Endcap Muon Trigger Simulation
Studies
D.Acosta, S.M. Wang
University of Florida
New since Nov-98 Tridas review:
1. Inclusion of DT primitives for overlap region
2. Misalignment studies
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 trigger level, to help in the design of
the End Cap Track-Finder.
Simulation:
use CMSIM 114
{ muon.tz has wrong strip staggering !
It was corrected for this study.
{ this should be xed in CMSIM 115 .
produced single muon events at various Pt, in 0:9 <
< 2:4 range
CMSIM produces ntuple which contains information
on the simulation of the CSC trigger primitives (, ,
... of the LCTs).
The information of the trigger primitives in the Barrel
Muon chamber was obtained from the Zebra banks.
Simulation of Trigger Primitives (LCTs):
old Fortran package.
high Pt patterns only.
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
Mean
0.75
0.5
σ(ηrec-ηgen)
ηrec-ηgen
ηrec-ηgen vs ηgen (Pt = 3 GeV)
0.25
0
1
1.5
2
2.5
0.2
RMS
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
0.2
0.15
0.1
0.05
0
ηgen
ME 4
large shift in rec at low gen
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)
Mean
1
1.5
2
2.5
0.05
0.04
0.03
0.02
0.01
0
ηgen
RMS
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
2
ηgen
2
ηgen
2.5
0.015
0.01
0.005
0
1
1.5
2.5
ME 3
0.005
0
-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
ME 4
0.02
0.015
0.01
0.005
0
1
1.5
2.5
ME 4
the \saw-tooth" eect in ME1 is due to the tilt in the
anode wires in ME1/1
vs gen at dierent Pt
Extrapolation
5
2.5
0
ME2-ME3
Φ2-Φ3 (degree)
7.5
7.5
5
2.5
0
(GeV)
1
3
0
-1
-2.5
1
2
1
ηgen
Φ1-Φ3 (degree)
3
2
1
2
1
ηgen
3
Φ2-Φ3 (degree)
-2.5
Φ1-Φ2 (degree)
ME1-ME3
Φ1-Φ3 (degree)
Φ1-Φ2 (degree)
ME1-ME2
Pt
2
1
2
ηgen
0.4
10
0.2
0
2
0
ηgen
0.4
0.3
0.2
0.1
0
1
2
0.4
0.3
0.2
0.1
0
1
2
ηgen
1
ηgen
Φ2-Φ3 (degree)
1
Φ1-Φ3 (degree)
Φ1-Φ2 (degree)
0
2
ηgen
0.4
0.3
100
0.2
0.1
0
1
2
ηgen
1
2
ηgen
the \error" bars are the RMS of the spread.
Max < 9 5 + 2 , 2.
< 15 ) drop 2 MSB from 60 range in TrackFinder.
the jump in at gen 1:6 for ME1-ME2 and ME1ME3 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.)
1 , 1
Ptrec Ptgen Distributions
150
2.35-2.40
Events
1.70-1.75
Events
Events
1.25-1.30
Pt
150
(GeV)
100
75
100
100
10
50
50
0
50
-0.2
0
0
0.2
25
-0.2
-1
-0.2
100
75
100
200
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
50
50
50
100
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
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 Gaussian. No signicant tails.
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
0.9
Pt = 10 GeV
Pt = 50 GeV
Pt = 100 GeV
0.8
0.7
ME1/3
ME1/2
ME1/1
MB1
0.6
0.5
0.4
0.3
0.2
0.1
MB1 / 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 MB1-ME1
(0:9 < < 1:2), and ME1-ME2 (1:2 < < 2:4).
∆(Pt)/Pt
Resolution of Pt as function of 1
Pt = 100 GeV
0.9
Pt = 50 GeV
0.8
Pt = 10 GeV
0.7
0.6
0.5
0.4
0.3
0.2
0.1
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)
Kalman Fit to all 4 stations with estimated LCT resolution.
σ( 1/Ptrec - 1/Ptgen )/( 1/Ptgen )
Without using Barrel Muon Chamber
in Over-Lap region
1.2
(Pt = 10 GeV)
Without MB info
ME1 - ME2
1
With MB info
MB1 - ME1 (0.9 < η < 1.2)
ME1 - ME2 (1.2 < η < 2.4)
0.8
0.6
0.4
0.2
σ( 1/Ptrec - 1/Ptgen )/( 1/Ptgen )
0
0.8
1
1.2
1.4
1.6
1.8
1.6
2
2.2
2.4
ηrec
(Pt = 100 GeV)
Without MB info
1.4
ME1 - ME2
With MB info
1.2
MB1 - ME1 (0.9 < η < 1.2)
ME1 - ME2 (1.2 < η < 2.4)
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
ηrec
resolution is poor in the overlap region if only the End
Cap Muon Chambers are used.
Eect from the size of the bin on the
resolution of Pt
(How many bits necessary for ?)
2 cases : parameterize the vs Pt in
8 bins of (0:9 < < 2:4) ) 3 bits
30 bins of (0:9 < < 2:4) ) 5 bits
< ( 1/Ptrec - 1/Ptgen )/( 1/Ptgen ) >
0.5
0.4
8 bins
0.3
30 bins
0.2
0.1
0
-0.1
-0.2
-0.3
MB1 / ME1 / ME2
-0.4
Pt = 10 GeV
-0.5
0.8
\Saw
1
1.2
1.4
1.6
1.8
2
2.2
2.4
ηrec
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
30 bins
0.7
MB1 / ME1 / ME2
0.6
Pt = 10 GeV
0.5
0.4
0.3
0.2
0.1
0
0.8
resolution
1
1.2
1.4
1.6
1.8
2
2.2
of Pt is similar in both cases
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. (due to multiple scattering ... more material to traverse)
For Pt=50 GeV, resolution of Pt is similar for ME1ME2 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
Denition of =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
2.2 < η < 2.4
2.0 < η < 2.2
1.8 < η < 2.0
1.6 < η < 1.8
1.4 < η < 1.6
1.2 < η < 1.4
1.0 < η < 1.2
5
4.5
<>
4
3.5
3
5.5
4.5
<>
4
3.5
3
2.5
2
2
1.5
1.5
1
10
ME-3
2
10 Pt (GeV)
Pt (GeV)
2.2 < η < 2.4
2.0 < η < 2.2
1.8 < η < 2.0
1.6 < η < 1.8
1.4 < η < 1.6
1.2 < η < 1.4
1.0 < η < 1.2
5
2.5
1
< # of 1/2 strips >
< # of 1/2 strips >
< # of 1/2 strips >
ME-1
5.5
1
1
10
2
10 Pt (GeV)
Pt (GeV)
5.5
2.2 < η < 2.4
2.0 < η < 2.2
1.8 < η < 2.0
1.6 < η < 1.8
1.4 < η < 1.6
1.2 < η < 1.4
1.0 < η < 1.2
5
4.5
<>
4
3.5
3
2.5
2
1.5
1
1
10
2
10 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
eV)
Pt (G
< > " with # Pt
< > " with " parameterize as function of Pt for each value of < ∆Φ12 > (degree)
σ( 1/Ptrec - 1/Ptgen )/( 1/Ptgen )
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.8
1
1.2
1.4
1.6
2.4
Without Ψ info
2.2
With Ψ info
2
ηrec
ME1 - ME2 (Pt = 10 GeV)
1.8
Pt=10 GeV
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.8
1
1.2
1.4
1.6
2.2
With Ψ info
2
ηrec
2.4
Without Ψ info
ME1 - ME2 (Pt = 50 GeV)
1.8
Pt=50 GeV
marginal improvement in Pt resolution for Pt=10 GeV
no improvement in Pt resolution for Pt=50 GeV
σ( 1/Ptrec - 1/Ptgen )/( 1/Ptgen )
Misalignment of the End Cap Chambers
100
Difference in Pt resolution (%)
Difference in 1/Ptrec (%)
from : ME1 ! ME2
rotate ME2 by 0:5 mrad
( 1.2 < η < 1.6 )
80
60
40
20
0
-20
-40
10
( 1.2 < η < 1.6 )
8
6
4
2
0
-2
-4
ME2 rotate +0.5 mrad
ME2 rotate +0.5 mrad
-60
-6
ME2 rotate -0.5 mrad
ME2 rotate -0.5 mrad
-80
-100
-8
0
20
40
60
80
100
-10
0
20
Ptgen (GeV)
40
60
80
100
Ptgen (GeV)
small oset in Pt1rec at low Ptgen, but large oset at
high Ptgen.
small eect on the resolution of Pt.
Misalignment Effect
• This simple simulation shows that a 1mm offset of
one chamber induces a trigger bias at high Pt
– This is roughly the expected tolerance on CSC
chamber positioning
• Endcap iron disks are expected to be aligned only to
3mm
– This will have dominant effect on trigger bias
• CSC Track-Finder absolutely must include alignment
corrections
– Natural place is the Sector Receiver, but precision is
only needed for PT assignment
D. Acosta, December CMS Week
12/8/98
2
Summary for the End Cap Muon Detector
Preliminary studies show that :
A coarse resolution of is sucient for the Track
Finder.
May ignore tilt of wires in ME1/1 .
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.
PtPt 30%
Further studies
More studies on the misalignment of the End Cap
Muon chambers, and its eect on trigger rates and
eciency.
Study of trigger rates.
rate (Hz)
10 8
10
All µ
7
µ in End Cap
µ from πK decays
10 6
µ from non-πK
decays
10 5
10 4
10 3
10 2
10
1
1
10
10
Ptmin (GeV)
2