Measuring momentum at the TIF

1. Measuring momentum at the TIF David Stuart, UC Santa Barbara June 25, 2007

2. Measure momentum from multiple coulomb scattering (MCS). In a B-field we use the sagitta: s  qBL2/pT Large BL2 maximizes sensitivity between s and pT. Similarly multiple scattering is: rms q √x/X0 /pT Large √x/X0 maximizes sensitivity between rms and pT. That is nomally not a good thing, but maybe we can learn something by using it in TIF data. We cannot measure momentum track by track, since rms is statistical. But we can check the momentum spectrum…and in fact this is really just for fun; a goal to head toward just to make a journey. Overview

3. q rms = Scattering Approximating each layer as x/X0 = 2.5%, gives rms = 1.9 mrad. So at p = 1 GeV/c, the MCS = 19 m per cm of projection.

4. q rms = 0 0 185 260 700 1000 1200 1400 1600 1800 Scattering Approximating each layer as x/X0 = 2.5%, gives rms = 1.9 mrad. So at p = 1 GeV/c, the MCS = 19 m per cm of projection. Since scattering in the outer layers has a large lever arm to the inner layers, it grows. Subsequent layers are added in quadruture to get the numbers listed. (For p = 1 GeV/c, approximating layer spacing as 5 and 10 cm and material uniform at 2.5% per layer). So, the scattering uncertainty remains above the resolution of the bottom layer until at least p>20 GeV. (Of course, the situation differs in collisions, e.g., opposite direction, higher p).

5. Method • General approach: • Measure P(2). • Events are simple, so non-flat component is due to scattering. • Float momentum until P(2) is flat. • Details: (Since my processing is non-standard. Define it here.) • Measure pedestals and noise and flag bad channels. • Do clustering and write clusters to ascii files. • Read cluster files on my mac and apply geometry • (reverse engineered from TIF ntuples). • Do tracking • Simple combinatoric seed finder with road search hit matching. • R- and R-Z done separately, ignore stereo hits. • Save seeds so subsequent analysis requires only a refit. • (Refit takes 0.5 ms/evt v.s. 13 ms/evt for patt. rec.)

6. Residuals Raw residuals are large. Alignment required since we want to see O(100 m) effects. Run 6215. Show one “middle layer” from each to minimize effect of pointing uncertainty. Offsets of a few hundred microns. Resolutions of about 150 and 300m.

7. Alignment • Measure alignment corrections with a crude, brute force approach: • vary alignment offsets until global 2 minimized. • Adjust TOB internals with TIB de-weighted. • Adjust TIB global offsets • Adjust TIB internals. • Adjust TIB+TOB internals. • Repeat last step a few times with resolutions and 2 cut reduced as procedure converges. • This is not fast, elegant or precise, but it gives enough improvement.

8. Residuals after alignment Run 6217, different to avoid bias. Offsets of ~20 m and widths of about 60 and 180m.

9. Resolution • To get a meaningful 2 distribution, I need to use the correct resolutions. • The residual width contains a contribution from pointing uncertainty. Assuming that all layers within one sub-detector have the same resolution, this is easy to subtract to get: • TOB = 50 m and TIB= 150 m • While the TOB number is reasonably close to the intrinsic resolution, I’m obviously doing something wrong with TIB. I don’t understand what yet. It may just take more iterations or allowing global x and y rotations. • Some specific layers are worse: • The “fringe layers” are be poorly constrained. Use TOB=100 and TIB=200 for them. • There is one TIB layer that has 500 m residuals, which I don’t understand. Use 500. • Tracks are refit with these specific resolutions.

10. 2 probability With these resolutions, the 2 probability is reasonably flat at the high end. guide line

11. Sample events To verify that these are not confused tracks, scan some selected on P(2)<1E-5

12. Sample events Scattering evident when zooming into a track. Recall, 1 GeV is O (0.1cm) on inner layer.

13. MCS Momentum 2/dof <1 regardless of MCS

14. Check sensitivity to assumed x/X0 2.0% 2.5% 3.0% Not too sensitive except at very low momentum.

15. Check sensitivity to resolution Smear hits but don’t compensate with the residuals. Matters if way off. *2.5 Nominal *sqrt(2)

16. Compare to Simulation Marco DeMattia and Patrizia Azzi helped me get some cosmic simulation. Compare directly to the muon momentum. I scale the simulation to crudely match (not by number of events). I should process the simulated data identically to the real data. Later. The agreement is surprisingly good. But, there is a discrepancy at low momentum.

17. Compare to Simulation Marco DeMattia and Patrizia Azzi helped me get some cosmic simulation. Compare directly to the muon momentum. I scale the simulation to crudely match (not by number of events). I should process the simulated data identically to the real data. Later. The agreement is surprisingly good. But, there is a discrepancy at low momentum. This is run 6502. Was the lead present then?

18. Recent data I couldn’t figure out when the lead was installed. So, I tried comparing to a recent run: Run 11909-11914, which is a huge run from this weekend. Run 6502 Run 11909 More low p. Larger resolution?

19. Recent data I couldn’t figure out when the lead was installed. So, I tried comparing to a recent run: Run 11909-11914, which is a huge run from this weekend. Run 6502 Run 11909 More low p. Larger resolution? Alignment change?

20. Summary • I played around with extracting the momentum spectrum using scattering. • Played = fun, and maybe useful. • It agrees fairly well with simulation, better than I expected. • There is an excess at low momentum. Resolution modeling? • Possible things to do: • I’d like to learn what the proper TIB alignment is. • I’d like to look as a function of run number. • Look at additional tracks to understand trigger bias. Rainbow Rain