chargeQSV = ∑i (qi pL

i)0.6 / ∑i (pLi)0.6

• event jet charge (outside cone around Bs)QEV = ∑i qi pt

i / ∑ pti

dtag=1−z1+z ; z = Πi

f b̄i (xi)

f bi (xi)combine via:

gives: ²D2 = 2.48± 0.21(stat)+0.08−0.06(syst)%


Flavour taggers at CDF

Opposite side (OS) taggers: calibrated on l+SVT data• soft μ±, e±

• jet charge: with secondary vertex, with displaced tracks,other high pt jets

Same side (SS) tagger : calibrated in Bs → Ds π channel

most powerful tagger!• use one OS tag and SS tag to determine initial flavour,

• OS taggers mutually exclusive.

tagger ²D2[%]

combined OS 1.54± 0.04± 0.05SS Kaon 4.0+0.9−1.2


Neural jet charge tagger

TrackNet:combines track quantities (e.g. pt,impact parameter, rapidity w.r.t., etc.)via NeuroBayes network⇒ probability to originate from B

B-Jet network:combines TrackNet + jet quantitiesvia NeuroBayes network⇒ identify B jets

⇒ significant improvementw.r.t. method based on impact parameter alone

note log-scale


Same side kaon tagging

Kaon is (often) leading fragmentation partner• identified Kaon ⇒ identify Bs• charge of Kaon determines production flavour

⇒ very powerful tagger !

Challenges:• need good PID to identify Kaon: dE/dx + ToF (no RICH!)• has to be calibrated using simulation

→ difficult in hadronic environment


Calibrating SSKTuse combined PID likelihood (ToF + dE/dx), select most “kaon-like” track in cone around B as tagging trackverify kinematic distributions (pT, tagging track pT, multiplicity, isolation) of light B mesons in Pythia simulationverify particle ID simulationtest for dependences on:

fragmentation modelbb production mechanismsdetector/PID resolutionmultiple interactionsPID content around B mesondata/MC agreement

test on high statistics lightB meson sample


Δ ms measurement⇒ all ingredients there, determine Δ ms

• Amplitude method: scan Δ ms range, fit for asymmetry amplitude

• unbinned likelihood fit:

signal

combinatorial background

prompt background

“physics” background(other particle decays)

each part: contribution from mass, cτ, σ(cτ)

L = fsigLsig +fcombLcomb+fpromptLprompt+fphysLphys


Bs mixing result

most probable value: Δ ms = 19 ps-1

17 < Δ ms < 21 ps-1 at 90% C.L.

resolution not sufficientto measure oscillationin this region

A/σA (19 ps-1) = 2.5

probability of bg fluctuation: (5.0 ± 0.3)%


A/σA (17.25 ps-1) = 3.5

Bs mixing result

Δms = 17.33 +0.42 (stat) ± 0.07 (syst) ps-1-0.21

Δms in [17.00, 17.91] ps-1 at 90% CL Δms in [16.94, 17.97] ps-1 at 95% CL

Probability of bg fluctuation: 0.5%


Systematic uncertainties on Δms

evaluated using toy MCsample compositionindividual event vertex uncertaintydilutiondetector resolution

Result is limited by statisticsdominant: lifetime measurement

Syst. Unc.

SVX Alignment 0.04 ps-1

Track Fit Bias 0.05 ps-1

PV bias from tagging 0.02 ps-1

All Other Sys < 0.01ps-1

Total 0.07 ps-1

All relevant systematic uncertainties are common between hadronic and semileptonic samples


Impact on CKM fit

prior to new CDF result: with new CDF result:


Impact on CKM fit

|Vtd||Vts| = 0.208

+0.08−0.07 (stat ⊕ syst)


Further improvementsCDF:

Improved selection in hadronic modes using Neural NetworksUse partially reconstructed hadronic modesUse semileptonic events from other triggersImprove vertex resolution

D0:Addition of other taggersUse of other semileptonicdecay modesUse of hadronic decay modesImprove vertex resolution (inclusion of Layer0)


Further improvementsdevelop inclusive B analysis package using NeuroBayes inspired by BSAURUS (DELPHI)

exploit all availableinformation vianeural networks


NeuroBayes (1)Inspired by nature:Neuron in brain “fires” if stimuli received from other neurons exceed threshold. (very simple model. . . )

Construct Neural NetworkOutput of node j in layer n is given by weighted sum of output of all nodes in layer n-1:

xnj = g³P

k wnjk · xn−1k + μnj

´g(t) μnjsigmoid function threshold (“bias-node”)

→ information is stored in connections


NeuroBayes (2)

Output

Input

Sign

ifica

nce

cont

rol

Postprocessing

Preprocessing

f t

Probability that hypothesisis correct

(classification)or probability densityfor variable t

t

Historic orsimulated data

Data seta = ...b = ...c = .......t = …!

NeuroBayesNeuroBayes®®TeacherTeacher

NeuroBayesNeuroBayes®®ExpertExpert

Actual (new real) data

Data seta = ...b = ...c = .......t = ?

ExpertiseExpertise

Expert system


Classical ansatz:f(x|t)=f(t|x)

approximately correctat good resolution

far away fromphysical boundaries

Bayesian ansatz:takes into accounta priori- knowledge f(t):•Lifetime never negative•True lifetime exponentially

distributed

NeuroBayes (3)example: measured lifetime distribution


Inclusive B analysisidentify B decay products and construct “best” B vertex


Inclusive B analysisflavour tagging on track level:


Inclusive B analysis(preliminary MC studies,for illustration only)


Inclusive B analysisexploit all information

combined flavour tag


Conclusions

Good performance of Tevatron and detectorsΔ ms (almost) measured

D0: two sided limit: 17 < Δ ms < 21 ps-1

A/σA ≈ 2.5 (for amplitude method) at 19 ps-1

Probability of background fluctuation: 5.0 ± 0.3 %

CDF: A/σA ≈ 3.5 (for amplitude method)Probability of background fluctuation: 0.5%

Aim for “5σ” discovery at summer conferencesextensive list of further improvements... no “new physics” here, it seems...

Δms= 17.33+0.42−0.21(stat)± 0.07(syst.)


BACKUP


• observe at• 1 fb-1 luminosity delivered early June• huge inelastic cross-section:≈ 5000 times bigger than for⇒ triggers are essential!

• events “polluted” by fragmentation tracks, underlying events⇒ need precise tracking and good resolution

pp̄ collision

Physics at the Tevatrons√s = 1.96 TeV

• dedicated trigger for J/Ψ→ μ+ μ-

• trigger events where m(μ+μ-) around m(J/Ψ)⇒ high quality J/Ψ events with large statistics

• channel J/Ψ→ e+e- much more challenging in hadronic environment

bb̄


SVT based Triggers hadronic channelrequire two SVT tracks

pT>2GeV/cpT1+pT2 > 5.5 GeV/copposite charge 120 μm < SVT IP < 1 mmLxy > 200 μm

semileptonic channel require 1 Lepton + 1 SVT track

1 muon/electron pT> 4 GeV1 additional SVT track with

pT > 2 GeV120 μm < SVT IP < 1 mm

DP.V.

Lepton

Bν

SVT trackDP.V.

SVT track

B SVT track


“Classic” B Lifetime Measurement

reconstruct B meson mass, pT, Lxycalculate proper decay time (ct)extract cτ from combined mass+lifetime fitsignal probability:psignal(t) = e-t’/τ⊗ R(t’,t)

● background pbkgd(t) modeled from sidebands

pp collision B decays

ct · pt/m


Hadronic Lifetime Measurement

SVT trigger, event selection sculpts lifetime distributioncorrect for on average using efficiency function:

p = e-t’/τ⊗ R(t’,t) ·ε(t)efficiency function shape contributions:

event selection, triggerdetails of efficiency curve

important for lifetime measurementinconsequential for mixing measurement

pattern limit|d0| < 1 mm

“trigger” turnon

0.0 0.2 0.4proper time (cm)


Hadronic Lifetime Results

ModeLifetime [ps](stat. only)

B0 → D- π+ 1.508 ± 0.017

1.638 ± 0.017

1.538 ± 0.040

B- → D0 π-

Bs → Ds π(ππ)

World Average:

B0 → 1.534 ± 0.013 ps-1

B+ → 1.653 ± 0.014 ps-1

Bs → 1.469 ± 0.059 ps-1

Excellent agreement!


Semileptonic Lifetime Measurement

neutrino momentum not reconstructed

correct for neutrino on average


lDs ct* Projections

Bs lifetime in 355 pb-1: 1.48 ± 0.03 (stat) psWorld Average value: 1.469 ± 0.059 ps

Lepton

Ds- vertex

P.V.Bs vertex


Unbinned Likelihood Δmd Fits

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 = 0.507 ± 0.005 ps-1

fit separately in hadronic and semileptonic sampleper sample, simultaneouslymeasure

tagger performanceΔmd

projection incorporatesseveral classes of tags

semileptonic, lD-, muon tag


Systematic uncertaintiesSilicon detector alignment

Effect of imperfect alignment of silicon vertex detector on lifetime measurement. Tested by introducing distortions into realistic simulation measuring lifetime with default alignment

Track-fit biasMis-measurement of pt introduces mis-measurement of Lxy and lifetime. Tested with realistic simulation.

Primary vertex biasMis-measurement of primary vertex leads to mis-measurement of Lxyand lifetime, cause a bias when tracks from opposite side are incorporated into primary vertex. Studied with large sample of fully reconstructed B events comparing reconstructed primary vertex with average beam position


Conditional probability densities f(t|x)

Conditional probability densities f(t|x) are functions of x, but also depend on marginal distribution f(t).

Conditional probability densities f(t|x) are functions of x, but also depend on marginal distribution f(t).

Conditional probability density for a special case x

(Bayesian Posterior)

Conditional probability density for a special case x

(Bayesian Posterior)

Inclusive distribution(Bayesian Prior)

Inclusive distribution(Bayesian Prior)

Marginal distribution f(t)Marginal distribution f(t)

Bayesian approach

bs mixing at tevatron - tu dresden main injector and recycler runi: 1992 – 1996 data taking period...

Documents