# Presentation: 082750

## SVT Alignment

*Marcelo G. Munhoz*
*Universidade de São Paulo*

## 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

## Basic question:

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

## 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 B=0 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.

## 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 B=0 data (can take longer to get started).

## 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...

## 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.

## 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:

## 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...

## First look, no correction:

- *x =* *-1.9 mm*
- *y = 0.36 mm*
-  *= -0.017 rad*

- Matches well the survey data

## After first correction (only x):

- *x =* *-0.72 mm*
- *y = 0.25 mm*
-  *= -0.019 rad*

## After second correction: (y and  included)

- *x =* *-0.25 mm*
- *y = 0.10 mm*
-  *= -0.0018 rad*

## 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.

## First look, no correction: only ladders at xz plane

## First look, no correction: only ladders at yz plane

## 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.

## 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.

## 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 (*x**local*) for each wafer;
- In this case, influence of miscalibration (*t**0* and drift velocity) cannot be neglected.

## 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:

## Ladder parameters: x shift, y shift and xy rotation

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

- 0, if t0 is Ok

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

## First look ladder by ladder after global  corrections:

- *x =* *-0.81 mm*
- *y = 0.56 mm*

## After first correction (only x and y):

- *x =* *-0.19 mm*
- *y = 0.024 mm*

## 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.

## 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.**

## Wafer parameters: x shift, y shift

## First approach: TPC tracks projection (B=0)

- The exactly same method can be applied to the B=0 data;
- It should give better results with the straight tracks;
- That can be done as soon as we have the data processed.

## Second approach: SVT hits only (B = 0)

- Associate two angles to each hit:
- 	where *x**0** , y**0 *and *z**0* are the coordinates of the primary vertex

## Second approach: SVT hits only (B = 0)

- Using the TPC+SVT 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;

## 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** ) *

## 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.

## 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 B=0 data.
- Start second approach once B=0 data is ready.

## 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).