13 Pattern Recognition and Reconstruction
575
but can be generalized to any other measure of distance. The method first constructs
a minimum spanning tree [77] in the edge-weighted graph connecting all particles
with each other and then proceeds to cut the tree along its longest edges. The
procedure stops when the longest remaining edge is shorter than a fixed multiple
of the median of all edge lengths.
Several non-hierarchical cluster algorithms have been proposed as well. Some
of them employ general unsupervised learning methods, such as deterministic
annealing [78] or k-means [79]. Others are specially designed for jet finding, for
instance the cone algorithm described in [72]. It is an iterating procedure which
constructs jets out of seeds. In contrast to the hierarchical clustering method the
jets may overlap and a unique assignment has to be forced at the end. A modified
cone algorithm suitable for the much larger multiplicity of heavy-ion collisions is
proposed in [80]. A specialized jet finder for the reconstruction of hadronic τ -decays
is described in [81].
13.1.4 Detector Alignment 1
Alignment is the general term used in experimental high energy physics to refer to
the process of obtaining and applying corrections to the nominal setup of a given
experiment. These corrections are typically related to geometrical displacements of
devices with a spatial resolution, in contrast to calibrations, where the corrections
are usually extracted from pedestal or reference measurements to compensate for
offsets in scalar measurements. Misalignment compromises tracking and vertex
finding [82] and thus directly affects physics measurements such as momentum
and invariant mass resolutions, or the efficiency of b-tagging algorithms. There are
various possibilities for the treatment of alignment corrections, ranging from simple
translations and rotations, equivalent to those of a rigid body, to more complex
deformations, like sags or twists.
To this end experiments typically use several independent strategies [83]. For
testing the long-term stability or the alignment of sub-detectors with respect to
each other, very often so-called hardware alignment is utilized, where special
reference markers are measured directly e.g. via optical systems or photogrammetry.
However, these techniques reach only a limited precision in the range of several
tens to hundreds of microns. If the intrinsic resolution of a tracking device is
smaller, an improved resolution can only be obtained with track-based alignment,
where the information from recorded particle tracks is used to obtain the alignment
parameters [83, 84]. For various examples of the track-based alignment methods
used in experiments since the LEP era, see [85–100].
1 The section on detector alignment was contributed by E. Widl (Institute of High Energy Physics,
Vienna; now at Austrian Institute of Technology).
575
but can be generalized to any other measure of distance. The method first constructs
a minimum spanning tree [77] in the edge-weighted graph connecting all particles
with each other and then proceeds to cut the tree along its longest edges. The
procedure stops when the longest remaining edge is shorter than a fixed multiple
of the median of all edge lengths.
Several non-hierarchical cluster algorithms have been proposed as well. Some
of them employ general unsupervised learning methods, such as deterministic
annealing [78] or k-means [79]. Others are specially designed for jet finding, for
instance the cone algorithm described in [72]. It is an iterating procedure which
constructs jets out of seeds. In contrast to the hierarchical clustering method the
jets may overlap and a unique assignment has to be forced at the end. A modified
cone algorithm suitable for the much larger multiplicity of heavy-ion collisions is
proposed in [80]. A specialized jet finder for the reconstruction of hadronic τ -decays
is described in [81].
13.1.4 Detector Alignment 1
Alignment is the general term used in experimental high energy physics to refer to
the process of obtaining and applying corrections to the nominal setup of a given
experiment. These corrections are typically related to geometrical displacements of
devices with a spatial resolution, in contrast to calibrations, where the corrections
are usually extracted from pedestal or reference measurements to compensate for
offsets in scalar measurements. Misalignment compromises tracking and vertex
finding [82] and thus directly affects physics measurements such as momentum
and invariant mass resolutions, or the efficiency of b-tagging algorithms. There are
various possibilities for the treatment of alignment corrections, ranging from simple
translations and rotations, equivalent to those of a rigid body, to more complex
deformations, like sags or twists.
To this end experiments typically use several independent strategies [83]. For
testing the long-term stability or the alignment of sub-detectors with respect to
each other, very often so-called hardware alignment is utilized, where special
reference markers are measured directly e.g. via optical systems or photogrammetry.
However, these techniques reach only a limited precision in the range of several
tens to hundreds of microns. If the intrinsic resolution of a tracking device is
smaller, an improved resolution can only be obtained with track-based alignment,
where the information from recorded particle tracks is used to obtain the alignment
parameters [83, 84]. For various examples of the track-based alignment methods
used in experiments since the LEP era, see [85–100].
1 The section on detector alignment was contributed by E. Widl (Institute of High Energy Physics,
Vienna; now at Austrian Institute of Technology).