svt alignment

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:

tan 1 y x

res x ydrift sin cos

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.

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.

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:

res x x y xdrift local local sin cos

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.

res xv

vx L v t t Ldrift local local

0 0

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.

Wafer parameters: x shift, y shift

wafer x (m) y (m)1 -190 1512 -62 673 -34 834 -92 58

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 x0 , y0 and z0 are the coordinates of the primary vertex

tan 1 0

0

y yx x

tan 1 0

0

2

0

2

z z

x x y y

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).

svt alignment

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