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LumiCal Optimization Simulations
Iftach Sadeh
Tel Aviv University
CollaborationHigh precision design
May 6th 2008
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Performance requirements
1. Required precision is:
2. Measure luminosity by counting the number of Bhabha events (N):
year/10,10~
year/10,10~
year/10decays) Z(hadronic GigaZ,10~
63
63
94
qqeeL
L
WWeeL
LL
L
max
min
gen
genrec
N
NN
N
N
L
L
3
1Bhabhad
d
NL
RIGH LEFTTΔθ - θθ
RIGHTθ
LEFTθ
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Design parameters
3. Layers:
Number of layers - 30
Tungsten Thickness - 3.5 mm
Silicon Thickness - 0.3 mm
Elec. Space - 0.1 mm
Support Thickness - 0.6 mm
1. Placement:
2270 mm from the IP
Inner Radius - 80 mm
Outer Radius - 190 mm
2. Segmentation:
48 azimuthal & 64 radial divisions:
Azimuthal Cell Size - 131 mrad
Radial Cell Size - 0.8 mrad
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Eres(θmax)Eres(θmin)
Choose constant which minimizes the resolution, σ(θ), but does not necessarily minimizes the bias as well.
Define minimal and maximal polar angles for a shower.
σ(θ) Δθ
Energy resolution (Eres) / Polar resolution and bias (σ(θ) , Δθ)
Min{Δθ}
Min{σ(θ)}
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MIP (muon) Detection Many physics studies demand the ability to detect muons (or the lack thereof) in
the Forward Region.
Example: Discrimination between super-symmetry (SUSY) and the universal extra dimensions (UED) theories may be done by measuring the smuon-pair production process. The observable in the figure, θμ, denotes the scattering angle of the two final state muons.
“Contrasting Supersymmetry and Universal Extra Dimensions at Colliders” – M. Battaglia et al. (http://arxiv.org/pdf/hep-ph/0507284)
1 1 1 1
2UED:
~ 1 coscos
e e
d
d
0 01 1
2SUSY:
~ 1 coscos
e e
d
d
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MIP (muon) Detection
Multiple hits for the same radius (non-zero cell size).
After averaging and fitting, an extrapolation to the IP (z = 0) can be performed.
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Induced charge in a single cell Energy/Charge conversion:
Distribution of the deposited energy spectrum of a MIP (using 250 GeV muons):MPV = 89 keV ~ 3.9 fC.
Distributions of the charge in a single cell for 250 GeV electron showers, and of the corresponding maximal cell signal (for 96 and 64 radial divisions).
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Digitization
σ(θ)
Δθ
Eres
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Number of radial divisions
σ(θ) Δθ
min
2
L
L
-1
5
500GeV
1.23nb
500 fb
4 10
s
L
N
N
Dependence of the polar resolution, bias and subsequent error in the luminosity measurement on the angular cell-size, lθ.
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Inner and outer radii
Beamstrahlung spectrum on the face of LumiCal: For the preferable antiDID case Rmin must be larger than 7cm.
( Shown by C.Grah at theOct 2007 FCAL meeting )
-1500 fbL
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Thickness of the tungsten layers
σ(θ) Δθ
Eres
Δθ
Min{Δθ}
Min{σ(θ)}
( The cut matters! )
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Clustering - Event Sample Bhabha scattering with √s = 500 GeV
θ ΦEnergy
Separation between photons and leptons:
- As a function of the energy of the low-energy-particle (angular distance).
- Distribution of the distance (on the face of LumiCal).
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Clustering - Algorithm
Phase I:Near-neighbor clustering in a single layer.
Phase II:Cluster-merging in a single layer.
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Clustering - Algorithm
Phase III:Global-clustering.
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Clustering - Results
Merging-cuts:
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Clustering - Geometry dependence
-1500 fbL
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Summary
Optimal parameters for the present detector-concept:
1. [Rmin → Rmax] = [80 → 190] mm → σB = 1.23 nb.
2. 64 radial divisions (0.8 mrad radial cell-size)→ Δθ = 3.2∙10-3 , σθ = 2.2∙10-2 mrad→ ΔL/L = 1.5∙10-4 .
3. 48 azimuthal → enough for clustering, but shouldn’t be lower…
4. Tungsten thickness of 3.5 mm → 30 layers are enough for stabilizing the energy resolution at Eres ≈ 0.21 √GeV.
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AuxiliarySlides
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Leakage through the back layers
(normalized) energy deposited per layer for a 90-layer LumiCal.
Distribution of the total energy for a LumiCal of 30 or 90 layers.
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Effective layer-radius, reff(l) / Moliere Radius, RM
Shower profile - RM is indicated by the red circle.
Dependence of the layer-radius on the layer number, l.
RM(layer-gap)
RMr(l)
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Clustering - Energy density corrections
Event-by-event comparison of the energy of showers (GEN) and clusters (REC).
Before After
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Clustering - Results (relative errors) Dependence on the merging-cuts of the errors in counting the number of
single showers which were reconstructed as two clusters (N1→2), and the number of showers pairs which were reconstructed as single clusters, (N2→1).
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Clustering - Results (event-by-event)
Event-by-event comparison of the energy and position of showers (GEN) and clusters (REC).
θ Φ
Energy
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Clustering - Results (measurable distributions)
Energyhigh
θhigh θlow
Energylow
Δθhigh,low
Energy and θ of high and low-energy clusters/showers.
Difference in θ between the high and low-energy clusters/showers.