Measuring momentumat the TIF

David Stuart,

UC Santa Barbara

June 25, 2007

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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.

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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.

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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.

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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 theresolution of the bottom layer until at least p>20 GeV.

(Of course, the situation differs in collisions, e.g., opposite direction, higher p).

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MethodGeneral 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.)

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ResidualsRaw 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.

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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 offsets3. 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.

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Residuals after alignment

Run 6217, different to avoid bias. Offsets of ~20 m and widths of about 60 and 180 m.

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ResolutionTo 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.

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2 probabilityWith these resolutions, the 2 probability is reasonably flat at the high end.

guideline

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Sample eventsTo verify that these are not confused tracks, scan some selected on P(2)<1E-5

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Sample eventsScattering evident when zooming into a track.

Recall, 1 GeV is O (0.1cm) on inner layer.

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MCS Momentum

2/dof <1 regardlessof MCS

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Check sensitivity to assumed x/X0

2.0%2.5%3.0%

Not too sensitive except at very low momentum.

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Check sensitivity to resolution

*2.5Nominal*sqrt(2)

Smear hits but don’t compensate with the residuals. Matters if way off.

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Compare to Simulation

Marco DeMattia and Patrizia Azzihelped 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.

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Compare to Simulation

Marco DeMattia and Patrizia Azzihelped 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?

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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 6502Run 11909

More low p. Larger resolution?

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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 6502Run 11909

More low p. Larger resolution? Alignment change?

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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