Studies on the Simulation of Muons
in the Muon End Cap Chambers
of CMS
D.Acosta, S.M.Wang
University of Florida
Goal: Study reconstruction of Pt of muons in the End Cap chambers at the
online level, to help in the design of the End Cap muon trigger.
Simulation:
use CMSIM 114
produced single muon events at various Pt, in 0:9 < < 2:4 range
CMSIM produces ntuple which contains informations on the simulation
of the CSC trigger primitives (, , ... of the LCTs).
Simulation of Trigger Primitives (LCTs):
the cathode strips and the anode wires that carry hits caused by the
traversing muon, are used to reconstruct the trigger primitives (refer to
CMS TN/96-69).
study rec as a function of gen in each station (for dierent Pt)
study as a function of gen for dierent Pt.
: 12 = 1 , 2
13 = 1 , 3
23 = 2 , 3
1
σ(ηrec-ηgen)
ηrec-ηgen
ηrec-ηgen vs ηgen (Pt = 3 GeV)
0.75
0.5
0.25
0
1
1.5
2
2.5
0.2
0.15
0.1
0.05
0
ηgen
1
1
0.75
0.5
0.25
0
1
1.5
2
2.5
σ(ηrec-ηgen)
ηrec-ηgen
0.5
0.25
0
2
2.5
0
1
1.5
2
ηgen
2
ηgen
2.5
0.2
0.15
0.1
0.05
0
ηgen
1
1.5
2.5
ME 3
1
σ(ηrec-ηgen)
ηrec-ηgen
ηgen
0.05
ME 3
0.75
0.5
0.25
0
1.5
2
0.1
ME 2
0.75
1
2.5
0.15
ηgen
1
1.5
ηgen
0.2
ME 2
1
2
ME 1
σ(ηrec-ηgen)
ηrec-ηgen
ME 1
1.5
2
2.5
ηgen
ME 4
large shift in rec at low gen
0.2
0.15
0.1
0.05
0
1
1.5
ME 4
2.5
0.04
0.02
0
-0.02
-0.04
-0.06
σ(ηrec-ηgen)
ηrec-ηgen
ηrec-ηgen vs ηgen (Pt = 50 GeV)
1
1.5
2
2.5
0.05
0.04
0.03
0.02
0.01
0
ηgen
1
0.01
0.005
0
-0.005
-0.01
1
1.5
2
2.5
σ(ηrec-ηgen)
ηrec-ηgen
0
-0.005
2
2.5
0
1
σ(ηrec-ηgen)
ηrec-ηgen
0
-0.005
ME 4
2
ηgen
2
ηgen
2.5
0.015
0.01
0.005
0
1
1.5
2.5
ME 3
0.005
1.5
1.5
0.02
ηgen
0.01
1
ηgen
0.005
ME 3
-0.01
2
0.01
ME 2
0.005
1.5
2.5
0.015
ηgen
0.01
1
ηgen
0.02
ME 2
-0.01
2
ME 1
σ(ηrec-ηgen)
ηrec-ηgen
ME 1
1.5
2
2.5
ηgen
0.02
0.015
0.01
0.005
0
1
1.5
2.5
ME 4
the \saw-tooth" eect in ME1 is probably due to the tilt in the anode
wires in ME1/1
7.5
5
2.5
0
5
2.5
0
1
0
-1
-2.5
1
2
1
ηgen
3
Φ1-Φ3 (degree)
Φ1-Φ2 (degree)
7.5
2
1
2
ηgen
3
Φ2-Φ3 (degree)
-2.5
Φ2-Φ3 (degree)
Φ1-Φ3 (degree)
Φ1-Φ2 (degree)
vs gen at dierent Pt
2
1
1
2
1
2
1
2
ηgen
0.4
0.2
0
2
0
ηgen
0.4
0.3
0.2
0.1
0
1
2
ηgen
0.4
Φ2-Φ3 (degree)
1
Φ1-Φ3 (degree)
Φ1-Φ2 (degree)
0
0.3
0.2
0.1
0
1
2
ηgen
ηgen
0.4
0.3
0.2
0.1
0
1
2
ηgen
ηgen
the \error" bars are the RMS of the spread.
Max < 9.
the jump in at gen 1:6 for ME1-ME2 and ME1-ME3 is due to
ME1/1 being closer to IP compare to ME1/2 and ME1/3.
Reconstruction of Pt
Pt is obtained from the measured in two muon stations
parameterize the to Pt relation at dierent xed ranges
1:80 < < 1:95
1:95 < < 2:10
2:10 < < 2:25
2:25 < < 2:40
t the as a function of Pt with the relation : = a Pt,1
the reconstructed Pt from measurement of will be : Pt1rec = meas
a
(Note: The inverse relation = a Pt,1 is not an accurate description of
the to Pt relation due to bending of the magnetic eld.)
150
Events
, Pt1gen Distributions
Events
Events
1
Ptrec
150
100
75
100
100
50
50
0
50
-0.2
0
0
0.2
25
-0.2
-1
-0.2
200
100
100
50
0.2
1/Ptrec-1/Ptgen (GeV )
Events
150
0
-1
1/Ptrec-1/Ptgen (GeV )
Events
Events
0
0.2
-1
1/Ptrec-1/Ptgen (GeV )
300
0
100
75
50
0
-0.1
0
0
0.1
25
-0.1
-1
200
150
100
100
50
0
0.1
-1
1/Ptrec-1/Ptgen (GeV )
Events
250
200
0
-0.1
1/Ptrec-1/Ptgen (GeV )
Events
Events
300
0
0.1
-1
1/Ptrec-1/Ptgen (GeV )
400
0
150
100
50
-0.1
0
0.1
-1
1/Ptrec-1/Ptgen (GeV )
0
-0.1
0
0.1
-1
1/Ptrec-1/Ptgen (GeV )
0
-0.1
0
0.1
-1
1/Ptrec-1/Ptgen (GeV )
distributions are quite symmetric
slight oset from zero may be due to the inaccurate direct inverse relation
used in the parameterization
σ( 1/Ptrec - 1/Ptgen )/( 1/Ptgen )
Resolution of Pt as function of 1.4
Pt = 100 GeV
Pt = 50 GeV
Pt = 10 GeV
1.2
1
0.8
0.6
0.4
0.2
ME1 - ME2
0
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
ηrec
Ptrec obtained from measured between ME1 and ME2
resolution is minimum at 1:6 , 1:8
resolution degrades with increase in Pt
resolution from this simulation study has the same shape as that obtained by Richard Breedon (for > 1:2), however the results from this
study are 5% , 10% higher (probably due to multiple scattering when
traversing through the detector)
(Refer to Breedon's talk at EMU meeting, UF Gainesville, 20-21 March
1998)
∆(Pt)/Pt
Resolution of Pt as function of 1.4
Pt = 100 GeV
Pt = 50 GeV
Pt = 10 GeV
1.2
1
0.8
0.6
0.4
0.2
0
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
η
studies of the resolution of Pt by R. Breedon for the case Half-strip
Resolution, 1-point staggering.
(EMU Meeting, UF Gainesville, 20-21 March 1998)
Eect from the size of the bin on the resolution of Pt
< ( 1/Ptrec - 1/Ptgen )/( 1/Ptgen ) >
2 cases : parameterize the vs Pt in
8 bins of (0:9 < < 2:4)
60 bins of (0:9 < < 2:4)
0.5
0.4
8 bins
0.3
60 bins
0.2
0.1
0
-0.1
-0.2
-0.3
ME1 - ME2
-0.4
Pt = 10 GeV
-0.5
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
ηrec
\Saw tooth" eect when a single -Pt parameterization for a large bin is used to reconstruct Pt in nner bins
σ( 1/Ptrec - 1/Ptgen )/( 1/Ptgen )
1
0.9
8 bins
0.8
60 bins
0.7
ME1 - ME2
0.6
Pt = 10 GeV
0.5
0.4
0.3
0.2
0.1
0
0.8
1
1.2
1.4
1.6
resolution of Pt is similar in both cases
1.8
2
2.2
2.4
ηrec
Pt resolution for obtained from dierent
sets of Muon Stations
σ( 1/Ptrec - 1/Ptgen )/( 1/Ptgen )
σ( 1/Ptrec - 1/Ptgen )/( 1/Ptgen )
from :
ME1 ! ME2
ME1 ! ME3
ME2 ! ME3
1.4
Pt = 10 GeV
ME2 - ME3
ME1 - ME3
ME1 - ME2
1.2
1
0.8
0.6
5
4
3
ME2 - ME3
Pt = 50 GeV
ME1 - ME3
ME1 - ME2
2
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.4
0.2
0.2
0
0.8
1
1.2
1.4
1.6
1.8
2
Pt = 10 GeV
2.2
2.4
ηrec
0.1
0.8
1
1.2
1.4
1.6
1.8
2
2.2
Pt = 50 GeV
For Pt=10 GeV, resolution of Pt for ME1-ME3 is slightly worse than
ME1-ME2, even though 13 is generally larger than 12. (probably
due to multiple scattering ... more material to traverse)
For Pt=50 GeV, resolution of Pt is similar for ME1-ME2 and ME1-ME3.
2.4
ηrec
Using bending angle to improve Pt resolution
is the angle between the direction of muon and the normal of the
station.
can be obtained from the width of the road pattern of the track in
the station
=5
5 half strip widths
=4
4 half strip widths
=3
3 half strip widths
=2
2 half strip width
=1
1 half strip widths
Road pattern of track in the station
(Plot taken from CMS TN/96-69)
vs Pt at dierent ME-2
5
2.2 < η < 2.4
2.0 < η < 2.2
4.5
<>
1.8 < η < 2.0
3.5
1.2 < η < 1.4
5
2
2
1.5
1.5
40
60
80
100
Pt (GeV)
Pt (GeV)
ME-3
1.6 < η < 1.8
1.4 < η < 1.6
1.2 < η < 1.4
1.0 < η < 1.2
3
2.5
20
1.8 < η < 2.0
3.5
1.0 < η < 1.2
0
2.0 < η < 2.2
4.5
2.5
1
2.2 < η < 2.4
4
1.4 < η < 1.6
3
5.5
<>
1.6 < η < 1.8
4
< # of 1/2 strips >
< # of 1/2 strips >
< # of 1/2 strips >
ME-1
5.5
1
0
20
40
60
80
100
Pt (GeV)
Pt (GeV)
5.5
5
2.2 < η < 2.4
2.0 < η < 2.2
4.5
<>
1.8 < η < 2.0
3.5
1.2 < η < 1.4
1.6 < η < 1.8
4
1.4 < η < 1.6
1.0 < η < 1.2
3
2.5
2
1.5
1
0
20
40
60
80
100
Pt (GeV)
Pt (GeV)
is large for low Pt tracks (Pt< 5 GeV) in ME1
road pattern is almost straight for high Pt tracks and tracks in ME2,
ME3
4
3
2
1
0
Ψ
(#
of
1/
2
st
s)
rip
< > " with # Pt
< > " with " parameterize as function of Pt for each value of < ∆Φ12 > (degree)
eV)
Pt (G
ME1 - ME2 (Pt = 10 GeV)
0.9
Without Ψ info
0.8
With Ψ info
0.7
0.6
σ( 1/Ptrec - 1/Ptgen )/( 1/Ptgen )
σ( 1/Ptrec - 1/Ptgen )/( 1/Ptgen )
1
1
ME1 - ME2 (Pt = 50 GeV)
0.9
Without Ψ info
0.8
With Ψ info
0.7
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0.8
1
1.2
1.4
1.6
1.8
2
Pt=10 GeV
2.2
2.4
ηrec
0
0.8
1
1.2
1.4
1.6
1.8
2
Pt=50 GeV
marginal improvement in Pt resolution for Pt=10 GeV
no improvement in Pt resolution for Pt=50 GeV
2.2
2.4
ηrec
Summary for the End Cap Muon Detector
Preliminary studies show that :
The selection of wider bins in the parameterization of -vs-Pt does
not have much eect on the Pt resolution. Thus a coarse resolution of
is sucient for the Track Finder.
The larger bending angle between ME1-ME3 (compared to ME1-ME2)
does not help to improve the Pt resolution due to multiple scattering.
Additional information from does not contribute much to the improvement of the Pt resolution.