TPOL Test Beam Telescope

1. TPOL Test Beam Telescope Chris Collins-Tooth (ZEUS, IC-London)

2. Outline • Test Beam setup of the Telescope and TPOL • What is the Telescope and what does it do? • What data was gathered? • Analysis of the data • Multiple Coulomb Scattering, Beam spread, and Telescope resolution • Relative rotations • between parts of the Telescope • between the Telescope and the TPOL silicon • What can be done about these factors? • What does this tell us about the TPOL silicon? • TPOL silicon resolution • TPOL silicon efficiency • Summary

3. Test Beam setup TPOL • 6 GeV e- beam enters from left • e- beam passes through Telescope then moves into the TPOL • Telescope mounted as close to TPOL as possible on movable table • Telescope has 3 position sensitive detectors T1,T2 and T3 (Td was ‘dead’ material being used for a second experiment) Telescope

4. 60 The Telescope P(%) 50 40 30 • Previously, degree of polarisation estimated using energy asymmetry in calorimeter (Calorimeter resolution ~1000 m) • Now measure polarisation using 80 m pitch Si • Something more accurate needed to probe TPOL silicon resolution - the Telescope. • 3 planes of 50 m pitch Si, with horizontal and vertical strips. • T1,T2,T3 detectors roughly 3cm × 3cm (TPOL silicon ~1 cm2) 20 10 0 -10 t(min)

5. The data • T1,T2,T3 used to predict Si strip to fire. • As expected, fitted line has slope =1  0.01 • Offset simply due to T1,2,3 being physically larger than TPOL Silicon • Width of data about fitted line gives indication of TPOL resolution

6. The width • Width =132.15 ± 2.93 m • TPOL Silicon strip pitch =80 m • Intrinsic resolution ~80/12 m -800 -400 0 0 400 800

7. Analysis of the data • Observed width does not relate directly to the TPOL resolution • Multiple Coulomb Scattering (MCS) of e- beam at T1,Td,T2,T3 and TPOL Aluminium Box • Finite resolution of the Telescope • e- beam not 100% collimated • Misalignments of the Telescope detectors T1,T2,T3 • Misalignments of the Telescope (as a whole) and the TPOL

8. Telescope internal misalignment • T1,T2 and T3 could all be misaligned with respect to each other. • Rotations would produce systematic shifts of ‘predicted minus actual’ strip firing from left-to-right • Most important are rotations about beam-axis (pictured). A 0.08o rotation would cause a shift of 1 strip across breadth of detector

9. ‘Predicted minus Actual’ shifts for T3,T2 and T1 from LR T3 T2 T1 • Using T1,T2 to predict T3 (left) we observe a shift from left to right of approximately 50 microns

10. Correction of misalignment • Iterative process invoked • Rotating T3 by 0.27o flattened off all the plots (to within errors)

11. TPOL misalignment • The TPOL silicon had no vertical strips • Track through T1,T2,T3 used to predict vertical strip to fire to give indication of horizontal position of impact • No discernable shift observed before or after T3 rotation applied • Correction for rotations caused no discernable reduction in observed ‘width’

12. MCS, Telescope resolution and beam collimation • Simple Monte-Carlo simulation using PDG formula for MCS with gaussian width: s=(13.6MeV/cp) (x/Xo) (1+0.038 n [x/ Xo]) • Telescope resolution and beam collimation are small factors in comparison to MCS • Together, all these factors contribute ~102 m to the width • Subtracting in quadrature, the TPOL resolution obtained is (1322-1022) 83 m • But - MCS is not actually gaussian • Attempting to use GEANT to improve estimate

13. Error propagation T1 Td T2 T3 Al T4 (TPOL) m3 • Alternative approach to Monte-Carlo • Use errors introduced by MCS etc., and propagate them to the TPOL silicon • T4=T3+Z4m3+Z43+(Z4-ZAl)Al • Var(T4)=Var(T3)+Z42Var(m3)+Z42Var(3)+(Z4-ZAl)2Var(Al)+Z4Cov(T3,m3) • T3=T1-Z1m3-Zdd-Z22 • Var(m3)=(1/Z12)(T1-T3-Zdd-Z22) • Variances are calculated, (e.g. Var(T1,T2,T3)=2T1,T2,T3 =208 m) • T4=[Var(T4)]=120 m= Error on TPOL Si due to uncertainties in Telescope • Resolution of TPOL Si = [1322-1202]=55m m3 m3+3 +z

14. TPOL Resolution • From Monte-Carlo Simulation we obtain RTPOL 83 m • From Error Propagation we obtain RTPOL 55 m

15. TPOL Silicon Efficiency Ratio of hits NOT registering in TPOL • Telescope used to predict TPOL events • Efficiency is the ratio of: events with TPOL Silicon signal events predicted by Telescope • TPOL Silicon edges found by looking at ratio of hits not registering in the TPOL as a function of position • Log plot reveals edges where Telescope predicts TPOL hits but TPOL does not register • Horizontal edges at 13000 & 20000 m • Vertical edges at 11000 & 18000 m • Consistent with active area of Silicon Horizontal Position (m) Vertical Position (m)

16. Efficiency cuts • Using the edges from previous slide, we must remove predicted events from efficiency calculations where they miss the boundaries of the TPOL Si • Figures show • events predicted by the Telescope and registered by the TPOL (black) • For effect, events in red are added. They are predicted events which had no TPOL response, but the event was inside the opposite direction boundary, and so should have registered. • Clearly, the boundaries look correct.

17. Final Efficiency • With the positional cuts made, the efficiency of the TPOL silicon can be calculated • This is the ratio of : events with a TPOL silicon response all predicted events inside the boundary • The efficiency is uniform across the detector, at ~97.8%

18. Summary • Misalignments, Coulomb Scattering and other factors contribute significantly to observed width of 132 m. • TPOL Silicon resolution TBA but preliminary studies suggest 55 and 83 m • TPOL Silicon efficiency uniform at 97.8%