Improvement of the muon reconstruction algorithm

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CDF/DOC/MUON/CDFR/9287
Draft 1.0
April 21, 2008

Improvement of the muon reconstruction algorithm in gen7 of the CDF software

Abstract:
In this note we describe an improvement of the muon reconstruction software for CMUP muons that has
been implemented in the gen7 frozen release. The change allows restoration of the tight cut CMU delta-X <
3 cm while preserving the same ID efficiency as the current CMU delta-X < 7 cm.

Contents:
Overview of CMU and CMP detectors
Limitations of the current algorithm
Muon reconstruction in gen7
Assumptions made
Results

Introduction

The muon detector
A muon detector at a hadron collider is a gas-ionizing tracking chamber that is located behind enough
interaction lengths of steel (usually in the form of the calorimeter) so that ideally only muons will be able to
reach the detector and leave a signal. A hit is detected by the sense wires of the muon chamber as the muon,
passing through, ionizes the gas. The ions then cascade down to the wire and a voltage signal is read out at
the associated electronics.

The CMU [Central Muon Detector] is the cylindrical muon detector lying directly outside the hadronic
calorimeter. Located at a radius of 347 cm from the beamline, it extends from =-0.65 to =0.65 and covers
a φ of 360 degrees with small gaps every 15 degrees corresponding to the cracks between the calorimeter
wedges.[1] It is divided into 24 wedges, following the geometry of the calorimeter. Each wedge has four
radial layers; each layer has 24 single-wire chambers filled with a mixture of 50% argon and 50% ethane.
The single sense wire in each chamber will record the passing of an ionizing track with a maximum drift
time of 800 ns; however, only the absolute value of the distance along the local x-coordinate can be
measured. The layers are stacked slightly offset from one another in order to use the stub reconstruction
algorithm [2] to differentiate between left and right hits, as shown in Figure 1.

1
x

Figure 1. The geometry of the CMU chambers.

For the sake of economy two adjacent chambers are linked by the same sense wire. A hit on this wire could
therefore be recorded on either chamber. The correct one is determined by charge division. The pulse
originating from the hit on the wire propagates along both directions until it reaches the electronics, namely
a shaper-discriminator circuit that produces a pulse with a width proportional to the incoming charge. Since
charge is inversely proportional to resistance, and resistance increases linearly with the length of the wire,
the readout electronics on either end of the ganged chambers will be able to discriminate between the pulses.
Those on the correct chamber will read a wider pulse signifying greater charge. See Figure 2 for a graphical
explanation of this.

Q1  Q2
zL
Q1  Q2

Figure 2. Charge division, a graphical representation.

The CMP [Central Muon Upgrade] is the rectangular muon detector lying outside the CMU behind an
additional 60 cm of steel. [1] Like the CMU, the CMP consists of four radial layers of single wire ionizing
chambers, although it is divided up differently due to its different geometry. These layers are also stacked
with an offset to avoid duplicate stubs from the left-right symmetry. There is no shared wire, hence no need
for charge division to determine the correct hit.

The muon chamber
The TDC [Time-to-Digital Converter] readout modules at either end of the individual CMU chambers
should be able to precisely distinguish the position of the hit along the sense wire. However, in between Run
I and Run II the re-calibration of this detector was poorly done and the precision of the z-coordinate
measurement dropped to ± 20 cm. [3]

2
The dimensions of a single CMU chamber are, in local coordinates, 6.3 cm in x by 2.7 cm in y by 226 cm in
z. Therefore, with the poorer z-coordinate calibration, a hit striking the last 20 cm of the chamber has a 50%
chance of being recorded about 6 cm, the width of a chamber, away from their true locations, which ends up
as around 5% of all hits. This problem did indeed surface in Run II and the Joint Physics group modified its
recommended muon cut on CMU delta-x from 3 cm to 7 cm to account for it. [4] The CMU delta-x is the
measure from the center of the muon stub to the muon track, extrapolated to the detector. We show in this
paper that it is possible to fix this problem and we recommend the restoration of the tight cut used in Run I
and for the analyses performed with the gen5 release.

Structure of the current CMU muon reconstruction code:
Muon reconstruction is done in three steps: hit finding, stub finding, and stub-track linking. [2] In the first
step, hits are recorded by the readout modules and the wider pulse from each pair of ganged chambers is
selected. In the second step, a stub is fit from at least three collinear hits in the four layers by minimization
of chi-squared. In the third step, a muon is reconstructed by matching the stub with the nearest track up to
30 cm away in local x-coordinate (the CMU delta-x variable), regardless of pT.
We worked within this structure to implement our upgrade.

Improvement of the reconstruction code:
The problem is of around 5% of hits being chosen incorrectly by hit-finding algorithm. So the first step is to
modify the hit finding algorithm in such a way that all hits are accepted. Each real hit will then have three
bogus copies of itself: a mirror image in the same chamber, a ghost hit in the neighboring chamber, and the
ghost hit of the mirror image. As a consequence, in the second step, the code will form duplicate—
“ghost”—stubs. The stub-forming step of the production algorithm was not modified.

Figure 4. Ghost stub in CMU

The third part of the code, the stub-track linking, will then match the actual muon track with the closest stub,
within the 30 cm cutoff, based on the sole quality variable of the CMU delta-X. By construction one
reconstructed muon will have the correct, tight stub-track matching in the CMU and the calibration problem
will be irrelevant. See Figure 5.

3
ganged! track

ganged! x
other stubs
y

Figure 5. Muon reconstruction code improvement in a nutshell.

Case consideration
However, the new algorithm, in forming a muon, will attempt to link every track reaching the muon detector
with every stub up to delta-X of 30 cm separation. Since there are more reconstructed stubs, there are more
possible stub-track combinations. A random track may fall within 30 cm of these duplicated stubs, in which
case a fake muon will be produced. To see how likely this was we investigated data in the raw stream
aphysr, consisting of events that triggered on J/psi -> two muon candidates, in run 186598 and period 0. Out
of 4955 events we found by comparison with gen6 code that a fake muon was produced in this way about
20% of the time. These fake muons must be removed.

Rejection Procedure
It is assumed that the new software is able to correctly identify and produce the true muon. Our input for the
fake rejection algorithm is the list of muons reconstructed with the new hit-finding algorithm. We then
identify the fake muons and remove them from the list of reconstructed muons.

To do this we first had to determine which stubs were duplicates, and then remove the muon made from
these stubs with the worse track-stub match. We begin our search for two stubs in the muon list falling in
the same wedge. Individual CMU chambers are ganged together only within the same wedge. Duplicate
stubs were identified by probing the electronic information of their constituent hits; stubs made out of two
or more identical hits are considered identical.

Arbitration between the two stub-track pairs is done using the likelihood ratio defined below:

f ( pT 1 , cmu _ dx1 )
L ,
f ( pT 2 , cmu _ dx2 )
where
2
1  cmu _ dx 
 1   2  
f ( pT , cmu _ dx)   e
 

 2 
and

4
2
 12 
    1
 pT 
The 12 GeV/c constant is an estimate of multiple scattering in the detector. [3] As the pT of the track
increases, the multiple scattering decreases, and therefore a high-pT muon is more constrained to have a
good stub-track match. The higher the track pT, of course, the straighter the track is.

Three categories of muons are treated separately: CMUP, CMU-only, and CMP-only muons. We assume
that a CMUP muon sharing its CMU stub with a CMU-only muon must be the real muon, as the particle has
made it through two separate muon detectors. Two CMUP muons sharing one CMU stub are arbitrated
between using the above formula; the CMU stub of the loser is removed and remains as a CMP-only. This
muon, being fiducial to the CMU, is likely to be excluded from any analysis.

The hit-finding algorithm is common to both CMU and CMP production. While the CMP detector does not
have ganged chambers, nonetheless noise pickup from neighboring chambers may create fake hits which
under the new algorithm lead to duplicate stubs in the CMP. Therefore it is necessary to remove fake CMP
muons as well. The algorithm employed is the same as described above.

Results:
Testing on the new code was primarily done on a J/psi->mumu raw data sample. Below is a plot showing
the improvement in a total sample of 37993 events (Figure 6).

Figure 6. Events in dataset with low calorimeter energy cut and pT > 10

5
There is a clear improvement in the delta-x variable: the shoulders decrease and the peak increases as the
track is matched to the true stub. The RMS of the old production is 4.032; the RMS of the new production is
2.684.

The CMP delta-x plot (Figure 7) does not show as significant an improvement in gen7 over gen6, with no
change in RMS; however, the gen7 shape is visibly superior. This slight improvement is a nice side-effect to
our improvement of CMU delta-x in gen7.

Figure 7. CMP delta-x for muons with CMU and CMP stubs, with low calorimeter energy.

Discussion
There are a number of other plots which we found interesting; most particularly, the plot of CMU delta-phi,
as shown in Figure 8. The delta-phi variable measures the relative angle between the track and the stub that
make up one muon.

Figure 8. Delta-phi of events with CMU stubs with low calorimeter energy and p T > 10; log plot on right.

6
Figure 9. CMU delta-x in lepton high-pT dataset with low calorimeter energy and pT > 10.

There are several curious bumps on either side of the central peak. We believe that these can be explained
by the geometry of the CMU. Since we do not take the delta-phi into account when we match stubs to
tracks, we make some allowance for the match to be a duplicate stub with a large delta-phi. The delta-x, you
recall, is measured from the center of the stub. When hits are duplicated, the adjacent stubs formed will have
the same angle as the real stubs; however, the abundance of hits allow for stubs with a good delta-x to be
formed at odd angles across the chambers, as in Figure 5. We believe these bumps are due to stubs formed
from hits in adjacent stacks, quantized by the number of stacks the stub is formed across.

In an effort to pin down the efficiency we also compared production between the old and new algorithms on
a high-pt lepton raw data sample. We continue to see the great improvement in CMU delta-x in this sample
(Figure 9). An attempt was made to reconstruct the Z using two high-pt muons in this sample and determine
the efficiency using one fully-identified muon and a second muon fully identified except for the CMU delta-
x variable (Figure 10). However, even in a sample of 143000 events we could not get enough statistics, and
running production takes a massive amount of time, disk space, and processing power.

7
Figure 10. N-1 two-muon events reconstructing Z; more statistics to produce a real efficiency measurement coming soon.

Instead, we can look at the N-1 plot of CMU delta-x for a single muon candidate (Figure 11), which shows a
clear increase in amplitude and narrowing of the peak, made clearer in the log plot. The RMS of the old
production is 1.981; the RMS of the new production is 1.125. The apparent asymmetry in the plot we
believe is a mere fluctuation.

Figure 11. Single N-1 muon events; log plot on right.

CMU dx cut: 8 cm 7 cm 6 cm 5 cm 4 cm 3 cm 2 cm 1 cm
Gen6 N-1 77 (100%) 77 (100%) 77 (100%) 77 (100%) 77 (100%) 77 (100%) 77 (100%) 65 (84%)
Gen7 N-1 77 (100%) 77 (100%) 77 (100%) 77 (100%) 77 (100%) 77 (100%) 77 (100%) 70 (91%)
Gen6 muon 4280 (100%) 4267 (99%) 4232 (98%) 4174 (97%) 4092 (95%) 4013 (93%) 3837 (89%) 3433 (80%)
Gen7 muon 4381 (100%) 4377 (100%) 4370 (100%) 4364 (100%) 4344 (99%) 4320 (99%) 4211 (98%) 3862 (88%)
Table 1. Events passing CMU dx cuts with efficiency measurement. Notice that a gen7 single muon with a 3 cm cut has the same
efficiency as a gen6 single muon with a 7 cm cut.

8
Based on these results we call for a change in the gen7 Joint Physics high-pT muon cut in CMU delta-x from
7 cm to 3 cm.

References:
1. CDF Technical Design Report, 1996.
2. CDF note 5870. Ken Bloom, Guide to Muon Reconstruction and Software for Run 2
3. Pasha Murat, private communication.
4. http://www-cdf.fnal.gov/internal/physics/joint_physics/instructions/muon_cuts_gen6.html