Final Tracks Selector Algorithms

Complete: 4

Goal of the page

This page is intended to familiarize you with the Final Track Selectors applied to remove fake tracks from the reconstructed track collections.

Contacts

Paolo Azzurri, Boris Mangano, Kevin Stenson

Introduction

Within an average LHC dense event the standard CMS combinatorial track finder (CTF) yields a significant fraction of fake reconstructed tracks. The fake rate can be effectively reduced by applying quality cuts that remove tracks with a bad fit-$\chi^2$ and a bad compatibility with the event interaction vertices. An optimal way to bring down the overall fake rate retaining the best possible efficiency for true tracks, is to adapt the quality cuts to the track $\eta$, $p_T$ and, most of all, to the track number of crossed layers with measurements.

The selection criteria

Quality cuts to reject fake tracks, have been optimized for each CTF track reconstruction step, adapting the cuts to the track number of layers, $p_T$ and η, and applying cuts on:

  • the track $\chi^2/\nu$ (chi-square per degree of freedom),
  • the track $d_0$ to the beam spot,
  • the track $\Delta z$ to the position closest HLT primary vertex,
  • the $d_0/\delta d_0$ transverse compatibility with the beam spot, and
  • the $\Delta z/\delta z_0$ longitudinal compatibility with the closest HLT vertex.

The HLT vertices are taken from the pixelVertices collection requiring at least three pixel tracks in the vertex and a vertex ${\rm Prob}(\chi^2)>1\%$, if available.

The resolutions on the track measured $d_0$ and $z_0$ have been parametrized as

$\sigma(d_0,z_0\sin\theta) \left( p_T \right) = a + \frac{b}{p_T (GeV/c)}$

where $a$ and $b$ are configurable parameters.

Finally the optimal cuts have been approximated with the following formulas

  1. $\chi^2/\nu < \alpha_0 n_{\rm layers}$
  2. $|d_0|< \left( \alpha_1 n_{\rm layers}\right)^{x_1} \sigma_{d_0}(p_T)$
  3. $|\Delta z|< \left( \alpha_2 n_{\rm layers}\right)^{x_2} \sigma_{z_0}(p_T,\eta)$
  4. $|d_0|/\delta d_0 < \left( \alpha_3 n_{\rm layers}\right)^{x_3}$
  5. $|\Delta z|/\delta z_0 < \left( \alpha_4 n_{\rm layers}\right)^{x_4}$.

where $\alpha_i$ and $x_j$ are configurable parameters.

The selection criteria are described also in the PAS TRK-10-001. Refer to the table below for the most updated parameter values.

4_2_X values for selection criteria

The table below gives the values used for the highPurity definition for the different iterations in the iterative tracking. In the table, $\beta = x_1 = x_2 = x_3 = x_4$.
  Track quality cuts Vertex compatibility cuts
Iteration $\alpha_0$ min layers min 3D layers max lost layers $\beta$ $\alpha_1$ $\alpha_2$ $\alpha_3$ $\alpha_4$
0 & 1 0.7 3 3 2 4 0.30 0.35 0.40 0.40
2 Trk 0.4 5 3 1 4 1.00 1.00 1.00 1.00
2 Vtx 0.7 3 3 1 3 0.85 0.80 0.90 0.90
3 Trk 0.3 5 4 0 4 0.90 0.90 0.90 0.90
3 Vtx 0.4 3 3 1 3 1.10 1.10 1.20 1.20
4 0.25 5 3 0 4 1.00 1.00 1.00 1.00
5 0.2 5 2 0 4 1.40 1.30 1.40 1.30
For iterations 2 and 3, there are two paths for a track. The Trk path emphasizes good quality tracks while the Vtx path emphasizes compatibility of the track with a pixel vertex.

4_4_X values for selection criteria

The table below gives the values used for the highPurity definition for the different iterations in the iterative tracking. In the table, $\beta = x_1 = x_2 = x_3 = x_4$.
  Track quality cuts Vertex compatibility cuts
Iteration $\alpha_0$ min layers min 3D layers max lost layers $\beta$ $\alpha_1$ $\alpha_2$ $\alpha_3$ $\alpha_4$
O, 1, 2 0.7 3 3 2 4 0.30 0.35 0.40 0.40
3 Trk 0.4 5 3 1 4 1.00 1.00 1.00 1.00
3 Vtx 0.7 3 3 1 3 0.85 0.80 0.90 0.90
4 Trk 0.3 5 4 0 4 0.90 0.90 0.90 0.90
4 Vtx 0.4 3 3 1 3 1.10 1.10 1.20 1.20
5 0.25 5 3 0 4 1.00 1.00 1.00 1.00
6 0.2 5 2 0 4 1.40 1.30 1.40 1.30
For iterations 3 and 4, there are two paths for a track. The Trk path emphasizes good quality tracks while the Vtx path emphasizes compatibility of the track with a pixel vertex.

5_X_X values for selection criteria

The table below gives the values used for the highPurity definition for the different iterations in the iterative tracking. In the table, $\beta = x_1 = x_2 = x_3 = x_4$.
  Track quality cuts Vertex compatibility cuts
Iteration $\alpha_0$ min layers min 3D layers max lost layers $\beta$ $\alpha_1$ $\alpha_2$ $\alpha_3$ $\alpha_4$
O, 1, 2 0.7 3 3 2 4 0.30 0.35 0.40 0.40
3 Trk 0.4 5 4 1 4 1.00 1.00 1.00 1.00
3 Vtx 0.7 3 3 1 3 0.85 0.80 0.90 0.90
4 Trk 0.3 5 4 0 4 0.90 0.90 0.90 0.90
4 Vtx 0.4 3 3 1 3 1.10 1.10 1.20 1.20
5 0.2 4 3 0 4 0.90 0.90 0.90 0.90
6 0.2 5 2 0 4 1.40 1.30 1.40 1.30
For iterations 3 and 4, there are two paths for a track. The Trk path emphasizes good quality tracks while the Vtx path emphasizes compatibility of the track with a pixel vertex.

Software architecture

The filtering of the track collection has been implemented inside the CMSSW framework as the AnalyticalTrackSelector EDProducer (AnalyticalTrackSelector.h, AnalyticalTrackSelector.cc). This module takes as input a collection of pre-filtered reco::Track and returns a new collection containing only the tracks which fulfill all the quality cuts used by the selection. In addition to the initial track collection, the module takes a collection of primary vertices as input: both track and vertices collections are specified in the configuration of the module with the two corresponding InputTag.

An example of configuration is in SelectHighPurity_cfi.py used for the first CTF step.

The above parameters for adapted optimal cuts are set with

chi2n_par = cms.double( $\alpha_0$ ),

res_par = cms.vdouble( $a$, $b$ ),

d0_par1 = cms.vdouble( $\alpha_1$, $x_1$ ),

dz_par1 = cms.vdouble( $\alpha_2$, $x_2$ ),

d0_par2 = cms.vdouble( $\alpha_3$, $x_3$ ),

dz_par2 = cms.vdouble( $\alpha_4$, $x_4$ ),

Documentation

Paolo Azzurri and Boris Mangano, Optimal filtering of fake tracks Internal Note CMS IN-2008/017

Review status

Reviewer/Editor and Date (copy from screen) Comments
KatiLassilaPerini - 29 Jan 2008 created template page
KevinStenson - 01 Oct 2011 updated to CMSSW440

Responsible: ResponsibleIndividual
Last reviewed by: Most recent reviewer

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Topic revision: r9 - 2013-01-31 - WellsWulsin
 
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