CombinatorialTrackFinder

A Gaudi algorithm for Key4hep that finds tracks in the planar hits of one tracking system (an inner tracker, a silicon wrapper, a muon system, ...) without using any other detector. It is built for displaced tracks, for example from long-lived particle decays, so it never assumes that a track comes from the interaction point. The detector, field and cuts are set in the steering file.

How it works

1. The hits are grouped by layer (barrel and endcap layers, from the cellID).
2. Track candidates are found with one of two strategies (Strategy):
   • Exhaustive: every combination of k hits on k different layers is fitted (a circle in xy, a line of z versus arc length). Good for sparse events.
   • SeedAndExtend: seeds of 3 to 5 hits on neighbouring layers are extended layer by layer along their helix. Good for dense events. With SeedAndExtendMode = BestFirst, the best seeds go first, take their hits and are judged with a kink χ² that includes multiple scattering.
3. Road, outlier and quality cuts remove wrong combinations. The best candidate becomes a track, its hits are removed, and the search repeats.
4. Each track stores its fitted helix as EDM4hep track states (below). A GenFit fit can be added (UseGenFit).

Track states

Location	What it is	When
AtFirstHit	the fitted helix at the innermost hit (referencePoint = that hit)	always
AtLastHit	the same helix at the outermost hit	StoreLastHitState = true (default)
AtIP	the track at its closest approach to the origin	IPStateMode (below)
AtOther	GenFit fit at the first hit	UseGenFit = true

All states follow the EDM4hep convention: the five parameters are relative to the referencePoint, the track moves outward, and omega > 0 means clockwise seen from +z.

IPStateMode says whether, and how, an AtIP state is made. The track is never forced to come from the IP. The state only describes it at the point closest to the origin.

IPStateMode	Use
None (default)	no AtIP state
Helix	the same helix at its closest approach to the origin. For tracks in a uniform field (inner trackers).
SolenoidCrossing	the helix is followed back to the solenoid boundary and matched there to a helix in the inner field. For tracks measured outside the solenoid (muon system).

Build

source /cvmfs/sw-nightlies.hsf.org/key4hep/setup.sh
cmake -S . -B build -DCMAKE_INSTALL_PREFIX=$PWD/install
cmake --build build -j8 --target install
(cd build && ctest)          # unit tests of the helix extrapolation and the kink chi2

GenFit is found on CMAKE_PREFIX_PATH or through GENFIT_INSTALL_DIR, or through GENFIT_INC / GENFIT_LIB (see cmake/FindGenFit.cmake).

Set up (in every new shell)

source /cvmfs/sw-nightlies.hsf.org/key4hep/setup.sh
export LD_LIBRARY_PATH=<path to>/install/lib64:$LD_LIBRARY_PATH
export PYTHONPATH=<path to>/install/python:$PYTHONPATH

Run

k4run options/runGlobalTrackerTracking.py

Steering	Detector
runGlobalTrackerTracking.py	IDEA vertex detector + silicon wrapper, merged with MergeTrackerHitPlanes; IPStateMode = Helix
runMuonSystemTracking.py	IDEA muon system, settings of the HNL muon-system studies; input, output and compact on the command line; IPStateMode = SolenoidCrossing
runCombinatorialTrackFinder.py	IDEA muon system, fixed example files; IPStateMode = SolenoidCrossing

The geometry compact in the steering must be the one the input file was digitised with. Every property is documented in components/CombinatorialTrackFinder.h.

Files

File	Content
components/CombinatorialTrackFinder.{h,cpp}	the algorithm
components/MergeTrackerHitPlanes.cpp	merges hit collections of several subdetectors
src/, include/	circle and helix tools, layer geometry, seed finder, kink χ², DD4hep field and material for GenFit
test/	unit tests
options/	example steering files

Author

Mahmoud Al-Thakeel