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Standard Model and motivation for rare charm decays
The LHCb detector
Potential of LHCb for 4-body rare charm decays
D0 K- π+ µ+µ-
D0 K- K+ µ+µ-
D0 π- π+ µ+µ-
D0 K+ π- µ+µ-
Measurement of D0 K- π+ ρ/ω(µ+µ-)
also used as a normalization mode
Tests of electronic board for the LHCb Calorimeter Upgrade
Systematic uncertainties D+(s)π+ µ+µ- analysis (not shown today) 2
6 quarks
6 leptons
4 gauge bosons
1 scalar boson, Higgs
26 free parameters:
12 quark and lepton masses
3+3 mixing quark and neutrino angles
1+1 quark and neutrino CPV phase
3 factors of the gauge group (αs, αem, sinθw)
2 for the shape of the Higgs potential
1 (QCD) vacuum phase implicated in the
strong CP problem
SU(3)3 SU(2)
L U(1)
Y
3
The SM is a very successful theory
Many of its predictions were spectacularly verified experimentally
However, it leaves a lot of questions open. Examples:
• Dark Matter and Dark Energy
• Hierarchy problem
• Large differences between the fermion masses
• CP violation too weak to explain the dominance of matter over antimatter
• Does not include Gravitation
→ The SM is the low-energy description of a more
fundamental theory (> 1 TeV)
4
Searches in quark sector
Couplings are possible between:
uu via Z0
ud via W+
Couplings are forbidden:
uc, ct, ut for up-type quarks
ds, sb, db for down-type quarks
c q=+2/3e u q=+2/3e
Trees - forbidden
5
Searches in quark sector
Couplings are possible between:
uu via Z0
ud via W+
Couplings are forbidden:
uc, ct, ut for up-type quarks
ds, sb, db for down-type quarks
c q=+2/3e u q=+2/3e
Trees - forbidden Loops - allowed
c q=+2/3e u q=+2/3e
Flavour changing Neutral Currents (FCNC) are very suppressed in the SM.
They are easily modified by NP: good probe 6
Rare charm decays are … “very rare” GIM suppression in up-type quark: mass of the quarks in loops
are more similar than in K and B decays, mb-m
d << m
t-m
u
GIM: s
If mb=ms=md complete annihilation !
d VV* VV* VV*
CP violation is very small Charm decays dominated by transitions between the first 2
families, thus no weak phases.
→ Any signal can be New Physics! + Small signal could be observed at the LHC (large s(cc)LHCb, 7TeV=(1419±154)µb)
7
10
BFSM
VMD
Addressed today
4 body rare charm decays
D0 K- π+ µ+µ-
D0 K- K+ µ+µ-
D0 π - π+ µ+µ-
D0 K+ π- µ+µ-
Short Distance (SD): sensitive to NP
BFSD(DXu e+e- ) = 3.7 10-9, slightly smaller for DXu µ+µ-
For exclusive modes BFSD~ O(10-10)
SD by far dominated by Long Distance (LD)
BF (D0π- π+µ+µ-)~ 10-6
BF (D0K+K-µ+µ- )~ 10-7
BF (D0K+π-µ+µ- )~ 10-8
L.Cappiello et al. arXiv:1209.4235v3
Via resonances
In SM:
11
In SM:
A. Paul et al., arXiv:1101.6053
m(µ+µ-), GeV/c2
Plan A: BF’s in regions away from resonances
Plan B: asymmetries in the full spectrum (interference between SD and LD)
• CP
• Forward backward
• T-odd
A=| ALD + ASD
|2 ~ | ALD |2 + 2Re(ALD ASD
*)
SD is very small compared to LD,
especially in the resonant zone.
12
SM
NP?
Can be generated by the interference between amplitudes with
CP violation: Different weak and strong phases
Forward-Backward asymmetry: amplitudes with different chiralities interfere
Asymmetry of m+to be emitted in
forward or backward
T-odd asymmetry
Angular asymmetry in the diplane angle ϕ (T-odd variable)
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In helicity frame
AFBCP = A
FB (D) - A
FB(D)
Can be generated by the interference between amplitudes with
CP violation: Different weak and strong phases
Forward-Backward asymmetry: amplitudes with different chiralities interfere
Asymmetry of m+to be emitted in
forward or backward
AFBCP = A
FB (D) - A
FB(D)
T-odd asymmetry
Angular asymmetry in the diplane angle ϕ (T-odd variable)
14
In helicity frame
In the SM: all these asymmetries ~ 0
Tree level FCNC
(Beak GIM supp.) Loop-mediated FCNCs
Z-enhanced model
(ex: Extra-vector like quarks) Leptoquark models
SUSY
Schematically: Most models have a moderate effect on Banching Ratios
Asymmetries reach O(1%), some models predict >~10%
BSD up to a few 10-9 ( SM: O(10-10) )
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[1]E791, PRL 86, 3969 (2001)
Exp Theory (total BF)
Cabibbo Favoured D0K- π+ µ+µ- <3.6×10-4[1] 6.2×10-6
Singly Cabibbo Suppressed D0K- K+ µ+µ- <3.3×10-5[1] 1.1×10-7
Singly Cabibbo Suppressed D0π- π+µ+µ- <5.5×10-7[2] 1.3×10-6
Doubly Cabibbo Suppressed D0K+ π- µ+µ- - 1.7×10-8
Upper limits of B, @90% CL
E791
No asymmetries studied yet!
LHCb is unique opportunity to measure BF and asymmetries in:
D0 K- π+ µ+µ-
D0 K- K+ µ+µ-
D0 π - π+ µ+µ-
D0 K+ π- µ+µ-
16
[2] LHCb, PLB728, 234-243 (2014)
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Not enough data to measure asymmetries
Measure BF to constrain NP and predict potential of future datasets
Measure BF(D0K-+ /(m+m-))
essential normalization for the other 4 body
modes
Prediction of the potential of future datasets
D0K-+ m+m-
m(µ+µ-), MeV/c2
φ ρ
ω Data Loose cuts..
/: window in m(m+m-) of [675;875] MeV/c2
Designed for precise study of
CP-violation and flavor-physics:
• forward geometry
• precise momentum and mass
reconstruction
• precise vertex reconstruction,
• lifetime reconstruction
• Adapted and highly configurable
trigger system
• identification: π, K, μ
B(D) hadrons are
producing in high rapidity
LHCb delivered 2.0 fb-1 in 2012, 1.1 fb-1 in 2010-2011
2 < η < 5 (15 – 300 mrad)
Design luminosity 2×10³² cm-2 s-1
pp 18 ×1013
cc 59 ×1011
bb 26 ×1010 19
Large cross-section!
interaction point
Tracking Particle ID
RICH system
K, π, p ID HCAL, ECAL, Preshower /SPD
Trigger+ e/γ energy and ID
Muon chambers
Trigger, µ ID VELO
Precise vertexing
Tracking stations
momentum
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Energy and position measurements
Hardware trigger decision (L0Hadron)
Particle identification (elections, hadrons)
ECAL
Shashlik (Pb-scint.)
6016 cells
HCAL
Tiles (Iron-scint.)
1488 cells
No hits in Scintillator Pad Detector (SPD)
+Shower in ECAL
Hits in SPD + Shower in ECAL
Hits in SPD + Shower in HCAL
Resolution:
21
Muon Chambers System
5 Muon stations interleaved with iron absorbers
Basic identification (trigger, preselection):
number of stations traversed as function of p
Sophisticated identification:
Distance between extrapolated tracks and hits in
muon system.
PIDmu (likelihood ratio),
ProbNNmu (neural network)
Additional information from RICH and Calo
22
Muon Chambers System
5 Muon stations interleaved with iron absorbers
Basic identification (trigger, preselection):
number of stations traversed as function of p
Sophisticated identification:
Distance between extrapolated tracks and hits in
muon system.
• muon-ID (mm) ~95%, mis-ID rate(m)~0.5%
PIDmu (likelihood ratio),
ProbNNmu (neural network)
Addition info from RICH and Calo
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L0 Hardware Trigger 40 MHz1 MHz
Search for high pt, µ, e, γ, hadron candidates
CALO pt > 3.6 GeV, MUON pt >1.4 GeV
High Level Software Trigger Farm
HLT1: Add Impact parameter cuts
HLT2: Global event reconstruction.
Exclusive or inclusive offline-like selection
(lines)
Adaptation to
physics priorities
variation of beam conditions
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L0 Hardware Trigger 40 MHz1 MHz
Search for high pt, µ, e, γ, hadron candidates
CALO pt > 3.6 GeV, MUON pt >1.4 GeV
Very important point of the analysis presented
today:
L0Hadron line use HCAL, ECAL
L0Muon line use muon stations
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Also useful for flavour tagging:
D0 K- π+ µ+µ-
D0 K+ π- µ+µ-
Rare decay: Priority is to reduce the background
Use D* tag, D0h- h’+µ+µ- from D*D0+
Sophisticated selection for maximal use of decay discriminative features
Keeping systematic uncertainties low: normalization mode
𝐵𝐹(𝑠𝑖𝑔𝑛𝑎𝑙) = 𝐵𝐹(𝑛𝑜𝑟𝑚) 𝜀(𝑛𝑜𝑟𝑚)
𝜀(𝑠𝑖𝑔𝑛𝑎𝑙) 𝑁(𝑠𝑖𝑔𝑛𝑎𝑙)
𝑁(𝑛𝑜𝑟𝑚)
Δm=m(D*+) - m(D0)
Efficiency ratio cancel most of systematics (σ, Luminosity, reco, acceptance, etc.)
p, pT, IP(D),
FD, PID(m)
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140 144 148 152 Δm, MeV/c2
1200
800
400
0
D0K-+ m+m-
m(µ+µ-), MeV/c2
φ ρ
ω
Motivation
Similar final state as signal decays
BF~4.9∙10-6
Not measured yet!
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Data Loose cuts
m(m+m-) in [675;875] MeV/c2
Strategy
D0K-+ + - – normalization:
Similar kinematics
BF=(8.3±0.2)%, with 2.5% precision
Not the same final state
D0K-+ m+m-
m(µ+µ-), MeV/c2
φ ρ
ω
Motivation
Similar final state as signal decays
BF~4.9∙10-6
Not measured yet!
29
Data Loose cuts
m(m+m-) in [675;875] MeV/c2
Strategy
D0K-+ + - – normalization:
Similar kinematics
BF=(8.3±0.2)%, with 2.5% precision
Not the same final state
D0K-+ m+m-
m(µ+µ-), MeV/c2
φ ρ
ω
Motivation
Similar final state as signal decays
BF~4.9∙10-6
Not measured yet!
30
Data Loose cuts
m(m+m-) in [675;875] MeV/c2
Strategy
D0K-+ + - – normalization:
Similar kinematics
BF=(8.3±0.2)%, with 2.5% precision
Not the same final state
Obtained in MC
Obtained in data
L0 trigger
Natural choice for L0 trigger
• D0K-+ + - : hadron line (use HCAL,ECAL)
• D0K-+ (/m+m-) : muon line (use Muon stations)
D0
D
signal
rest of event Two categories of trigger
decision:
TOS: There is at least one
trigger object which
is a part of the signal
TIS: There is at least one
trigger object which is
independent of the signal
L0 Hadron TIS:
Efficiencies do not cancel in ratio Problematic for systematics
• εL0TIS DKmm , ε L0TIS
DK should very similar as the rest of event is similar
• HadronTIS is the most efficient among TIS
• Measurement is still possible
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L0 trigger
HLT1 trigger
HLT2 trigger
Stripping
MVA+Muon ID
Online
Offline
We developed dedicated cut-
based lines
Scan the level of cuts to find the
optimal and that respect:
- impact retention rate and CPU
- maximize signal significance
HLT2 and Stripping lines are
based on similar cuts
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Daughter particles
Momentum, p Transverse momentum, pt
Impact parameter (IP) χ2 Track χ2
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Signal from MC
Background from data
(sideband, after stripping)
D meson
Transverse momentum, pt Vertex χ2
Distance Of Closest Approach Impact parameter (IP) χ2
36
Signal from MC
Background from data
(sideband, after stripping)
D meson
Transverse momentum, pt Vertex χ2
DIRection Angle Flight Distance (FD) χ2
37
Signal from MC
Background from data
(sideband, after stripping)
20%
sel.
optimiz
ation
78%
measurement
D0K-+m+m- sample:
2% BDT training
L0HadronTOS|| L0MuonTOS
Control sample
50% for
measurement
50% control
sample
D0K- ++- sample:
Sample for BDT training
K-+m+m-: 3M events
Sample for efficiencies and systematics:
K-+m+m-: 4M events
K- ++-: 2M events
K- ++-: 2M events, more realistic
resonant model
2012 data, 2 fb-1 , 8 TeV, untagged sample (from PV)
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D0K-+m+m- control sample:
Correlation between variables
Decision Tree Boosted Decision Tree
α1 +α2
+αn …
Performant classifier
Only one variable (BDT)
40
Boosted Decision Tree combines variables shown before
Training + testing samples
Signal proxy: MC (3M)
Background proxy: 2% upper sideband of D0K-+/(m+m-) sample
41
Optimal cut on BDT and ProbNNmu Fit yields for each cut on BDT and ProbNNmu
Find the point of the best significance
50
25
0
50
25
0
1800 1850 1900
1800 1850 1900 m(D0), MeV/c2
m(D0), MeV/c2
1800 1850 1900 m(D0), MeV/c2
50
25
0
1800 1850 1900 m(D0), MeV/c2
50
25
0
BDT > 0.2, ProbNNmu>0.3
20% signal sample
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Signal: Cruijff function
Combinatorial background: 1st order polynomial
20% signal sample
mD0
σ
αL αR
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Peaking background: 2 non-parametric PDF
20% signal sample
mD0
σ
αL αR
D0K- ++- , higher PT
D0K- ++- , lower PT
D0K- ++- D0
K-+m+m-
Just 20 MeV/c2 below
Decays in flight µν (single and double) create
a tail easily misfitted as combinatorial background
46
Not enough statisitcs in our MC for double decays in flight
zoom
If we apply ProbNNmu on 1 or 2 pions
MC2012, Stripping level
m(D0), MeV/c2 m(D0), MeV/c2
m(D0), MeV/c2 m(D0), MeV/c2
Single misID Double misID
47
Before the neutrino loss
𝑝
Not enough statistics in MC for double decays in flight:
It is rare to have decays before the end of the tracking stations
This sample of events can be used to
characterize the effect on the p of the losing
neutrino
Distributions of 𝜹𝒑 as a function of
(𝒑, charge)
After the neutrino loss
𝑝 − 𝜹𝒑
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Before the neutrino loss
𝑝
Not enough statistics in MC for double decays in flight:
It is rare to have decays before the end of the tracking stations
This sample of events can be used to
characterize the effect on the p of the losing
neutrino
Distributions of 𝜹𝒑 as a function of
(𝒑, charge)
After the neutrino loss
𝑝 − 𝜹𝒑
49
Smear (𝒑) in D0K- ++- MC full sample to reproduce the effect of energy
losing due to decays in flight, recalculate the mass
Before the neutrino loss
𝑝
Not enough statistics in MC for double decays in flight:
It is rare to have decays before the end of the tracking stations
This sample of events can be used to
characterize the effect on the p of the losing
neutrino
Distributions of 𝜹𝒑 as a function of
(𝒑, charge)
After the neutrino loss
𝑝 − 𝜹𝒑
50
Smear (𝒑) in D0K- ++- MC full sample to reproduce the effect of energy
losing due to decays in flight, recalculate the mass
High PT Low PT
Forms
Fit fractions in the data control sample D0K-+(/ m+m-), selected with
(D_L0Hadron_TOS || D_L0Muon_TOS)
High PT
51 Forms
Low PT
52
Fit fractions in the data control sample D0K-+(/ m+m-), selected with
(D_L0Hadron_TOS || D_L0Muon_TOS)
From real data with PIDCalib: a tag-and-probe technique using J/ψµµ
unbiased sample to get efficiency in bins of (P,η,nTracks)
For each µ-track from D0K-+m+m-
efficiency from J/ψµµ
Looked for an optimal binning:
Fine enough to be sensitive to efficiency variation inside a
kinematical bin
Coarse enough to have enough statistic in each bin
Details in backup
Obtained efficiency (75.7 ± 0.4)% 56
nTracks
Muons from D0K-+m+m- and J/ψµµ
Compare three binnings: Fine, Default, Coarse
Default
nTracks
60
Comparison of results from three binnings (fine, default and coarse)
Systematic uncertainty: 2.5%
Muons from D0K-+m+m- and J/ψµµ
Compare three binnings: Fine, Default, Coarse
62
Efficiency ratio: difference between data and MC
Uncertainty on the BDT cut : < 2%
The variables used in the selection are not perfectly described by MC
Data/MC comparison helps to evaluate this effect
BDT combines all these variables
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D0K-+ /(m+m-)
L0HadronTOS||L0MuonTOS)
D0K-+ + -
-1 -0.6 -0.2 0.2 0.6 1 BDT
-1 -0.6 -0.2 0.2 0.6 1 BDT
500
400
300
200
100
0
2500
2000
1500
1000
500
0
Data
MC
Data
MC
L0 Hadron TIS efficiencies should be similar at first order for D0K-+m+m- and
D0K- ++- as the rest of event is similar
Overlap of the clusters in HCAL has the different effect?
D0K- ++- has 3 ’s higher TIS efficiency?
TIS cluster
Signal cluster
64
Compare two TIS efficiencies involving two very different detectors
L0HadronTIS (use HCAL, ECAL)
L0MuonTIS (use Muon stations)
L0 Hadron TIS efficiencies should be similar at first order for D0K-+m+m- and
D0K- ++- as the rest of event is similar
(D
0
K-
+m
+m
- )/
(D0
K-
+
+
- ) MuonTIS
HadronTIS
MC
65
No such effect seen in MC
Very similar!
L0 Hadron TIS efficiencies should be similar at first order for D0K-+m+m- and
D0K- ++- as the rest of event is similar
(D
0
K-
+m
+m
- )/
(D0
K-
+
+
- ) MuonTIS
HadronTIS
MC
66
No such effect seen in MC
Very similar!
A look at the data is necessary!
Check the difference in data
One conservative way:
Compare measured BF on HadronTIS, MuonTIS
Not precise test!
Uncertainty on the comparison is 7.7%
Can be quoted as a conservative systematic uncertainty
This is too conservative. Work continues to find a better approach
67
BF L0HadronTIS = (4.37 ± 0.19) × 10-6
BF L0MuonTIS = (4.66 ± 0.28) × 10-6
ΔBF = (0.29 ± 0.34) × 10-6
Highest uncertainty is due to L0:
No physical reasons to be that high
Too conservative
New tests are ongoing
68
First measurement of:
Overall uncertainty: 12.5%
Can now be used as suitable normalization mode for the next step:
the measurement of total and partial BFs’ of other D0h- h’+µ+µ- decays
69
Our ultimate goals: Branching ratios and Asymmetries in
D0 K- π+ µ+µ-
D0 K- K+ µ+µ-
D0 π - π+ µ+µ-
D0 K+ π- µ+µ-
Can we find NP here ??
Test sensitivities with
Run I (2012, 2fb-1 at √s = 8 TeV)
Run II (5 fb-1 at √s = 13 TeV)
Upgrade (50 fb-1, √s =14 TeV)
First step is to design an optimal selection
What we already have: Stripping, HLT2
To finalize: we tested several Multivariate methods (BDT, ANN)
71
Study of the performances of different Multivariate methods in order to
find the best!
2 training methods:
- Boosted Decision Tree (BDT)
- Artificial Neural Network (ANN)
2 boosting methods:
- Gradient (GradBoost)
- Adaptive (AdaBoost)
7 sets of variables
2 MVA packages:
- TMVA (Root)
- MutliBoost (AppStat@LAL)
11 approaches in total
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Find best significance
1800 1850 1900
1800 1850 1900
m(D0),
MeV/c2
1800 1850 1900
1800 1850 1900 m(D0),
MeV/c2
50
25
0
50
25
0
Find the best possible performance with this method is looked for
Each method is first trained Sample:
Signal: MC 2012, generated 2M
BKG: K- π+ µ+ µ sideband 10% of the data
Then it is tested for overtraining
ΔM
=M(D
*)-M
(D0),
Me
V/c
2
M(D0), MeV/c2
73
40% of the K- π+ µ+ µ- sample
50
25
0
50
25
0
Results: Signal significance from 11 methods:
MVA performs better than rectangular cuts
Properties of data are such that all methods perform similarly
Confirmed by fast convergence of tested approaches
Test sensitivities with
need other variables?
Work before the trigger and stripping?
Choose newVarB as the working hypothesis for the rest of the studies
Le
arn
ing
err
or
Number of trees
74
Study the sensitivity to
Asymmetries
Total Branching fractions
Branching fractions that would be a clear sign of NP
D0 K+ π- µ+µ- : (BF~5 ∙10-9) at low m(µ+µ-)
D0 K- K+ µ+µ- (BF~10-8) at low m(µ+µ-)
Tot. BF (Theory)
D0K- π+ µ+µ- 6.2×10-6.
D0K- K+ µ+µ- 1.1×10-7
D0π- π+µ+µ- 1.3×10-6
D0K+ π- µ+µ- 1.7×10-8
Consider three dataset Run I (2012, 2fb-1 at Vs = 8 TeV)
Run II (5 fb-1 at Vs = 13 TeV)
Upgrade (50 fb-1, Vs =14 TeV)
Extrapolate Signal and Background yields Signal: D* π+ D0(K- π+ µ+µ-) peak from
Background: sideband data
Re-scaled: BF, luminosity, cross section, MC
efficiencies.
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1800 1850 1900
1800 1850 1900
m(D0),
MeV/c2
1800 1850 1900
1800 1850 1900 m(D0),
MeV/c2
50
25
0
50
25
0
50
25
0
50
25
0
D0 K+ π- µ+µ-
For D0 K- K+ µ+µ- (B~10-7-10-8)
D0 K- K+ µ+µ-
Branching fractions
Measurement
Possible observation
Asymmetries
In D0 K- π+ µ+µ-: asymmetry O(5%) measurable in Run II
In D0 K- K+ µ+µ-: measuring 5% takes the upgrade + an improved selection
(100% efficient trigger)
77
D0 K+ π- µ+µ-
For D0 K- K+ µ+µ- (B~10-7-10-8)
D0 K- K+ µ+µ-
Branching fractions
Measurement
Possible observation
Asymmetries
In D0 K- π+ µ+µ-: asymmetry O(5%) measurable in Run II
In D0 K- K+ µ+µ-: measuring 5% takes the upgrade + an improved selection
(100% efficient trigger)
78
Reminder: Most models predict asymmetries ~ 1%
Some models >~ 10%
New data taking period at 14 TeV with 40MHz beam
Change of the trigger strategy will allow to benefit from new luminosity
Changes in detector:
a 40MHz readout electronics for all subsystems
Calorimeter reviewed
the VELO, tracking stations will be upgraded completely
the PS, SPD sub-detectors, M1 muon station, aerogel in RICH1 will be removed
Low Level Trigger:
Hardware trigger L0 is
replaced by LLT, that
will be used at the
beginning, for testing
During data taking
runs readout detector
information at 40MHz
Decision is taken with
software at PC-farms
L=2×1033 cm-2 s-1
80
Requirements
Energy/position measurement
Identification of γ, electrons, hadrons
High sensitivity
Fast response (40MHz)
Clean sampling in 25ns (no spill-over)
L0 trigger input (present detector)
81
Prototypes of the analog/digital parts of the electronics have been redesigned
The PMT gain reduction is compensated by the gain of electronics
Needed the same performances as for the present electronics
Key parameters to look at: noise, linearity, full integration of the signal pulse in
the 25ns interval
A test beam is necessary for tests in realistic conditions
The amplification and integration of the signal in 25 ns 2 alternated integrators running at 20MHz
One integrates during 25ns
The other is readout, present result to ADC and reset
83
ECAL
module
e
Electron beam at 50 GeV, 100GeV,
125GeV
ECAL module
2 parallel acquisitions tested FE board with fast integration
Lecroy board with a long time interval
integrator
The time arrival of the particles is
asynchronous with respect to the clock of
the electronics Two scintillators provide the trigger
acquision and give the measurement of
the time arrival of the particles
84
ECAL module
e1
e2
Trigger
Time arrival
Noise at the level of ~1 ADC (=2.5 MeV) is negligible
1.6 ADC counts
OK
Linearity, dependence on energy of electrons, should be < 1%
< 1%
OK 50GeV
100GeV
125GeV
85
Spill-over should be < 1%
If pulse is too broad, part of the signal remains in the next 25ns sample
Need to check if signal pulse is
fully integrated during 25ns
> 1% !
Too broad pulse
86
1600 2000 2400
2500
1500
500
TDC t, ns
FE
AD
C
-2 -1 0 1 2 Δt(TDC), ns
1.4
1
0.6
0.2
Δ A
DC
, %
Plateau should be stable over 4 ns (<1%)
0
± 1ns, 2ns
Linearity and noise level are acceptable
Solution: filter pole-zero removes some frequencies and improves shape this
way
Plateau and spill over are too large
Signal pulse is too Broad or tail is too long
87