The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
Flavour tagging developments for the LHCb experiment
Antonio Falabella
Universita di FerraraDottorato di Ricerca - Ciclo 26
December 16, 2013
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The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
Overview
1 The LHCb experiment
2 Flavour Tagging
3 Tuning on data
4 Development of SS proton algorithm
5 Conclusion
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The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
The LHCb detector
VELO
TRACKER
RICH1
MAGNET
MUON
CALORIMETERSRICH2
LHCb measurements
Improve the determination ofCKM matrix parameters inb-meson decays.
New Physics from rare decaysof B and D mesons.
Detector requirements
Very efficient Trigger system (Twolevels L0(hardware), HTL(software))
Mass resolution and Particle ID
(RICHs, CALOs and MUON)
Excellent Vertexing and Tracking
(VELO and TRACKING SYSTEM)
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The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
Flavour Tagging
Why Flavour Tagging
CP violation studies usually involve the study of time-dependent ratesasymmetries.
A(t) =N(B0 → f )(t)− N(B0 → f )(t)
N(B0 → f )(t) + N(B0 → f )(t)
The determination of this observable rely on the knowledge of the productionB flavour.
How to perform Flavour Tagging
p-p collisions produce b − b pairs by strong interactions. The signal-Bflavour can be inferred by the decay of the accompanying b−hadron decay(Opposite Side tagging) or exploiting the fragmentation process of the bto the signal B meson (Same Side tagging).
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The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
Flavour Tagging algorithms
OS : muon, electron, kaon and inclusive vertex
SS : pion, kaon, proton
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The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
Flavour Tagging - Some definitions
The flavour is determined by the charge of the particle used to tag.
Flavour tagging performances are quantified by:
εeff = (1− 2ω)2 · εtag , ω =W
R + W, εtag =
R + W
R + W + U
The error on the asymmetry A can be calculated (Am is the measuredasymmetry)
Am ∝ (1− 2ω)e−(∆mqσt )2/2A(t) , σA ∝√
1− A2m√
εtagN(1− 2ω)
which shows that to minimize the statistical error the εeff need to bemaximized
Measure and optimize (εeff ) the performances of tagging algorithms usingflavour specific control channels:B+ → J/ΨK+,B0 → D∗−µ+νµ,B0 → J/ΨK∗0, B0 → D−π+
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The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
Calculation and Calibration of the predicted mistag
Per-event mistag estimation (η)
Using per-event mistag (η) is proved to improve tagging power(+20/30%).
For each tagger it is estimated using multivariate methods (Neuralnetworks, BDT,...) that uses as inputs kinematical and geometricalinformation on taggers and is trained to identify the correct chargecorrelation.
When more than one tagging algorithm give a decision they are combinedto give a final decision according to individual decisions and probabilities.
η calibration
To provide a correct estimation of the mistag η must be calibrated
The calibration is made assuming a linear dependencyω = p0 + p1(η− < η >).
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The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
Tuning on data
Contributions to tagging from my 2012 studies: new NNet structure,training on 2012 data
with 2010 and 2011 data training was not possible due to the lack ofstatisticsavoid complications due to different variable distribution between MC/dataPerformance improvements
year statistics εtagD2 tagging physics results
2010 35pb−1 1.97± 0.18 OS ∆ms , φs
2.38± 0.18 OS + SSπ sin(2β)
2011 0.37fb−1 2.07± 0.11 OS2011 1.0fb−1 2.35± 0.06 OS ∆md , sin(2β),B0
s → DsK ,B → hh
2011 + 2012 3.0fb−1 2.80± 0.082011 + 2012 3.0fb−1 0.47± 0.04 SSp
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The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
Development of SS proton algorithm
Idea behind Same Side algorithms is to use the charge correlation betweena B and a closed-by track to infer B flavour at production.
Two possible sources of charge correlation:Origin in the decay of a higher mass resonanceCorrelation in the b hadronization process ”associate production” (AP)
Bu and Bd cases
For B+ you can have a companion π,K or p track with the same chargecorrelation, while in B0 you have π and p with opposite charge correlation.Studying a B neutral channel a SSπ and SSp tagging algorithm can thanbe developed
Main focus of my studies is on SS proton
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The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
Implementation details
Tuning on data
I used 2012 data (2fb−1). Data sample
corresponds to B0 → D−(→ Kππ)π+
Train a Boosted Decision Tree (BDT → backup)to select right/wrong charge closed-by tracks
B0p → wrong signB0p → right sign
The BDT is trained from a set of input variablesand using per-event sWeights (→ backup) to takeinto account the background contamination
B0 → D−(→ Kππ)π+
)2m (MeV/c5200 5250 5300 5350 5400
)2E
vent
s / (
2 M
eV/c
0
2000
4000
6000
8000
10000
12000
14000
16000 2637±N_bkg = 70101
13465±N_sig = 357917
Signal
Background
Total
)2m (MeV/c
5200 5250 5300 5350 5400
Pul
l
-5
0
5
# of entries = 428018
# of Bd signal candidates =357917
S/B = 5.11
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The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
Preselection Cuts and Multiplicity
Cannot use all B candidates for training.For mixed event the correlation is opposite→ cut on decay time: For t < 2.2psfraction of non oscillated events 0.93
t [ps]0 5 10
Mix
ing
Asy
mm
etry
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Track related cut:PIDp > 5 → selecting protonsGhost Prob < 0.5,IPPU > 9
B plus track system related cuts:dQ < 1050MeV where dQ = MB+track −mB −mtrack
∆φ < 1.2, ∆η < 1.2
m, t, pidP,CUTS m m, t dQ,∆φ,∆η, Ghost Prob, IPPU
Signal events 357801 227420 111275Multiplicity 5.2 5.1 1.6
ε 0.84 0.53 0.41
Preselection Cuts → reduce number of tagging tracks and the multiplicityper candidate
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The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
Input Variables
The best set of input variables to train the BDT that I found are:For B plus track system: dQ, pT (B + comp), ∆φ, ∆ηFor the companion track: PIDp, p, pT , IPχ2,Ghost Prob, IPPUFor the B: pT
For the event : Ntracks in PV
dQ [F]200 400 600 800 1000 1200
33.3
F /
(1/N
) dN
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014 RightWrong
U/O
-flo
w (
S,B
): (
0.0,
0.0
)% /
(0.0
, 0.0
)%
Input variable: dQ
log(B+track_PT) [F]8.5 9 9.5 10 10.5 11
0.07
98 F
/ (1
/N)
dN
0
0.2
0.4
0.6
0.8
1
U/O
-flo
w (
S,B
): (
0.0,
0.0
)% /
(0.0
, 0.0
)%
Input variable: log(B+track_PT)
log(Track_PT) [F]6 6.5 7 7.5 8 8.5 9
0.08
45 F
/ (1
/N)
dN
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
U/O
-flo
w (
S,B
): (
0.0,
0.0
)% /
(0.0
, 0.0
)%
Input variable: log(Track_PT)
log(B_PT) [F]7.5 8 8.5 9 9.5 10 10.5 11
0.09
88 F
/ (1
/N)
dN
0
0.2
0.4
0.6
0.8
1
U/O
-flo
w (
S,B
): (
0.0,
0.0
)% /
(0.0
, 0.0
)%
Input variable: log(B_PT)
log(Track_P) [F]7.5 8 8.5 9 9.5 10 10.5 11 11.5 12
0.12
5 F
/ (1
/N)
dN
0
0.1
0.2
0.3
0.4
0.5
0.6
U/O
-flo
w (
S,B
): (
0.0,
0.0
)% /
(0.0
, 0.0
)%
Input variable: log(Track_P)
log(Dphi) [F]-8 -6 -4 -2 0
0.25
1 F
/ (1
/N)
dN0
0.1
0.2
0.3
0.4
0.5
0.6
U/O
-flo
w (
S,B
): (
0.0,
0.0
)% /
(0.0
, 0.0
)%
Input variable: log(Dphi)
Small differences between right and wrong charge correlated tracks
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The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
Input Variables
log(Deta) [F]-8 -6 -4 -2 0
0.26
F /
(1/N
) dN
0
0.1
0.2
0.3
0.4
0.5
U/O
-flo
w (
S,B
): (
-0.0
, 0.0
)% /
(0.0
, 0.0
)%
Input variable: log(Deta)
log(Track_PIDp) [F]2 2.5 3 3.5 4 4.5
0.08
09 F
/ (1
/N)
dN
0
0.1
0.2
0.3
0.4
0.5
0.6
U/O
-flo
w (
S,B
): (
0.0,
0.0
)% /
(0.0
, 0.0
)%
Input variable: log(Track_PIDp)
log(N_tracks) [I]2 2.5 3 3.5 4 4.5 5 5.5
0.09
46 I
/ (1
/N)
dN
0
0.2
0.4
0.6
0.8
1
1.2
U/O
-flo
w (
S,B
): (
0.0,
0.0
)% /
(0.0
, 0.0
)%
Input variable: log(N_tracks)
log(Track_IPCHI2) [F]-10 -8 -6 -4 -2 0 2
0.36
6 F
/ (1
/N)
dN
0
0.05
0.1
0.15
0.2
0.25
0.3
U/O
-flo
w (
S,B
): (
0.0,
-0.
0)%
/ (0
.0, 0
.0)%
Input variable: log(Track_IPCHI2)
Small differences between right and wrong charge correlated tracks
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The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
BDT Training and Variable Ranking
Use all tracks
Use event number to split the sample (EVEN=training, ODD=test)
AdaBoost for training
ssProton response
-0.4 -0.2 0 0.2 0.4 0.6 0.8 1
dx / (1
/N)
dN
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2Right (test sample)
Wrong (test sample)
Right (training sample)
Wrong (training sample)
U/O
-flo
w (
S,B
): (
0.0,
0.0
)% /
(0.0
, 0.0
)%
TMVA overtraining check for classifier: ssProton
Rank Variable Variable Importance1 PIDp 1.706e-012 log(pcomp) 1.267e-013 log(pT comp) 1.207e-01
4 dQ 1.177e-015 log(∆phi) 1.064e-016 log(∆eta) 7.947e-027 log(pTB ) 7.550e-028 log(Ntracks inPV ) 7.201e-029 log(pTB+comp) 6.780e-02
10 log(IPχ2comp) 6.318e-02
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The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
Performances
Performances computed in both samples to test overtraining
In the plots εtag (1− 2ω)2 as a function of BDT cut for training (EVEN)and for testing samples (ODD)
ω = W /R + W for t < 2.2ps (slightly overestimated due to B mixing)
In case of multiple candidates choose the one with largest BDT
Average εtagD2 vs BDT cut
BDT-1 -0.5 0 0.5 1
eD2
[%]
0
0.05
0.1
0.15
0.2
0.25
Best average tagging power for BDT > 0.5 (EVEN) : εtagD2 = 0.23%
Best average tagging power for BDT > 0.5 (ODD): εtagD2 = 0.13%
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The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
Fit to oscillation
Unbiased determination of ω from the fit to B oscillation (no time cut). In caseof multiple proton candidates choose the one with highest BDT response
I define a binning to have the same statistics in each one:
BDT bin [−1.0, 0.0] [0.0, 0.15] [0.15, 0.3] [0.3, 0.4] [0.4, 0.55] [0.55, 0.7] [0.7, 0.8] [0.8, 1.]ω[%](Odd) 49.5± 0.6 49.4± 0.6 47.2± 0.6 45.1± 0.6 43.4± 0.7 41.4± 1.0 37.2± 1.7 25.3± 1.8ω[%](Even) 50.9± 0.5 49.6± 0.6 46.2± 0.6 46.7± 0.8 42.8± 0.7 38.0± 1.0 33.0± 1.6 26.5± 1.9
[−1.0, 0.0] [0.0, 0.15] [0.15, 0.3] [0.3, 0.4]
t [ps]0 5 10
Mix
ing
Asy
mm
etry
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
t [ps]0 5 10
Mix
ing
Asy
mm
etry
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
t [ps]0 5 10
Mix
ing
Asy
mm
etry
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
t [ps]0 5 10
Mix
ing
Asy
mm
etry
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
[0.4, 0.55] [0.55, 0.7] [0.7, 0.8] [0.8, 1.0]
t [ps]0 5 10
Mix
ing
Asy
mm
etry
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
t [ps]0 5 10
Mix
ing
Asy
mm
etry
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
t [ps]0 5 10
Mix
ing
Asy
mm
etry
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
t [ps]0 5 10
Mix
ing
Asy
mm
etry
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Oscillation clearly visible; amplitude increase as a function of the BDT output
Mistag determination from each bin compatible in the two subsamples
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The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
Calibration of the BDT output
Find per-event ω estimation as a function of BDT output
Plot ω VS BDT for each BDT bin (ODD sample) → polynomial (left plot)
η = pol(BDT ) should be already calibrated (middle plot)
BDT-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
ω
0
0.1
0.2
0.3
0.4
0.5
0.6
/ ndf 2χ 6.485 / 5p0 0.003608± 0.4892 p1 0.01313± -0.08681 p2 0± 0 p3 0± 0 p4 0± 0 p5 0.04131± -0.2945
/ ndf 2χ 6.485 / 5p0 0.003608± 0.4892 p1 0.01313± -0.08681 p2 0± 0 p3 0± 0 p4 0± 0 p5 0.04131± -0.2945
) Calibration SSprotonωMistag (
η0 0.1 0.2 0.3 0.4 0.5 0.6
ω
0
0.1
0.2
0.3
0.4
0.5
0.6
/ ndf 2χ 3.778 / 4
p0 0.003163± 0.4547
p1 0.08536± 1.016
> η< 0± 0.453
/ ndf 2χ 3.778 / 4
p0 0.003163± 0.4547
p1 0.08536± 1.016
> η< 0± 0.453
) Calibration SSprotonωMistag (
heta__etaEntries 79323
Mean 0.453
RMS 0.03839
η0 0.1 0.2 0.3 0.4 0.5 0.6
a.u
.
0
0.02
0.04
0.06
0.08
0.1
0.12heta__eta
Entries 79323
Mean 0.453
RMS 0.03839
p1 p0 < η > ε[%] εeff [%]Odd Sample 1.015± 0.085 0.454± 0.003 0.453 31.3± 0.1 0.471± 0.045Even Sample 1.236± 0.085 0.449± 0.003 0.453 31.2± 0.1 0.624± 0.051
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The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
Validation on B → Dπ 2011 unbiased sample
Use B → Dπ 2011 sample (1fb−1) forvalidation
Similar data analysis (no BDTtraining, only performances evaluationand calibration cross-check)
S/B similar to 2012 data
)2m (MeV/c5200 5250 5300 5350 5400
)2E
vent
s / (
2 M
eV/c
0
1000
2000
3000
4000
5000
6000
7000 4710±N_bkg = 30034
24006±N_sig = 153217
Signal
Background
Total
)2m (MeV/c
5200 5250 5300 5350 5400
Pul
l
-5
0
5
# of entries = 183251
# of Bd signal candidates=153217
S/B = 5.10
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The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
Validation on Dπ 2011
Using the BDT trainied on 2012 data, and the same polynomial function
η0 0.1 0.2 0.3 0.4 0.5 0.6
ω
0
0.1
0.2
0.3
0.4
0.5
0.6
/ ndf 2χ 6.25 / 4
p0 0.003308± 0.4625
p1 0.08778± 1.05
> η< 0± 0.4519
/ ndf 2χ 6.25 / 4
p0 0.003308± 0.4625
p1 0.08778± 1.05
> η< 0± 0.4519
) Calibration SSprotonωMistag (
heta__etaEntries 183078
Mean 0.458
RMS 0.03299
η0 0.1 0.2 0.3 0.4 0.5 0.6
a.u
.
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14 heta__etaEntries 183078
Mean 0.458
RMS 0.03299
p1 p0 < η > ε[%] εeff [%]1.050± 0.087 0.462± 0.003 0.452 33.0± 0.1 0.418± 0.046
Calibration: p1 OK, p0− < η > compatible with 0 in ∼ 3σ
Performances: compatible with 2012 unbiased sample
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The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
Validation on B0 → J/ψK ∗
Use J/ψK∗ for validation2012 data sample (2fb−1) (left plot)2011 data sample (1fb−1) (right plot)
2012 2011
)2m (MeV/c5240 5260 5280 5300 5320
)2E
vent
s / (
0.9
MeV
/c
0
2000
4000
6000
8000
10000
12000
14000 16642±N_bkg = 227250
18333±N_sig = 250101
Signal
Background
Total
)2m (MeV/c
5240 5260 5280 5300 5320
Pul
l
-5
0
5)2m (MeV/c
5240 5260 5280 5300 5320
)2E
vent
s / (
0.9
MeV
/c
0
1000
2000
3000
4000
5000
6000 17243±N_bkg = 78488
25917±N_sig = 118104
Signal
Background
Total
)2m (MeV/c
5240 5260 5280 5300 5320
Pul
l
-5
0
5
# of entries candidates = 477351
# of Bd signal candidates = 250101
S/B = 1.10
# of entries candidates = 196592
# of Bd signal candidates = 118104
S/B = 1.5020/25
The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
Validation on J/ψK ∗ 2012 - Fit to oscillation
Oscillation clearly visible as a function of the BDT output
[−1.0, 0.0] [0.0, 0.15] [0.15, 0.3] [0.3, 0.4]
t [ps]0 5 10
Mix
ing
Asy
mm
etry
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
t [ps]0 5 10
Mix
ing
Asy
mm
etry
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
t [ps]0 5 10
Mix
ing
Asy
mm
etry
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
t [ps]0 5 10
Mix
ing
Asy
mm
etry
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
[0.4, 0.55] [0.55, 0.7] [0.7, 0.8] [0.8, 1.0]
t [ps]0 5 10
Mix
ing
Asy
mm
etry
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
t [ps]0 5 10
Mix
ing
Asy
mm
etry
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
t [ps]0 5 10
Mix
ing
Asy
mm
etry
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
t [ps]0 5 10
Mix
ing
Asy
mm
etry
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
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The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
Validation on J/ψK ∗ 2012
Using the BDT trained on 2012 data, and the same polynomial function
2012 2011 2011+2012
η0 0.1 0.2 0.3 0.4 0.5 0.6
ω
0
0.1
0.2
0.3
0.4
0.5
0.6
/ ndf 2χ 2.053 / 4
p0 0.003165± 0.4632
p1 0.09358± 0.9419
> η< 0± 0.4581
/ ndf 2χ 2.053 / 4
p0 0.003165± 0.4632
p1 0.09358± 0.9419
> η< 0± 0.4581
) Calibration SSprotonωMistag (
η0 0.1 0.2 0.3 0.4 0.5 0.6
ω
0
0.1
0.2
0.3
0.4
0.5
0.6
/ ndf 2χ 4.243 / 4
p0 0.004419± 0.4677
p1 0.1276± 0.9451
> η< 0± 0.4574
/ ndf 2χ 4.243 / 4
p0 0.004419± 0.4677
p1 0.1276± 0.9451
> η< 0± 0.4574
) Calibration SSprotonωMistag (
η0 0.1 0.2 0.3 0.4 0.5 0.6
ω
0
0.1
0.2
0.3
0.4
0.5
0.6
/ ndf 2χ 1.017 / 4
p0 0.002726± 0.4634
p1 0.08002± 0.9339
> η< 0± 0.458
/ ndf 2χ 1.017 / 4
p0 0.002726± 0.4634
p1 0.08002± 0.9339
> η< 0± 0.458
) Calibration SSprotonωMistag (
p1 p0 < η > ε[%] εeff [%]2012 0.942± 0.093 0.463± 0.003 0.458 25.7± 0.1 0.23± 0.032011 0.945± 0.128 0.468± 0.004 0.457 26.0± 0.1 0.25± 0.04
2012+2011 0.934± 0.080 0.463± 0.003 0.458 26.0± 0.1 0.24± 0.02
Calibration: p1 OK, slight offset forp0 → p0− < η > compatible with 0in ∼ 3σ
Performances: smaller εeff due todifferent BpT spectrum
Reweighting → εeff [%] = 0.35± 0.02
B0 → Dπ B0 → J/ψK∗
Entries 79711
Mean 8374
RMS 3649
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Entries 79711
Mean 8374
RMS 3649
B_pT22/25
The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
Conclusion
Development of a new SS tagging algorithm using protons based on aBDT:
Used B0 → D−(→ Kππ)π+ 2012 data sample for trainingFor the unbiased B0 → Dπ sample → εeff [%] = 0.471± 0.045For the B0 → J/ψK∗ sample (2011+2012) → εeff [%] = 0.24± 0.02
Calibration proved to be portable across different data samples and adifferent channel
23/25
The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
My 3nd year of Ph.D.
I spent the 3nd of my Ph.D. covering two main activities:Development and optimization of a new same side proton FT algorithm forthe LHCb experiment;I worked with the offline computing group of the LHCb experiment and inparticular with the LHCbDirac developers group.
Report regularly at the Flavour Tagging working group meeting aboutresults and progresses of my studies
A partecipated with a poster contribution to Beauty 2013 Internationalconference in Bologna;
I partecipated to IFAE in Cagliari with a poster contribution on LHCbFlavour Tagging;
I partecipated to IUSS Niccolo Cabeo school about Beyond StandardModel physics in Ferrara;
24/25
The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
Thank you!
25/25
The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
BACKUP
26/25
The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
sPlots technique1
Statistical tool to unfold data distributions
Event characterized by a set of variables:Discriminating variables: the distribution of all the sources of events areknownControl variables: the distribution of some sources of events are unknown
→ sPlots technique reconstruct the distribution of the control variables foreach source of events
used to unfold signal and background event in a data sample
for example given Fs (y) and Fb(y) distributions for the discriminatingvariable y for signal and background assuming Ns and Nb number ofevents for the two sources
1arxiv.org/abs/physics/040208327/25
The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
sPlots technique - cont’d
Define the sWeight as:
Ws (y) =VssFs (y) + VsbFb(y)
NsFs (y) + NbFs (y), where V−1
ij =N∑
e=1
=Fi (ye)Fj (ye)
(NsFs (ye) + NbFs (ye))2
weighting the control variable disitribution x by the Ws (ye) gives the truedistribution for the signal component of x
28/25
The LHCb experiment Flavour Tagging Tuning on data Development of SS proton algorithm Conclusion
Boosted Decision Trees
Decision tree are binary tree classifiersan event is classified after repeating a yes/no decision on one singlevariablethe phase space is then split in many regions that can be classified assignal or background
boosting → build several trees: forestfinal decision is the weighted average of each individual decision treeboosting improve stability with respect to fluctuations of the training sample
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