alignment of the zeus micro- vertex detector using cosmic tracks · 2005. 5. 22. · internal...
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ACAT05, DESY, Zeuthen 1
Alignment of the ZEUS Micro-Vertex Detector Using Cosmic Tracks
Takanori Kohno (University of Oxford), ZEUS MVD Group
X International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT05)
DESY, Zeuthen, May 22-27, 2005
ACAT05, DESY, Zeuthen 2
Contents
HERA-II and the ZEUS detector upgrade.Alignment of the Micro-Vertex Detector (MVD)ResultsSummary & Conclusion
ACAT05, DESY, Zeuthen 3
ZEUS experiment
e
p
FCAL
RCALBCAL
CTD
BMUON
RMUON
XZ
Y
HERA: Electron-proton colliderat DESY, Hamburg.Ep=920 GeVEe=27.5 GeV
ZEUS detector: Multi-purpose particle detector
ZEUS
ACAT05, DESY, Zeuthen 4
HERA-II and ZEUS Upgrade
CTDHERA upgrade• Luminosity increase (×5)• Electron longitudinal polarization.
ZEUS detector upgrade• Micro-Vertex Detector (MVD)
• Polarization depended charged current interaction.• Improve the efficiency of tagging charm and beauty particles using their lifetime information.
ACAT05, DESY, Zeuthen 5
ZEUS Micro-Vertex Detector (MVD)
FMVD BMVD
Single-sided Si strip sensor with 120 µm readout pitch (intermediate strips : 20 µm)
Motivation of installing the MVD• Precise tracking of charged particle near the interaction point.• Reconstruction of secondary vertex from long-lived particles, like c- or b-hadrons.
Precise position measurement required!
ACAT05, DESY, Zeuthen 6
Alignment of the MVD
Position measurement of the hit on a sensor ~ 20 µm.Track reconstruction : fitting hits on various sensors with a helix.
Necessary to know real positions of sensors at high precision.
From the 3D survey during construction, we know• positions of sensors on each ladder were measured to 5 µm during construction.Most unknown factors• relative positions of ladders• position of the entire MVD wrt. ZEUS.
Knowledge of real positions of ladders.Alignment
Goal : Alignment precision < 10 µm.
ACAT05, DESY, Zeuthen 7
Alignment method
Basic strategyUse particle tracks andminimize the residuals between the hit and the track.
movementafter for : 'onintersecti track :
positionhit :
)(2
2
2
2
tracksallin hits all2
2
2
P
Q
DDDDPQ
DDD
′
′
+−′=
′=
′−′= ∑∑∑
r
r
rrrrrr
σσσχ
Measurable
Small linearize wrt. alignment parameters : Xv
XaDD Tx
rrrr=−′
PQ
Before
P’Q’
After
ACAT05, DESY, Zeuthen 8
χ 2 minization
( ) ( ){ }
∑∑
∑
∑
∑
⎟⎠⎞
⎜⎝⎛−===⇒=
∂∂
++=
+=
+−′=
−22
12
22
2
2
2
22
, , 0
21
)(
σσχ
σ
σ
σχ
aDvaaMvMXX
DDXaXaaX
DXa
DDD
T
a
TTT
T
rr
rrrr
rrrrrr
rr
Alignment parameters : calculated by one 6×6 matrix inversion + matrix-vector product
ACAT05, DESY, Zeuthen 9
Alignment using cosmic tracks
Track sample (cosmic muons) : • Rate ~ few Hz• 1 week of dedicated cosmic runs 60k cosmic tracks for the alignment.
Disadvantage• Non-uniform angular coverage.• Only possible for the barrel MVD.• Needs a special cosmic run.
Advantage• Tracks with many MVD hits.• Less ambiguities in pattern recognition.
• 30 ladders in 3 layers• 3 translation + 3 rotation degrees of freedom 180 parameters
ACAT05, DESY, Zeuthen 10
Alignment procedure
Global alignment(x 10)
Internal alignment(x 5)
ZEUS frame
MVD frame
ladder frame
Global alignment(x 10)
Iteration is needed in each step due to, 1. the linear approximation used in the formula and 2. for the internal alignment, alignment of one ladder depends on the geometry
of other ladders.
ladder frame ladder frame
ladder frame
ACAT05, DESY, Zeuthen 11
Global alignment
( )
321v
44444 344444 21v
X
RRRTTT
a
XYXZYZ
DD
Z
Y
X
Z
Y
X
Ti
i
⎟⎟⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜⎜⎜
⎝
⎛
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
−−
−≈−′
01000010
0001r-φ hit
r-z hit
Extrapolate the CTD track into the MVD.• residual information• 3D position of the hit.
∑∑ ⎟⎠⎞
⎜⎝⎛−==
= −
22
1
,
,
σσaDvaaM
vMXT r
rrr
rr
ACAT05, DESY, Zeuthen 12
Residual (mm)-2 -1 0 1 2
Ent
ries
0
200
400
600
r-z (before global)=1.6 (mm)σ
Residual (mm)-2 -1 0 1 2
Ent
ries
0
1000
2000
3000 (before global)φr-
=0.34 (mm)σ
Residual (mm)-2 -1 0 1 2
Ent
ries
0
200
400
600
r-z (after global)=1.5 (mm)σ
Residual (mm)-2 -1 0 1 2
Ent
ries
0
1000
2000
3000
4000
(after global)φr-=0.27 (mm)σ
• Residual centered• Resolution by CTD
Effect on residual distributions.
Before global alignment
After global alignment
ACAT05, DESY, Zeuthen 13
Internal alignment (among MVD ladders)
1. Define χ2 for each ladder. (30 χ2 with 6 DOF each)2. Loop over all events
1. Loop over all tracks in the event1. Loop over all hits in the track
1. Find the ladder where the hit resides2. Exclude all hits in the ladder.3. Refit the track with all other hits.4. Calculate the intersection of the refitted
track and the ladder.5. Calculate the residual between the hit and
the intersection.6. Update the matrix (M) and the vector (V)
using the track direction, intersection and the residual.
3. Once M and V are calculated using all hits/tracks, calculate the alignment parameters.
refitted track(no geometry of the ladder to be aligned)
ACAT05, DESY, Zeuthen 14
Expression for internal alignment (X-measurement)
( )
321r
44444444 344444444 21 r
X
RRRTTT
a
zppzzppppDD
Z
Y
X
Z
Y
X
T
yxyxyxxx
⎟⎟⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜⎜⎜
⎝
⎛
⋅−⋅−=−′ 01
Ingredients for the χ2 minimization • the residual of the hit to the track with the starting geometry. • the hit position on the sensor and • the direction of the track at the intersection. av
D
x
z
∑∑ ⎟⎠⎞
⎜⎝⎛−==
= −
22
1
,
,
σσaDvaaM
vMXT r
rrr
rr
ACAT05, DESY, Zeuthen 15
Convergence after iterations
Iterations10 12 14 16
dof
/N2χ
0
1
2
3
4
5
Iterations10 12 14 16
m)
µ (
XT
-100
0
100
Iterations10 12 14 16
m)
µ (
YT
-100
0
100
Iterations10 12 14 16
m)
µ ( Z
T
-100
0
100
Iterations10 12 14 16
(m
rad)
XR
-2
-1
0
1
2
Iterations10 12 14 16
(m
rad)
YR
-0.1
-0.05
0
0.05
0.1
Iterations10 12 14 16
(m
rad)
ZR
-0.1
-0.05
0
0.05
0.1
trans
latio
nro
tatio
n
along X along Y along Z
around X around Y around Z
Improvement of χ2 after each iteration (single ladder).beforeafter
Good convergence after a few iterations.
< 5 µm< 0.1 mrad
Size of the alignment~< 100 µm~< 1 mrad
(Similar convergences seen for all ladders)
Computation time : ~10 hours on a single CPU (Intel XEON 2.4 GHz)
ACAT05, DESY, Zeuthen 16
m)µResidual (-200 -100 0 100 200
Ent
ries
0
10000
20000
r-z (before internal)
m)µ=121 (σ
m)µResidual (-200 -100 0 100 200
Ent
ries
0
10000
20000
30000 (before internal)φr-
m)µ=99 (σ
m)µResidual (-200 -100 0 100 200
Ent
ries
0
20000
40000
60000
r-z (after internal)
m)µ=47 (σ
m)µResidual (-200 -100 0 100 200
Ent
ries
0
20000
40000
(after internal)φr-
m)µ=62 (σ
Effect on residual distributions
Before internal alignment
After internal alignment
• Residual centered• Width became narrow
m 62m 47
µσµσ
φ ==
r
rz
ACAT05, DESY, Zeuthen 17
Residual offsets after alignemnt
• Residual offsets of centered around zero, within 10 µm.• Both r-z and r-φ directions.
Ladder number0 10 20 30
m)
µR
esid
ual o
ffse
t (
-40
-20
0
20
40 r-z
Ladder number0 10 20 30
m)
µR
esid
ual o
ffse
t (
-40
-20
0
20
40 φr-
ACAT05, DESY, Zeuthen 18
Effect on impact parameter resolution
(GeV)Tp2 4 6 8 10 12 14 16 18 20
D (
mm
)δ
0
0.02
0.04
0.06
0.08
0.1
0.12
T vs. pH D∆
0.097 (mm)⊕ TDesign: 0.223/p
0.053 (mm)⊕ TAligned: 0.151/p
T vs. pH D∆
Improvementσ(DH): 97 53 µm
x
y
ACAT05, DESY, Zeuthen 19
Summary & Conclusion
Alignment of the ZEUS barrel MVD using cosmic tracks.Local χ2 minimization with linear approximation.
Good convergence observed after a few iterations to < 5 μm.Alignment precision estimated from the residual offset <10 μm.
Impact parameter resolution : 100 μm 50 μm.
ACAT05, DESY, Zeuthen 20
Backup slides
ACAT05, DESY, Zeuthen 21
Residual offsets on individual sensors (after alignemnt)
• Residual offsets of centered around zero. (sensors with more than 50 hits)• Offsets more spread around zero than in the whole ladder .(σ~10 µm)
• Non-uniform distribution of hits in sensors. Some sensors not well constrained.• Residual mis-alignment of sensors in ladders.
r-z sensor number0 100 200 300
m)
µR
esid
ual o
ffse
t (
-200
-100
0
100
200r-z
sensor numberφr-0 100 200 300
m)
µR
esid
ual o
ffse
t (
-200
-100
0
100
200φr-
m)µResidual offset (-200 -100 0 100 200
Ent
ries
0
50
100
r-z
m)µResidual offset (-200 -100 0 100 200
Ent
ries
0
20
40
60 φr-
ACAT05, DESY, Zeuthen 22
Residual offsets on individual sensors (no alignemnt)
r-z sensor number0 100 200 300
m)
µR
esid
ual o
ffse
t (
-200
-100
0
100
200
r-z
sensor numberφr-0 100 200 300
m)
µR
esid
ual o
ffse
t (
-200
-100
0
100
200
φr-
m)µResidual offset (-200 -100 0 100 200
Ent
ries
0
5
10
r-z
m)µResidual offset (-200 -100 0 100 200
Ent
ries
0
5
10
15
20φr-
Before the internal alignment, residuals not centered at zero.Sensors scattered around within ±100 µm especially for r-z sensors.