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

2 Overview Measure momentum from multiple coulomb scattering (MCS). In a B-field we use the sagitta: s  qBL 2 /p T Large BL 2 maximizes sensitivity between s and p T. Similarly multiple scattering is:  rms  q √x/X 0 /p T Large √x/X 0 maximizes sensitivity between  rms and p T. 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.

3 Scattering  rms = q Approximating each layer as x/X 0 = 2.5%, gives  rms = 1.9 mrad. So at p = 1 GeV/c, the  MCS = 19  m per cm of projection.

4 Scattering  rms = q Approximating each layer as x/X 0 = 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 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. 1.Adjust TOB internals with TIB de-weighted. 2.Adjust TIB global offsets 3.Adjust TIB internals. 4.Adjust TIB+TOB internals. 5.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/X 0 2.0% 2.5% 3.0% Not too sensitive except at very low momentum.

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

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 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 , which is a huge run from this weekend. Run 6502 Run 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 , which is a huge run from this weekend. Run 6502 Run 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