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 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.

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 B=0 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:

9. 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

12. After second correction: (y and  included) x =-0.25 mm y = 0.10 mm  = -0.0018 rad

13. 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.

14. First look, no correction: only ladders at xz plane

15. First look, no correction: only ladders at yz plane

16. 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. • These two equations can be used to fit the “residuals” distribution fixing the same geometrical parameters for all wafers. 0, if t0 is Ok

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

23. 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 (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.

27. Second approach: SVT hits only (B = 0) • Associate two angles to each hit: where x0 , y0 and z0are the coordinates of the primary vertex

28. 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;

29. 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 )

30. 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.

31. 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.

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).