B oscillations at LEP - UC Homepageshomepages.uc.edu/~kinoshky/hep/FCP2/Thomas_Allmendinger.pdf · oscillations at LEP, T. Allmendinger (IEKP Karlsruhe) 6 Hadronic events decay in

FCP01, Vanderbilt University, Nashville Bs oscillations at LEP, T. Allmendinger (IEKP Karlsruhe)

Bs oscillations at LEP

T. Allmendinger, DELPHI Collaboration,Institut für Experimentelle Kernphysik

Frontiers in Contemporary Physics IIVanderbilt University

Nashville9.03.2001

Bs oscillations at LEP, T. Allmendinger (IEKP Karlsruhe)

2

Introduction

Theory − CKM Matrix and Bs oscillation

Experimental environment − B Physics at LEP

Analysis

Exclusive Ds lepton from OPAL

Semi−inclusive lepton from ALEPH

Fully inclusive from DELPHI

Results

LEP combined results

World combined results

Summary

Outline of the talk Outline of the talk

FCP01, Vanderbilt University, Nashville


3The CKM Matrix in the Standard modelThe CKM Matrix in the Standard model

d’s’b’

=

V ud V us V ub

V cd V cs V cb

V td V ts V tb

⋅dsb

LCC=�g2

2⋅ uL , cL , t L ⋅γ

µ ˆV CKM

dL

sL

bL

Wµ++h. c.

ˆV CKM=

1�1

2λ2 λ Aλ3 ρ�iη

�λ 1�1

2λ2 Aλ2

Aλ3 1�ρ�iη �Aλ2 1

Mass and weak eigenstates are linked via the Cabibbo−Kobayashi−Maskawa (CKM) Matrix in the Standard Model.

The elements of the CKM Matrix describe charged−current couplings.

The 3×3 mixing matrix can be described by 3 real angles and 1 complex phase. The complex phase causes CP−violation.

Commonly used is the approximate Wolfenstein parametrization :



4From theory to measurement From theory to measurement

(by Pietro Faccioli)

Rb=1

λ1�

λ2

2

V ub

V cb

= ρ2+η2

Rt=1

λ

V td

V cb

= 1�ρ2 +η2

V td

V ts

=ξmBs

mBd

∆ Md

∆ Ms

Extend Wolfenstein parametrization beyond leading order:

ρ≡ρ 1�λ2 ⁄2 η≡η 1�λ2 ⁄2

From semileptonic b → u and b → c decays:

B mixing (direct way):

BUT: Theoretical uncertainties from hadronic matrix elements ! (~25 %)

Ratio ξ of hadronic matrix elements better under control ⇒ B

s mixing measurement is important !

ξ≡f Bs

BBs

f Bd

BBd

=1.16±0.05



5LEP LEP



6

Hadronic events decay in 21 % to bb� Clean experimental environment.

B hadron keeps ≈70 % of the b quark energy in the fragmentation process. Boost of the B hadron and lifetime (∼ 1.5 ps) � secondary vertex.

LEP I from 1991−1995 on the Z0. Each experiment collected ≈ 4 Mio. hadronic Z0decays �840000 b events.

e+

e−

Z0

q

q

B Physics at LEP B Physics at LEP



7Experimental environment Experimental environment

P tBs

0→ Bs0=Γ e�Γ t

21�cos ∆ms t

P tBs

0→ Bs0=Γ e�Γ t

21+cos ∆ms t

Time evolution of initially produced B0

s meson states:

Measurement of proper decay time is crucial.

t=lDEC mB

pB

Momentum reconstruction (Resolution depends on channel: Exclusive, Semi−inclusive, Inclusive)

Decay length resolution similar in all analyses due to detector restrictions.

Typical core resolution values are of the order of ~ 200 µm



8The strategy of BThe strategy of Bss reconstruction reconstruction

Enrichment of Bs mesons

Keep as much statistics as possible

Gain good purity fBs

of the

selected sample

Initial state tag of Bs mesons

Most of the information comes from opposite side hemisphere. (e.g. : Jet charge, Vertex charge, lepton candidate)

Some additional information can be extracted from fragmentation tracks on candidate side.

Flavour tag at decay time

depends on kind of analysis Exclusive reconstruction

delivers decay tag for free. Very small mistag rate. (e.g. OPAL)

Semi−Inclusive approach determines tag using a high p

T−lepton from direct decay

(e.g. ALEPH) Inclusive reconstruction using

a "dipole moment" of the hadronic decay products. (e.g. DELPHI)


Opposite sidehemisphere

Candidate sidehemisphere


9The Amplitude Method The Amplitude Method

Monte Carlo test for different ∆ms

values (∆ms = 2.0, 4.0, 6.0 and 8.0 ps−1)

From OPAL semi−leptonic analysis

Method allows easy combination of different analyses.

Fitting amplitude A at a fixed oscillation frequency ω [H.G. Moser and A. Roussarie NIM A384 (1997) 491]

A = 1 expected for frequency ω = true ∆ms

A = 0 expected for frequency ω ≠ true ∆ms

Set 95 % Confidence Level limit for : ∆m

s value for which A + 1.65 σ

A = 1

Determine Sensitivity:∆m

s value for which 1.65 σ

A = 1

P Bs0→ Bs,

0 Bs0 =

Γ e�Γ t

21±A⋅cos ω t



10Exclusive DExclusive Dss−− − lepton analysis − OPAL − lepton analysis − OPAL

Bs→ D

s

− l+ ν

�K*0K− , K*0→Κ+π−

�φπ− , φ →Κ+Κ−

�Ks

0K− , Ks

0→π+π−

�φl−υX , φ →Κ+Κ−

Reconstruction in four Ds

− decay chains

In total 244 candidates are selected.(Estimated signal 116 ± 10)Background sources:

Combinatorial background from Ds

−

and φ reconstructionOther B hadron decays with D

s

− l+

Misidentified leptons



11

Event by event decay length error estimateAverage width of 2.30 GeV for signal events

from momentum reconstruction

τexpectation

− τtrue

well characterized by gaussian

distribution of width 0.175 ± 0.011 ps


Exclusive DExclusive Dss−− − lepton analysis − OPAL − lepton analysis − OPAL


12

Decay tag:Determined from lepton charge.

Initial state tag:Jet charge measurements in

both hemispheres.Opposite to B

s candidate side

lepton charge.Charge of a fragmentation

Kaon in candidate hemisphere.

Mixing tag calculated:Deviations of the mixing tag from the a posteriori probability were corrected and taken as sys error.




13

Estimated sensitivity of the analysis is 4.1 ps−1

Lower limit is 1.0 ps−1 (both 95 % C.L.)

Combined with inclusive OPAL measurement a limit of 5.1 ps−1 (Sensitivity: 8.0 ps−1) is derived.

Lifetime fit also done: τ = 1.57 ± 0.17 ps




14Inclusive semileptonic analysis − ALEPH Inclusive semileptonic analysis − ALEPH

PV

Lepton

Neutrino

Kaon

Bs

Event selection mainly from lepton candidate and p,p

T (neural net)

Bs enrichment with neural net by

Charged vertex estimatorCharged track multiplicityFragmentation kaon presenceKaon − lepton charge correlation

Event by event Bs estimator




Initial state tag :Combined charged estimator of opposite sidePrimary vertex charge of candidate sideCharged Kaon fragmentation estimator

Effective mistag probability η ≈ 24 %

Decay state tag :Lepton p,p

T

Impact parameter significanceEvent topology

Mistag on event by event basis η ≈ 0−10 %




74026 events selected. b purity of 98.6 % (87.2 % of b events from direct decay)

Decay length resolution: ∼ 200 µm in core; ∼ 1 mm in tailEnhanced sensitivity through subclasses

Momentum resolution:∼ 6 % in core; ∼ 20 % in tailsE

ν estimated from energy and momentum

conservation in whole event.

Limit ∆ms > 11.1 ps−1 at 95 % C.L.

Sensitivity of analysis: ∆ms > 11.9 ps−1



17Fully inclusive analysis − DELPHI Fully inclusive analysis − DELPHI

Event sample:B−enriched hadronic Z decays. Leptons with p

T > 1.2 GeV excluded (other analysis!)

� big statistics ~ 320k data events (1994/95)

Enrichment of Bs mesons:

Neural network with 15 input variables trained.

Vertex charge and error estimate

Charged pion multiplicity

Kaon content at fragmentation and decay

Quality information from whole hemisphere

Increase by a factor of two reached for 30 % efficiency.




PDECAY

Bs =∑i∈ tracks

TNET>0.5log

1+Ptrack

Bs i

1�Ptrack

Bs i⋅Q i

Production flavor:Opposite flavor tag built on Jet Charge, Vertex Charge, ...Fragmentation information improves purity ~ 4%.

Decay flavor:Track based neural network trained on correlation between produced flavor and track charge.Combination of track probabilities by likelihood sum yields B

s decay

flavor variable.

Sample purity at 100 %efficiency point:Production standard : ~72 %Production extended: ~75 %Decay flavour : ~64 %




B Vertex

D Vertex Vertex resolution:Standard approach delivers bias from casacade D decay. Use of BD−net reduces conterminatiom from D vertices. Resolution up to 200 µm.



20Fully inclusive analysis − DELPHIFully inclusive analysis − DELPHI

Limit of 1.2 ps−1 @ 95 % C.L.

Sensitivity of 4.9 ps−1

Separate parametrizations given for decay length l and momentum estimate p.

→ Likelihood fit based on two dimensional integration for l and p.

→ Due to huge available statistics a fast integration method is needed.

Numerical integration:

1. Use of quasi random number

2. Variable transformation "follows" resolution shapes

Only 2048 points/integration needed.



21LEP combined average LEP combined average

LEP combined limit: ∆m

s > 11.8 ps−1 @ 95 % C.L.

Sensitivity on ∆ms : 14.5 ps−1

WORLD combined limit: ∆m

s > 15.0 ps−1 @ 95 % C.L.

Sensitivity on ∆ms : 18.0 ps−1

from ALEPH, CDF, DELPHI, OPAL and SLD.

Interesting:An effect of ~ 2σ is visible at around 17 ps−1 Still improvements possible ...


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B oscillations at LEP - UC Homepageshomepages.uc.edu/~kinoshky/hep/FCP2/Thomas_Allmendinger.pdf · oscillations at LEP, T. Allmendinger (IEKP Karlsruhe) 6 Hadronic events decay in