SVT Alignment

1
SVT Alignment

• Marcelo G. Munhoz
• Universidade de São Paulo

2
Introduction

• We seek for 6 parameters that must be adjusted in
  order to have the SVT aligned to the TPC
• x shift
• y shift
• z shift
• xy rotation
• xz rotation
• yz rotation

3
Basic question

• How to disentangle and extract them without
  ambiguity from the data?
• Many approaches are possible. We are using two of
  them...

4
Approaches

• First approach
• calculate the residuals between the projections
  of TPC tracks and the closest SVT hit in a
  particular wafer
• Advantage
• can be done immediately after some TPC
  calibration is ready, even without B0 data
• Disadvantage
• highly dependent on TPC calibration
• the width of these residuals distributions and
  therefore the precision of the procedure is
  determined by the projection resolution.

5
Approaches

• Second approach
• use only SVT hits in order to perform a
  self-alignment of the detector
• Advantage
• a better precision can be achieved
• does not depend on TPC calibration
• Disadvantage
• it is harder to disentangle the various degrees
  of freedom of the detector (need to use primary
  vertex as an external reference)
• depends on B0 data (can take longer to get
  started).

6
First approach TPC tracks projection (B ? 0)

• Try to disentangle the 6 correction parameters in
  2 classes
• x shift, y shift and xy rotation
• z shift, xz rotation and yz rotation.
• They are not completely disentangled, but it
  works as a first approximation...

7
First approach TPC tracks projection (B ? 0)

• Make the alignment in steps
• 1 - global alignment, i.e., one set of parameters
  for the whole detector
• 2 - ladder by ladder alignment, i.e., a set of
  parameters for each ladder
• 3 - wafer by wafer alignment, i.e., a set of
  parameters for each wafer.

8
Global parameters x shift, y shift and xy
rotation

• Look at residuals from the SVT drift direction
  (global x-y plane)
• Study them as a function of
• x shift (?x), y shift (?y) and xy rotation (??)
  should show up, approximately, as

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Global parameters x shift, y shift and xy
rotation

• The equation
• is just an approximation because
• tracks are not straight lines
• a xz rotation, for instance, can change the
  parameter ?x as a function of z
• miscalibration of the detector (t0 and drift
  velocity) also changes the residuals
  distribution.
• But overall, the method is a very good starting
  point...

10
First look, no correction
?x -1.9 mm ?y 0.36 mm ?? -0.017 rad
Matches well the survey data
11
After first correction (only ?x)
?x -0.72 mm ?y 0.25 mm ?? -0.019 rad
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After second correction (?y and ?? included)
?x -0.25 mm ?y 0.10 mm ?? -0.0018 rad
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Global parameters z shift, xz rotation, yz
rotation

• Look at residuals from the SVT anode direction
  (global z direction)
• Choose tracks that have dip angle close to zero (
  tracks parallel to the xy plane)
• Study them as a function of z
• The parameters should show up as deviations from
  a flat distribution centered at zero.

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First look, no correction only ladders at xz
plane
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First look, no correction only ladders at yz
plane
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Conclusion - I

• Global alignment for x and y shifts and xy
  rotation is done
• Z shift and xz and yz rotations can be worked
  out
• Moved to next step (ladder alignment) of x and y
  shifts since it involves some calibration issues
  as well.

17
First approach TPC tracks projection (B ? 0)

• Make the alignment in steps
• 1 - global alignment, i.e., one set of parameters
  for the whole detector
• 2 - ladder by ladder alignment, i.e., a set of
  parameters for each ladder
• 3 - wafer by wafer alignment, i.e., a set of
  parameters for each wafer.

18
Ladder parameters x shift, y shift and xy
rotation

• Look at residuals from the SVT drift direction
  (global x-y plane)
• Study them as a function of drift distance
  (xlocal) for each wafer
• In this case, influence of miscalibration (t0 and
  drift velocity) cannot be neglected.

19
Ladder parameters x shift, y shift and xy
rotation

• Once more, x shift (?x), y shift (?y) and xy
  rotation (??) should show up, approximately, as

20
Ladder parameters x shift, y shift and xy
rotation

• But, we must add the effect of an eventual
  miscalibration,
• where v is the correct drift velocity and t0
  is the correct time zero.

0, if t0 is Ok

• These two equations can be used to fit the
  residuals distribution fixing the same
  geometrical parameters for all wafers.

21
First look ladder by ladder after global
corrections
?x -0.81 mm ?y 0.56 mm
22
After first correction (only ?x and ?y)
?x -0.19 mm ?y 0.024 mm
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Conclusion - II

• Need to go ladder by ladder (36 total) checking
  the correction numbers and the effect of them on
  the residuals
• Next step is to fit each wafer separately
• Still need to consider the rotation degree of
  freedom.

24
First approach TPC tracks projection (B ? 0)

• Make the alignment in steps
• 1 - global alignment, i.e., one set of parameters
  for the whole detector
• 2 - ladder by ladder alignment, i.e., a set of
  parameters for each ladder
• 3 - wafer by wafer alignment, i.e., a set of
  parameters for each wafer.

25
Wafer parameters x shift, y shift
26
First approach TPC tracks projection (B0)

• The exactly same method can be applied to the B0
  data
• It should give better results with the straight
  tracks
• That can be done as soon as we have the data
  processed.

27
Second approach SVT hits only (B 0)

• Associate two angles to each hit
• where x0 , y0 and z0 are the coordinates of the
  primary vertex

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Second approach SVT hits only (B 0)

• Using the TPCSVT tracking, identify the 3 hits
  belonging to a track
• In order to study x and y shifts and xy
  rotations, calculate the distributions of
• ??12(?1 , z) ?1 - ?2 as a function of ?1, for
  each z slice and ?1 ? 0
• ??13(?1 , z) ?1 - ?3 as a function of ?1, for
  each z slice and ?1 ? 0

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Second approach SVT hits only (B 0)

• These distributions can be fit with similar
  equations as the first approach in order to get
  the alignment parameters
• We will get corrections as a function o z, that
  can bring information about xz and yz rotations
• ?x(z) z ?tan(?xz )
• ?y(z) z ?tan(?yz )

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Second approach SVT hits only (B 0)

• In order to study z shift, xz and yz rotations,
  calculate the distributions of
• ??12(?1 , ?1) ?1 - ?2 as a function of ?1
  for each ?1
• ??13(?1 , ?1) ?1 - ?3 as a function of ?1 for
  each ?1
• These distributions can be treated as the
  residuals in the anode direction.

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Near future perspectives

• Finalize first approach
• calculate ?x, ?y, and ?? ladder by ladder
• extend it to wafer by wafer making small
  corrections if necessary
• calculate z shift, xz rotation and yz rotation
  (global, ladder by ladder and wafer by wafer -
  they should be small)
• use B0 data.
• Start second approach once B0 data is ready.

32
Near future perspectives

• It is a lot of work, but it depends mostly on man
  power. Software is ready
• The whole procedure does not depend on many
  iterations of the reconstruction chain.
  Corrections can be applied and tested without
  reconstruction (although final tests need that).