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
Bs oscillations at LEP, T. Allmendinger (IEKP Karlsruhe)
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 :
FCP01, Vanderbilt University, Nashville
Bs oscillations at LEP, T. Allmendinger (IEKP Karlsruhe)
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
FCP01, Vanderbilt University, Nashville
Bs oscillations at LEP, T. Allmendinger (IEKP Karlsruhe)
5LEP LEP
FCP01, Vanderbilt University, Nashville
Bs oscillations at LEP, T. Allmendinger (IEKP Karlsruhe)
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
FCP01, Vanderbilt University, Nashville
Bs oscillations at LEP, T. Allmendinger (IEKP Karlsruhe)
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
FCP01, Vanderbilt University, Nashville
Bs oscillations at LEP, T. Allmendinger (IEKP Karlsruhe)
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)
FCP01, Vanderbilt University, Nashville
Opposite sidehemisphere
Candidate sidehemisphere
Bs oscillations at LEP, T. Allmendinger (IEKP Karlsruhe)
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
FCP01, Vanderbilt University, Nashville
Bs oscillations at LEP, T. Allmendinger (IEKP Karlsruhe)
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
FCP01, Vanderbilt University, Nashville
Bs oscillations at LEP, T. Allmendinger (IEKP Karlsruhe)
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
FCP01, Vanderbilt University, Nashville
Exclusive DExclusive Dss−− − lepton analysis − OPAL − lepton analysis − OPAL
Bs oscillations at LEP, T. Allmendinger (IEKP Karlsruhe)
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.
FCP01, Vanderbilt University, Nashville
Exclusive DExclusive Dss−− − lepton analysis − OPAL − lepton analysis − OPAL
Bs oscillations at LEP, T. Allmendinger (IEKP Karlsruhe)
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
FCP01, Vanderbilt University, Nashville
Exclusive DExclusive Dss−− − lepton analysis − OPAL − lepton analysis − OPAL
Bs oscillations at LEP, T. Allmendinger (IEKP Karlsruhe)
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
FCP01, Vanderbilt University, Nashville
Bs oscillations at LEP, T. Allmendinger (IEKP Karlsruhe)
15Inclusive semileptonic analysis − ALEPH Inclusive semileptonic analysis − ALEPH
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 %
FCP01, Vanderbilt University, Nashville
Bs oscillations at LEP, T. Allmendinger (IEKP Karlsruhe)
16Inclusive semileptonic analysis − ALEPH Inclusive semileptonic analysis − ALEPH
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
FCP01, Vanderbilt University, Nashville
Bs oscillations at LEP, T. Allmendinger (IEKP Karlsruhe)
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.
FCP01, Vanderbilt University, Nashville
Bs oscillations at LEP, T. Allmendinger (IEKP Karlsruhe)
18Fully inclusive analysis − DELPHI Fully inclusive analysis − DELPHI
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 %
FCP01, Vanderbilt University, Nashville
Bs oscillations at LEP, T. Allmendinger (IEKP Karlsruhe)
19Fully inclusive analysis − DELPHI Fully inclusive analysis − DELPHI
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.
FCP01, Vanderbilt University, Nashville
Bs oscillations at LEP, T. Allmendinger (IEKP Karlsruhe)
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.
FCP01, Vanderbilt University, Nashville
Bs oscillations at LEP, T. Allmendinger (IEKP Karlsruhe)
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 ...
FCP01, Vanderbilt University, Nashville
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