diff --git a/docs/figures/tracking/vertexing_flowchart.svg b/docs/figures/tracking/vertexing_flowchart.svg new file mode 100644 index 00000000000..d5900e89efc --- /dev/null +++ b/docs/figures/tracking/vertexing_flowchart.svg @@ -0,0 +1,554 @@ + +image/svg+xmlSeedtracks +T +s +Vertexseeder +Vertexseed +⃗v +s +Removetracksin +T +∗ +from +T +s +iftheirweightisabovethreshold +Impactpointestimator +Setofalltracks +T +Tracks +T +∗ +⊂ +T +compatiblewith +⃗v +s +andtheirweights +Multi-vertexftter +Setoffoundvertices +V +Vertexcandidate +⃗v +Addvertexcandidateto +V +ifitisnotmerged + \ No newline at end of file diff --git a/docs/tracking.md b/docs/tracking.md index afbafaf7fb4..2091b983152 100644 --- a/docs/tracking.md +++ b/docs/tracking.md @@ -952,53 +952,80 @@ See [](vertexing_core) for a dedicated description of the vertexing as implemented in ACTS. ::: -One very immediate use case for tracks is the reconstruction of interaction -vertices in the event. These are needed for many aspects of higher-level -reconstruction algorithms. Vertices are used in different ways. As shown in -{numref}`vertexing_illust`, a single event can have a primary vertex, usually -associated with the hard-scatter event, as well as a number of secondary -vertices. Typically, the primary vertex will be located in the luminous -region. The reconstruction of secondary vertices can help with the -identification of particles, for instance in the form of *$b$-tagging* -jets originating from $b$-quarks. Here, a characteristic displaced vertex -located inside a jet is a sign for a $b$-hadron decay. Additionally, pile-up -interactions can produce vertices that are not associated with the -interaction of interest. Signatures from pile-up interactions can be -rejected, if they can be associated to a pile-up vertex. - +A vertex is a point within the detector, where an interaction or a +decay occurred. We distinguish between primary vertices (from +collisions/interactions) and secondary vertices (from subsequent particle +decays), see {numref}`vertexing_illust`. Primary vertices are further divided +into hard-scatter and pile-up vertices. While primary vertices are located in +the luminous region, secondary vertices are slightly displaced due to the finite + life time of the decaying particle. (vertexing_illust)= :::{figure} /figures/tracking/vertexing.svg :width: 400px :align: center Illustration of a set of three vertices in a proton-proton -collision. A primary vertex and a secondary vertex are shown in addition to -a pile-up vertex. +collision. We distinguish between primary hard-scatter, primary pile-up, and +secondary vertices. ::: -Vertex reconstruction can be divided into two stages: vertex finding and -vertex fitting, in close analogy to the reconstruction of tracks themselves. -Reconstruction begins with a seeding stage. Vertex seeding can be performed -in a number of ways. Algorithms differ for primary and secondary vertex -reconstruction. For primary vertex seeding, one option is an algorithm, which -uses a histogram approach to cluster tracks in the $z$-axis. This is based on -the assumption that primary vertices will align with the beam spot. Other -approaches include the use of a Gaussian track density to identify regions -with high track multiplicity as vertex seeds. For secondary vertexing, -seeds are formed from pairs of reconstructed tracks, as the constraint to the -beam spot does not apply. - -With a set of vertex seeds determined, tracks compatible with the vertex are -selected. Using a linearized approximation of the helical trajectories in the -vicinity of the vertex, a fitting procedure based on the Kalman formalism can -estimate the vertex parameters. - -One issue with an approach like this is the fact that the assignment of tracks -to vertices is not unambiguous. Improvements exist, where tracks that turn out -to be a bad fit with the vertex in question are weighted down, avoiding -degradation in the obtained result. On the other hand, multi-vertex fit methods -can reassign such outlier tracks to a more compatible vertex, yielding improved -results for both vertices. +Vertices play an important role in higher-level reconstruction algorithms. For +example, secondary vertices can help with the identification of particles: +During *$b$-tagging*, a displaced vertex located inside a jet is a sign for the +decay of a $b$-hadron. + +In analogy to track reconstruction, vertex reconstruction can be divided into +two stages: vertex finding and vertex fitting. As a first step of vertex +finding, we compute a rough estimate of the vertex position from a set of +tracks. This first estimate can be calculated in many different ways, and is +referred to as "vertex seed". Seeding algorithms differ for primary and +secondary vertexing. For primary vertex seeding, one option is to use a +histogram approach to cluster tracks on the $z$-axis[^phd:piacquadio:2010]. +This is based on the assumption that primary vertices will be close to the +beamline. Other approaches model tracks as multivariate Gaussian distributions +and identify regions of high track density as vertex seeds[^phd:schlag:2022]. +For secondary vertexing, seeds are formed from pairs of reconstructed tracks as +the constraint to the beamline does not apply. + +Once a vertex seed is determined, tracks that are compatible with it are +selected as part of the vertex finding. + +Before the vertex fit, we linearize tracks in the vicinity of the vertex seed +under assuming that they follow a helical (for constant magnetic field) or +straight (for no magnetic field) trajectory[^phd:piacquadio:2010]. The vertex +fitter then uses this linearization to improve the position of the vertex seed. +Furthermore, the track momenta are refitted under the assumption that the tracks +originate at the vertex[^Fruhwirth:1987fm] [^billoirfitting:1992] . + +One issue with an approach like this is that the assignment of tracks to +vertices is ambiguous. As an improvement, one can perform a multi-vertex fit, +where vertices compete for tracks. This means that one track can be assigned to +several vertices. Their contribution to each vertex fit is determined by a +weight factor, which, in turn, depends on the tracks' compatibility with respect +to all vertices[^fruwirth:amvfitting:2004]. + +A flowchart of a multi-vertex reconstruction chain is shown in +{numref}`vertexing_flowchart`. + +(vertexing_flowchart)= +:::{figure} /figures/tracking/vertexing_flowchart.svg +:width: 600px +:align: center +Simplified flowchart of multi-vertex reconstruction. From a set of seed tracks, +we first compute a rough estimate of the vertex position, i.e., the vertex seed. +Then, we evaluate the compatibility of all tracks with the the latter. If a +track is deemed compatible, it is assigned a weight and attached to the vertex +seed. Next, the vertex seed and all previously found vertices that share tracks +with it are (re-)fitted. Finally, after convergence of the fit, we check whether +the vertex candidate is merged with other vertices and discard it if that is the +case. For the next iteration, all tracks that were assigned to the vertex seed +and that have a weight above a certain threshold are removed from the seed +tracks. +::: [^phd:gessinger:2021]: Gessinger-Befurt, Paul, 30.04.2021. Development and improvement of track reconstruction software and search for disappearing tracks with the ATLAS experiment. [10.25358/openscience-5901](https://doi.org/10.25358/openscience-5901) -[^Fruhwirth:1987fm]: F. Frühwirth, 1987, Application of Kalman filtering to track and vertex fitting, , [11.1016/0168-9002(87)90887-4](https://doi.org/10.1016/0168-9002(87)90887-4) +[^Fruhwirth:1987fm]: R. Frühwirth, 1987, Application of Kalman filtering to track and vertex fitting, , [11.1016/0168-9002(87)90887-4](https://doi.org/10.1016/0168-9002(87)90887-4) +[^phd:piacquadio:2010]: G. Piacquadio, 2010, Identification of b-jets and investigation of the discovery potential of a Higgs boson in the $W H \rightarrow l \nu \bar{b} b$ channel with the ATLAS experiment. +[^phd:schlag:2022]: B. Schlag, 2022, Advanced Algorithms and Software for Primary Vertex Reconstruction and Search for Flavor-Violating Supersymmetry with the ATLAS Experiment. +[^billoirfitting:1992]: P. Billoir et al., 2022, Fast vertex fitting with a local parametrization of tracks. +[^fruwirth:amvfitting:2004]: R. Frühwirth et al., 2004, Adaptive Multi-Vertex fitting. \ No newline at end of file