Central Track Matching of muon tracks at Level 3
Paul Balm ( p.balm@nikhef.nl ), April 2001
Introduction
This document describes a tool for the Level 3 trigger, that attempts to match tracks found in the muon system, with tracks in the central tracker. These central tracks may either be found in the CFT only, or they may be found by using the information from both CFT and SMT. The implementation as it is described is the implementation first available in release of the D0RunII software version t01.42.00.
Goals
When this note mentions “muon tracks”, or “tracks found in the muon system”, those track are meant that have been found using information from the muon system only. Track reconstruction in the muon system only can be done reasonably fast, and in a well-understood way, since no information from other subdetectors is used. However, the best pT resolution that can be theoretically be attained with the muon system stand-alone is of the order of 15-20%. Current software imperfections make the current pT resolution about 35% (software version t01.39.00).
The primary objective of the central track matching tool, is to improve on the pT resolution of tracks found in the muon system, by matching them to tracks found in the central tracker. The central tracker a relative resolution on 1/ pT of ~0.5%. For a 10 GeV track, this yields a resolution on pT of 5%, which is superior to the muon system. Therefore, when a muon track can be matched to a central track, its pT resolution can be improved by taking the pT measurement from the central tracker.
Secondary objectives are for the muon system to obtain a usable vertex resolution. The central tracking software will benefit from reduced running time, because tracks do not have to be reconstructed in the entire tracker, if muons need to be found. That is because the muon was found in the muon system constrains the region in the central tracker, where the central part of the muon track has to be. Also, the possibility is created to tag central tracks as muons.
Algorithm
Currently, the implemented algorithm is as follows:
1) Find all tracks by using the muon system only
2) For all found muon tracks:
a) Predict region in the central tracker where the central track should be found
b) Find central tracks in that region
c) For all found central tracks, calculate c2 of the match
3) Match muon track with one of the central tracks
Finding muon tracks and tracks in the central tracker is done by tools external to the central track matching tools. The steps that are performed by the central track matching tool, 2a, 2c and 3, are described in the sections below.
Predicting the region
The
reason for predicting a region in the central tracker and reconstructing only
that part of the tracker, is to minimize the time it takes to do the
reconstruction. Consequently, the variables used to define the region are aimed
at minimizing that time.
The first restriction on the region in the central tracker is that the track should exit the CFT through a ‘curved square’ on the outer surface of the CFT (see illustration). The curved squared is given by a phi range and a z range. In addition to these conditions, the central tracks are required to have a polar angle in a given range. Finally, the z-coordinate of the vertex of the central tracks is restricted to what is maximally allowed by the z-range of the curved square and the restrictions on the slope. That means the lower end of the z-range of the vertex is calculated by taking the lower bound on z of the curved square and the highest allowed slope, and the higher end of the z-range is calculated by taking the highest bound on z of the curved squared and the lowest slope.
The muon reconstruction of the track in the muon system
gives a position of the track in the A-layer, and j and
q of the track, plus errors on these
quantities. We estimate the multiple scattering in the calorimeter by 
(in [cm], at 4s),
where pT is the transverse momentum measured by the muon
system. To calculate the region in which the central track is expected within
at least 3s, we use 3s on the errors given by the muon
reconstruction and 4s on the multiple
scattering, because the multiple scattering does not have Gaussian tails.
A variable that can further reduce the running time of the central track reconstruction, is the minimum pT of the central track. This has as of yet not been implemented, because it was feared too much efficiency would be lost, due to the poor accuracy of the muon system measurement of pT. Recently, improvements in the muon reconstruction have been made, so it is likely that this cut will be implemented in the near future.
Calculating the quality of matches
Once the region has been predicted and the central tracks in that region have been found, for each central track that was found, it has to be determined how good the central track matches with the muon track. Therefore, each central track is being extrapolated from its distance of closest approach to the beamline, first to the outer radius of the CFT. This is done using the helix parameters provided by the central track reconstruction. From there on, the central track is extrapolated to the A-layer of the muon system as a straight line, ignoring the 0.2 T return field of the solenoid in the calorimeter.
For the comparison to the muon track, first we look at the j and q of
the extrapolated central track and the muon track at the A-layer and calculate
the difference in these variables. We also compute a variable we call ddrift, which is the distance between the extrapolation
and the muon track, in the plane of the wires of the A-layer muon chambers,
perpendicular to the wires. In the central muon system this will be along the z-direction,
in the forward muon system in the x- or y-direction, depending on
the octant. This is a variable in which the muon system is expected to attain a
resolution of the order 1 mm, dominated by alignment of the chambers. Note
that the direction in which this distance is measured, is dependent on the
octant. Finally we use these variable to calculate a c2 of the match. We do this by taking into account the three variables
that have been described, and divide by the number of degrees of freedom, which
is 3.
It should be noted that we are not yet using the momentum in comparing central tracks with muon tracks. The reason for this is that at the moment of implementation, the pT measurement of the muon system was deemed to unreliable. It is expected this will be added to the calculation of c2 in the near future.
Making the match
In the current implementation, a muon track is matched with
the central track found in the predicted region, that yields the lowest c2.
It has to be
investigated whether this is always the best choice. When many tracks are found
in the region, the chance of matching the muon track to a central track that
wasn’t generated by the same particle increases. When mismatches like this
occur, non-Gaussian tails will be introduced to the pT
resolution plots.
The primary objective of central track matching is to improve the pT resolution of the muon system. It may be, that when the number of central tracks found in the region is high, the pT resolution will no longer be improved by matching the muon track with one of the central tracks. This has yet to be investigated.
Results
Currently, only results from a single muon file with on average 1.1 minimum bias events are available. The plots in this paragraph show the variables described in the section “Calculating the quality of matches”:
- “delta phi” and “delta theta” are the difference in the j and q direction between the extropaloted central track and the muon track
- the meaning of “delta drift” can also be found in the section mentiond above.
- the c2 plot shows the combination of these values, taking into account a theoretical error
The number of entries in the plots is the total number of
candidates for a match, which is equivalent to the number of tracks found in
the muon system. This means not necessarily only one candidate per event, since
the muon reconstruction finds 2 tracks in the muon system in approximately 85
events. There are also some events where 3 or even 4 tracks were found. The
plots have been generated using 1000 single muon events.
The number of underflows in the c2 plot is the number of tracks in the muon system that could not be matched. That means there were no central tracks found in the region predicted in the central tracker. This generally means the muon track was reconstructed poorly, and in some cases it means the central track was not reconstructed.
The fact that the
average of the c2 plot is well below 1, means that the errors
in real life are smaller than the theoretical errors as they were estimated to
calculate the c2.
The average running time of the tool is 2.9 ms/event on d0mino, when compiled against the optimized version of the D0RunII software, version t01.41.00. This excludes the central track finding, and muon tracking and the other tools that need to be run, namely the SMT, CFT and muon unpacking. Also, further improvements in speed have been made, that haven’t been included in this measurement.
Simulated central tracks
The plots below are made with “simulated central tracks”. These are central tracks, where the helix parameters are calculated from MC information. These helix parameters are considered exact, even though the MC track is not a perfect helix due to multiple scattering within the central tracker. The reconstruction efficiency of these tracks is 100%.
Central track reconstructed with CFT information only
The plots below are made with central tracks produced by a central tracking tool called L3TCFTTracker, which has been written by Raymond Beuselinck and uses CFT information only.
Central tracks reconstructed with CFT and SMT information
The plots below have been made using central tracks produced by a central tracking tool called L3TGlobalTrack, which has been written by Daniel Whiteson. It uses information from the SMT and the CFT and is described in D0 note 3808.
Conclusions
The ‘mechanics’ of the central track matching tool (prediction of the region, invoking central track finding in the predicted region, matching the central tracks) are working, as has been demonstrated using single muon events. It has yet to be investigated what the impact on the pT resolution is, especially when the tool is run on events that are more complex than single muon events. It may also be investigated what the effect is of ignoring the solenoid return field in the calorimeter, when central tracks are extrapolated from the CFT outer radius to the muon A-layer.
The plots showing ‘delta phi’ are dominated by multiple scattering and the j resolution of the muon system. Relative to these quantities, the j measurement from the central tracker is exact. This is proven by the fact that the width of the plots made with MC central tracks is identical to those made with reconstructed central tracks. If the measurement of the j of the central track were poor, the width of the ‘delta phi’ plot would have been larger for reconstructed central tracks.
The width of the ‘delta theta’ and ‘delta drift’ plots have contributions from multiple scattering and the resolution of the muon system on one hand, and the resolution of the central tracker in these variables on the other. The scale of these contributions must be comparable, since the width of the plots grows by a factor of the order of magnitude of sqrt(2), when we compare MC central tracks to reconstructed central tracks.