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Analysis Tools


Contents:


This section presents more advanced topics on the Beta analysis packages covering the basics on how to manipulate candidates with operators, Monte Carlo truth associators, and introduces several concepts useful for running physics analyses at BaBar. Users who are new to using Beta candidates should first read the Workbook Event Information section, and in particular the BtaCandidate section.

Particle Identification (PID)

Quick links:
Charged PID Homepage
Neutral PID Homepage

About PID

Particle Identifcation (PID) is concerned with the identification of detected particles - ones that live long enough to leave an actual signal in the detector. The detected particles are electrons, muons, pions, kaons, protons, and photons. Other particles decay too quickly to be detected, and must be reconstructed by combining the detected particles to form composite candidates, and testing these candidates. You will learn about particle composition later in this section.

The responsibility for Particle ID is divided between two groups: the Charged PID Group and the Neutral PID Group.

The PID groups develop, tests and maintain particle selectors, standard sets of selection criteria used in all BaBar analyses to identify the detected particles.

The efficiency of a selector is the fraction of signal events accepted by the selector. The purity is the fraction of all events selected that are signal events. In general, you want high efficiency and high purity. However, there is usually a tradeoff between efficiency and purity: if you tighten your selection criteria, you will cut out more background events, but you will lose more signal events as well.

To provide each user with the level of selection required for his or her analysis, each particle typically has several levels of selector, from VeryLoose (most efficient, least pure) to VeryTight (most pure, least efficient). You will need to determine which level of selector you require by studying the efficiencies and purities of those selectors for your specific analysis.

A PID list is a list of BtaCandidates that have passed a given particle selector. For example, one of the lists provided by the Charged PID group is the eMicroTight list of BtaCandidates that have passed the selector "TightElectronMicroSelection". The complete list of available PID lists can be found in the Workbook's Table of Run-time Lists.

PID and Monte Carlo

Since Monte Carlo (simulated data) is not a perfect imitation of data, the performance of the particle selectors is not the same for data and Monte Carlo. So whenever an analysis uses Monte Carlo simulations to estimate the effect of a PID selector on data, the result must be corrected for differences between data and Monte Carlo.

The PID groups both provide methods for implementing data/MC corrections in your analysis. For Charged PID, you have a choice between two main methods: PID tweaking or PID weighting, which can be set via tcl. For Neutral PID, the procedure usually involves adding or changing some lines in a tcl file, and possibly adding a package with a given tag.

Unfortunately, in both groups (especially the Neutrals Group) the recommended procedure tends to change over time, so you need to consult the PID Group webpages at the time you do your analysis to find out what is the current method for data/MC corrections.

Related Links: (last updated: April 2007)
Charged PID data/MC corrections
18-series recipe for neutrals data/MC corrections

(I was unable to find links to instructions for R22 recipes. Probably they have not been created yet. If/when you find them, please email me and let me know so I can update this page.)


Beta Operators

Accessing the lists of BtaCandidates in the event store was the first step for the analysis; we now have to learn which kind of operations can be performed. In the BtaCandidate section you saw some of the member functions of the BtaCandidate class: functions to access the charge, energy, mass, 3-momentum, and 4-momentum of any Beta Candidate. These functions belong to the BtaCandidate class.

There are also many functions that can be performed on BtaCandidates. These functions are not members of the BtaCandidate class; rather, they take BtaCandidates as input. Vertexing, mass-constrained fitting, and simple 4-vector addition are examples of such operators. The analyst selects the operator needed at particular stages in the analysis, trading off accuracy and completeness for speed and flexibility. This is just the beginning of the list of all the possible operations that can be performed on BtaCandidates:

  • Cloning
  • Setting particle type
  • Combining 4-vectors
  • Vertexing
  • Applying constraints
  • Obtaining Monte Carlo Truth
  • Changing a reference frame
  • ...............
In the following section you will learn about some of the tools available for manipulating BtaCandidates.

Combining BtaCandidates

A basic operation of analysis is creating acceptable candidates for a particular reaction from scratch. There are many tools available for combining Beta Candidates:
Simple addition
Beta Candidate (class BtaCandidate) can be simply combined to form a new Beta Candidate. This type of addition imposes no constraints.
Vertex and Kinematic Fitting
These are fitters that can be used within a BaBar Framework application to create composite candidates, incorporating geometric constraints, kinematic constraints, or both.
SimpleComposition
SimpleComposition is a package full of BaBar Framework modules that create lists of composite particles, automating the work of making combinations, performing fits, and making cuts.

Simple Addition of Beta Candidates

Two BtaCandidates can be combined by simply adding their 4-momenta:
    BtaCandidate* c1;
    BtaCandidate* c2;
    BtaOpAdd4 op;
    BtaCandidate c3= op.combine( *c1, *c2 );
This operation combines BtaCandidates c1 and c2 to give the (putative) mother, c3. BtaOpAdd4 specifies a simple kinematic addition.

This type of addition does not take into account any geometric or kinematic constraints. The two BtaCandidates could be separated by a long distance in space, or combine to form a BtaCandidate with an impossible mass (for example, a mass that does not belong to any existing particle). So you will need to test the new BtaCandidate before you can be confident that it really is the mother.

Vertexing and Kinematic Fitting

A more sophisticated way of combining BtaCandidate is the vertexing/kinematic fitting procedure in which one uses physical constraints governing a particle interaction or decay to improve the measurements describing the process. Fitters can use geometric constraints, kinematic constraints, or both; and can treat single-level or more complicated decay trees.

Vertexers and kinematic fitters are both Beta operators. The input is a list or tree of BtaCandidates. A vertexer returns the most likely common vertex position, vertex momentum, and their errors. A kinematic fitter returns the best fit to the momenta/masses/energies of the candidates. Many Beta operators do both. The output is a modified version of the tree with improved vertices and momenta.

An example of the use of a vertexer can be found in the module, which came in your BetaMiniUser package. This module forms K0 candidates by vertexing pairs of pion candidates. Looking at MyK0Analysis.cc, you can see that the code #includes the required vertexing header files,


#include "VtxBase/BtaAbsVertexer.hh"
#include "VtxFitter/VtxFitterOper.hh"
#include "VtxBase/VtxAbsAlgorithm.hh"
initiates some vertexers,

, vtxFitAlgo("vtxFitAlgo", this, VtxAbsAlgorithm::GeoKin)
, vtxFitMode("vtxFitMode", this, VtxAbsAlgorithm::Standard)
and uses them to obtain a "fitted Vee" (that is, a fitted hypothetical K -> pi+ pi- decay).

VtxFitterOper veeVertexer(initialVee,vtxFitAlgo.value(), vtxFitMode.value());
  veeVertexer.fit();
fittedVee = veeVertexer.getFittedTree();
To learn how to use the vertexing operators go at the Vertexing/Kinematic Fitting User's Guide. This is a well-written, detailed and up-to-date guide based on analysis-21. (Note that it is based on a different release than analysis-30, the release used in the Workbook Quicktour.)

Related Documents:

SimpleComposition

SimpleComposition is a package that takes existing lists of BtaCandidates (such as ChargedTracks, GoodTracksLoose, piDefault, KDefault, gammaDefault) and produces lists of composite BtaCandidates. A composite BtaCandidate is really a decay tree, so geometric and kinematic fits can be performed on each composite candidate.

SimpleComposition provides an interface for fitting and refitting, applying and refining selection. Each "operation" that SimpleComposition supports is given a module, and that module is configure by the user via tcl

The SimpleComposition home page has links to many useful tutorials and examples on how to use the SimpleComposition package. Another good way to get started using SimpleComposition is to try the Workbook tutorial, How to generate a set of CM2 ntuples using SimpleComposition and BtaTupleMaker.


BetaTools and BetaCoreTools

The BetaTools and BetaCoreTools packages provide a diverse set of tools for use with analyses at the Beta level. Those tools that are considered core for any physics analysis are placed in BetaCoreTools. The BetaTools package provides tools for carrying out Monte Carlo truth analyses.

Some of the more useful BetaCoreTools include:

  • Tools for calculating event shape variables, such as thrust, sphericity, the Fox Wolfram moment.
  • Monte Carlo truth associators, which associate the reconstructed objects in the event store to the corresponding Monte Carlo truth candidate (if it exists).
  • Tools providing additional event information, such as total momentum and B variables like deltaE, mes, and eBeam.
  • Utility functions to carry out tasks such as boosting a candidate and all its decay products, and doing simple vertexing (adding 4 momenta)
Some of the more useful BetaTools include:
  • Selectors and particle candidate makers.
  • Tools for making cuts/histogramming.
  • Beta Candidate counters

Descriptions and documentation for these and other BetaTools can be found on the BetaTools and BetaCoreTools page.

Some of the more useful tools are described below.

BtaBooster, BtaHelicity and helicity angle calculations

A useful quantity in many analyses is the helicity angle. In the reaction Y -> X -> a + b, the helicity angle of particle a is the angle measured in the rest frame of the decaying parent particle, X, between the direction of the decay daughter a and the direction of the grandparent particle Y. (Source: BAD 529 (V5) p.5-6)

The following short C++ routine can be used to compute the cosine of the helicity angle.


#include <TLorentzVector.h>
#include <Vector3.h>

Float_t coshel(TLorentzVector particle, TLorentzVector parent, 
TLorentzVector grandparent) {

TVector3 boosttoparent = -(parent.BoostVector());

particle.Boost(boosttoparent);
grandparent.Boost(boosttoparent);

TVector3 particle3 = particle.Vect();
TVector3 grandparent3 = grandparent.Vect();

Float_t numerator = particle3.Dot(grandparent3);
Float_t denominator = (particle3.Mag())*(grandparent3.Mag());
Float_t temp = numerator/denominator;

return temp;

}

Alternatively, the helicity is expressed in terms of Lorentz invariant quantities in BAD 522 (V6), Eq. 141, page 120. This expression avoids the need to do boosts for calculating the helicity angle.

NOTE: You should NOT use BtaBooster to compute helicity, because you cannot compare angles between a BtaBooster'ed vector and an un-BtaBooster'ed vector, as the two coordinate systems have a relative rotation. Instead, a straight Lorentz boost should be used. In the special case where X and a are already boosted to the Y reference frame, you can use the BetaCoreTools package BtaHelicity to compute the helicity. The syntax is:


#include "BetaCoreTools/BtaHelicity.hh"

  BtaHelicity h(a, b);  // a and b are BtaCandidates in X -> a + b
  double hel = h.helicity();
For example, in the BetaMiniUser package, BtaHelicity is used in MyK0Analysis.cc to compute the helicity of d1 in the decay K-candidate -> d1 d2.

Associators

It is often useful to associate one candidate with another during analysis. Reconstruction candidates are associated with their appropriate Monte Carlo truth candidates, etc. the BtaAssociator classes provide a family of ways to do this with a consistent interface.
For example in efficiency studies it is important to be able to associate the Monte Carlo truth to the reconstructed objects. An example of how to do use associators is in our very own MyMiniAnalysis.cc, where a truth map is initiated,

 , _btaTruthMap( "btaTruthMap", this, "GHit")
made framework-accessible,

  commands()->append( &_btaTruthMap );
accessed,

  // get the default truth mapping
  //
  BtaMcAssoc* truthMap =
    Ifd< BtaMcAssoc >::get(anEvent, _btaTruthMap.value());
and finally used to associate each Beta Candidate in the list *btaMicroList with its MC partner.

  // Simple example of map usage

    HepAListIterator<BtaCandidate> recoIter(*btaMicroList);
    while (BtaCandidate* reco = recoIter()){
      BtaCandidate *mcPartner = truthMap->mcFromReco(reco);
Then the difference between the momentum of the MC partner and the original candidate is written to a histogram:

        _aHisto->accumulate(mcPartner->p() - reco->p());

Other useful analysis tools


B Flavor Tagging

At BaBar, B-mesons are always produced in pairs: one B and one anti-B. In many studies, including the measurement of sin2beta, it is important to be able to determine the flavor (b or anti-b) of one (and thus both) of the B-mesons. Developing and maintaining a B-flavor tagging algorithm is the responsility of the B Tagging Tools Group.

A typical scenario is that one of the B-mesons (the signal B) decays in the mode of interest, while the other B-meson (the tagging B) is used to determine the flavor. The tagging B decays to a charged lepton or kaon. Then the b-quark flavor can be determined from the correlation between the b-quark charge and the charge of the "tagging" lepton or kaon.

The home page of the B Tagging Tools Group includes links to BaBar Analysis Document (BAD) 729, which describes Tag04, the latest (2004) B-tagging algorithm, and a recipe for making ntuples in CM2 with release 14.5.2.

Related Documents:

These older BADs describe earlier versions of the B-tagging algorithm:


Roofit: A ROOT toolkit

The RooFit packages provide a toolkit for modeling the expected distribution of events in a physics analysis. Models can be used to perform likelihood fits, produce plots, and generate "toy Monte Carlo" samples for various studies. The RooFit tools are integrated with ROOT.

Related Documents:


WIRED: The BaBar event display

An event display is a graphical tool for viewing detector structure and events. BaBar's tool of choice is called WIRED. Instructions on how to set up and run WIRED can be found at the links below:

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