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R. Frühwirth et al.
In practice it is useful to distinguish between several types of vertices:
1. The primary vertex is the point of collision of two beam particles (in a
collider experiment) or of a beam particle and a target particle (in a fixed-target
experiment).
2. A secondary decay vertex is the point where an unstable particle decays in the
detector volume or in the beam pipe. An example is the decay K 0
S → π + π − .
3. A secondary interaction vertex is the point where a particle interacts with the
material of the detector. Examples are bremsstrahlung, pair production, and
inelastic hadronic interactions.
Vertex reconstruction frequently proceeds in several steps:
1. Vertex finding: Finds the tracks that belong to a common primary or secondary
vertex.
2. Vertex fitting: Estimates for each vertex candidate the location of the common
vertex and computes the associated covariance matrix.
3. Test of vertex hypothesis: Tests for each vertex candidate whether all tracks do
indeed belong to the vertex and identifies outliers.
4. Update: Uses the vertex constraint to improve the location and momentum
estimate of the tracks belonging to the vertex.
5. Kinematic fit: Kinematic constraints such as momentum and energy conservation
are imposed on the mother and daughter particles of a vertex, and mass
hypotheses are tested. Kinematic fits are most frequently applied to secondary
decay vertices.
Vertex finding can be accomplished in many different ways. A few of them will
be described in Sect. 13.2.2. The vertex fit takes a vertex candidate and estimates
the vertex location from the estimated track parameters of the outgoing particles
(Sect. 13.2.3). As a rule, only charged particles are used, but sometimes also neutral
particles contribute to the vertex fit. In the test stage (Sect. 13.2.3.2) outliers are
identified, i.e., particles that apparently do not belong to the estimated vertex.
As this can lead to a different assignment of particles to vertices, it can be
considered as a method of vertex finding. If outliers are expected, the estimation
procedure should be robust so that the estimated vertex is not significantly biased
by the outliers (Sect. 13.2.3.3). Kinematic constraints (Sect. 13.2.4) are usually
imposed via Lagrange multipliers. By repeating the kinematic fit under various mass
hypotheses of the mother and/or daughter particles the most likely mass assignment
can be found out.
13.2.2 Vertex Finding
Vertex finding is the process of dividing the reconstructed tracks in an event into
classes such that presumably all tracks in a class are produced at the same vertex.
The primary vertex in an event is usually easy to find, especially if prior information
R. Frühwirth et al.
In practice it is useful to distinguish between several types of vertices:
1. The primary vertex is the point of collision of two beam particles (in a
collider experiment) or of a beam particle and a target particle (in a fixed-target
experiment).
2. A secondary decay vertex is the point where an unstable particle decays in the
detector volume or in the beam pipe. An example is the decay K 0
S → π + π − .
3. A secondary interaction vertex is the point where a particle interacts with the
material of the detector. Examples are bremsstrahlung, pair production, and
inelastic hadronic interactions.
Vertex reconstruction frequently proceeds in several steps:
1. Vertex finding: Finds the tracks that belong to a common primary or secondary
vertex.
2. Vertex fitting: Estimates for each vertex candidate the location of the common
vertex and computes the associated covariance matrix.
3. Test of vertex hypothesis: Tests for each vertex candidate whether all tracks do
indeed belong to the vertex and identifies outliers.
4. Update: Uses the vertex constraint to improve the location and momentum
estimate of the tracks belonging to the vertex.
5. Kinematic fit: Kinematic constraints such as momentum and energy conservation
are imposed on the mother and daughter particles of a vertex, and mass
hypotheses are tested. Kinematic fits are most frequently applied to secondary
decay vertices.
Vertex finding can be accomplished in many different ways. A few of them will
be described in Sect. 13.2.2. The vertex fit takes a vertex candidate and estimates
the vertex location from the estimated track parameters of the outgoing particles
(Sect. 13.2.3). As a rule, only charged particles are used, but sometimes also neutral
particles contribute to the vertex fit. In the test stage (Sect. 13.2.3.2) outliers are
identified, i.e., particles that apparently do not belong to the estimated vertex.
As this can lead to a different assignment of particles to vertices, it can be
considered as a method of vertex finding. If outliers are expected, the estimation
procedure should be robust so that the estimated vertex is not significantly biased
by the outliers (Sect. 13.2.3.3). Kinematic constraints (Sect. 13.2.4) are usually
imposed via Lagrange multipliers. By repeating the kinematic fit under various mass
hypotheses of the mother and/or daughter particles the most likely mass assignment
can be found out.
13.2.2 Vertex Finding
Vertex finding is the process of dividing the reconstructed tracks in an event into
classes such that presumably all tracks in a class are produced at the same vertex.
The primary vertex in an event is usually easy to find, especially if prior information