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  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.
3
Scattering
rms =
q
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
Scattering
rms =
q
0
0
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.
185
260
700
1000
1200
1400
1600
1800
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.
1.
2.
3.
4.
5.
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