TPC sector alignment Marian Ivanov Outlook o o

TPC sector alignment Marian Ivanov

Outlook o o o Simulation Alignment algorithm – Inner outer sectors Results

Simulation o o o Stand alone simulator Ideal helix Pt range >0. 4 Ge. V n Exp(-x/0. 4) distribution Magnetic field 0. 5 T Tracks inside of one sector, inner and outer n o Pads and pad-rows and time bins inside chamber perfectly aligned Outer sector misaligned n Characterize by TGeo. HMatrix

Motivation o Why to use tracks in the magnetic field for the alignment? n Rotation and translation of the chambers can be affected by the presence of the magnetic field

Pt spectra and tracks

Simulation o Example results: n n n Misalignment matrix: . 999999 0. 000873 -0. 000698 -0. 000873 0. 000698 1. 000000 -0. 000174 0. 000175 1. 000000 Tx = -0. 2 Ty = 0. 2 Tz = 0. 2 Space charge effect and Ex. B switched off

Track fitting o Ali. Rieman (new standalone class) used for track fitting n o Less than 1 s for track fitting (20000 tracks) Picture: n Pt resolution for non aligned sectors 1/ptrec-1/pt

Alignment (0) Inner sector Outer sector

Alignment (1) o o o Separate track –fitting in inner and outer sector Parabolic track approximation at the middle reference plane in both chambers Minimization of the chi 2 distance between space point in reference plane of upper chamber and corresponding extrapolation of the inner track n TMinuit used

Alignment (2) o FCN=1257. 14 FROM MIGRAD STATUS=CONVERGED 132 CALLS 133 TOTAL EDM=2. 42528 e-12 STRATEGY= 1 ERROR MATRIX UNCERTAINTY 0. 0 per cent EXT PARAMETER STEP FIRST NO. NAME VALUE ERROR SIZE DERIVATIVE 1 2 3 4 5 6 rx ry rz sx sy sz 1. 07144 e-02 3. 95478 e-02 4. 82396 e-02 -1. 96256 e-01 2. 05511 e-01 1. 99985 e-01 8. 90503 e-04 1. 99467 e-03 5. 75040 e-03 4. 94420 e-03 1. 60506 e-02 5. 07757 e-03 1. 58139 e-05 6. 68023 e-06 9. 11108 e-06 4. 00290 e-05 2. 49723 e-05 2. 49634 e-05 -2. 35997 e-01 -2. 30862 e+01 1. 29964 e-01 -3. 84583 e+00 7. 85195 e-02 5. 15010 e+00

Alignment – Covariance matrix o o PARAMETER CORRELATION COEFFICIENTS NO. GLOBAL 1 2 3 4 5 6 1 0. 86752 1. 000 0. 018 -0. 192 -0. 025 0. 266 0. 014 2 0. 99573 0. 018 1. 000 0. 023 -0. 921 -0. 021 0. 971 3 0. 99896 -0. 192 0. 023 1. 000 -0. 005 -0. 996 0. 027 4 0. 97508 -0. 025 -0. 921 -0. 005 1. 000 0. 002 -0. 819 5 0. 99900 0. 266 -0. 021 -0. 996 0. 002 1. 000 -0. 025 6 0. 99065 0. 014 0. 971 0. 027 -0. 819 -0. 025 1. 000

Results (5000 tracks) o Original misalignment matrix - Amis n o matrix - tr=1 rot=1 refl=0 0. 999999 -0. 000873 0. 000698 0. 000873 1. 000000 -0. 000174 -0. 000698 0. 000175 1. 000000 Tx = -0. 2 Ty = 0. 2 Tz = 0. 2 Residual matrix – Afit. Inverse()*Amis n matrix - tr=1 rot=1 refl=0 1. 000000 -0. 000020 0. 000085 0. 000020 1. 000000 0. 000016 -0. 000085 -0. 000016 1. 000000 Tx = -0. 0121112 Ty = -0. 00518356 Tz = 0. 0116462

Results –Rotation Z o o Left side – 2000 track samples Right side – 5000 track samples

Results –Rotation Y o o Left side – 2000 track samples Right side – 5000 track samples

Results –Rotation X o o Left side – 2000 track samples Right side – 5000 track samples

Translation X o o Left side – 2000 track samples Right side – 5000 track samples

Translation Y o o Left side – 2000 track samples Right side – 5000 track samples

Translation Z o o Left side – 2000 track samples Right side – 5000 track samples

Result (Pt residuals)

Conclusion o Huge statistic needed to develop and validate alignment procedure n o First estimation made How to proceed? n n Use and develop stand alone simulator for calibration study? o 5000 tracks *100 samples =500000 tracks Or use Ali. Root framework to generate space points o Apply different systematic shift on the level of space points n Rotation, translation, Ex. B, space charge (parameterization needed)