Week 3 Notebook: Feature Engineering¶

Many different kinds of features have been specially engineered to perform b-tagging. We will consider several of these today.

b hadrons¶

B hadrons contain bottom quarks. These hadrons are unstable, meaning they naturally (and spontaneously) decay to hadrons containing lighter quarks, after a period of time (with a known median lifetime).

Because of the large mass difference between bottom quarks and the lighter quarks, the lifetime of b hadrons tends to be relatively long: around \(10^{-12}\) s. Given the fact that they are traveling near the speed of light, this means they can travel \(O\)(mm) in the detector before dacaying. The particle sproduced from this decay also tend to be higher energy

Therefore, we can consider the properties of displaced tracks and secondary vertices (points of origin of collections of displaced tracks). In particular we quantify how displaced a track is in terms of its impact parameter.

Single b-tagging¶

For single b-tagging, consider the following image:

For more information, read [5].

Double b-tagging¶

For double b-tagging, consider the following image:

For this, we can also take advantage of the so-called jet substructure. For more information, read [2, 6].

import uproot
f = uproot.open('root://eospublic.cern.ch//eos/opendata/cms/datascience/HiggsToBBNtupleProducerTool/HiggsToBBNTuple_HiggsToBB_QCD_RunII_13TeV_MC/train/ntuple_merged_10.root')

tree = f['deepntuplizer/tree']

labels = tree.arrays(['label_QCD_b', 
                      'label_QCD_bb', 
                      'label_QCD_c', 
                      'label_QCD_cc', 
                      'label_QCD_others', 
                      'label_H_bb', 
                      'sample_isQCD'], 
                     entry_stop=20000,
                     library='np')

# label QCD: require the sample to be QCD and any of the QCD flavors
label_QCD = labels['sample_isQCD'] * (labels['label_QCD_b'] + \
                                      labels['label_QCD_bb'] + \
                                      labels['label_QCD_c'] + \
                                      labels['label_QCD_cc'] + \
                                      labels['label_QCD_others'])

# label Hbb
label_Hbb = labels['label_H_bb']

Let’s load a sampling of track, secondary vertex, and jet features.

track_features = tree.arrays(['track_pt',
                              'track_dxy',
                              'track_dxysig',
                              'track_dz',
                              'track_dzsig',
                              'trackBTag_Sip2dSig',
                              'trackBTag_Sip2dVal',
                              'trackBTag_Sip3dSig',
                              'trackBTag_Sip3dVal',
                              'trackBTag_PtRatio',
                              'trackBTag_PParRatio'],
                             entry_stop=20000,
                             library='ak')

sv_features = tree.arrays(['sv_pt',
                           'sv_mass'],
                          entry_stop=20000,
                          library='ak')

jet_features = tree.arrays(['fj_pt', 
                            'fj_sdmass',
                            'fj_mass',
                            'fj_tau21',
                            'fj_jetNTracks',
                            'fj_trackSipdSig_0',
                            'fj_trackSipdSig_1'],
                           entry_stop=20000,
                           library='np')

Visualize Separation of Track Features¶

Let’s visualize the separation by plotting the signal and background for several track features that may be important.

Number of tracks
Maximum relative track \(p_T\)
Maximum signed 3D impact parameter value
Maximum signed 3D impact parameter significance: this is the value above divded by the estimated uncertainty of the measurement. This enables us to tell how “significant” (far from impact parameter of 0), this value is.

import matplotlib.pyplot as plt
import numpy as np
import awkward as ak

# number of tracks
plt.figure()
plt.hist(ak.num(track_features['track_pt']), weights=label_QCD, bins=np.linspace(0,80,81), density=True, alpha=0.7, label='QCD')
plt.hist(ak.num(track_features['track_pt']), weights=label_Hbb, bins=np.linspace(0,80,81), density=True, alpha=0.7, label='H(bb)')
plt.xlabel('Number of tracks')
plt.ylabel('Fraction of jets')
plt.legend()

# max. relative track pt
plt.figure()
plt.hist(ak.max(track_features['track_pt'], axis=-1)/jet_features['fj_pt'], weights=label_QCD, bins=np.linspace(0,0.5,51), density=True,alpha=0.7,label='QCD')
plt.hist(ak.max(track_features['track_pt'], axis=-1)/jet_features['fj_pt'], weights=label_Hbb, bins=np.linspace(0,0.5,51), density=True,alpha=0.7,label='H(bb)')
plt.xlabel(r'Maximum relative track $p_{T}$')
plt.ylabel('Fraction of jets')
plt.legend()

# maximum signed 3D impact paramter value
plt.figure()
plt.hist(ak.max(track_features['trackBTag_Sip3dVal'], axis=-1), weights=label_QCD, bins=np.linspace(-2,40,51), density=True, alpha=0.7, label='QCD')
plt.hist(ak.max(track_features['trackBTag_Sip3dVal'], axis=-1), weights=label_Hbb, bins=np.linspace(-2,40,51), density=True, alpha=0.7, label='H(bb)')
plt.xlabel('Maximum signed 3D impact parameter value')
plt.ylabel('Fraction of jets')
plt.legend()

# maximum signed 3D impact paramter significance
plt.figure()
plt.hist(ak.max(track_features['trackBTag_Sip3dSig'], axis=-1), weights=label_QCD, bins=np.linspace(-2,200,51), density=True, alpha=0.7, label='QCD')
plt.hist(ak.max(track_features['trackBTag_Sip3dSig'], axis=-1), weights=label_Hbb, bins=np.linspace(-2,200,51), density=True, alpha=0.7, label='H(bb)')
plt.xlabel('Maximum signed 3D impact parameter significance')
plt.ylabel('Fraction of jets')
plt.legend()

plt.show()

Visualize Separation of SV Features¶

Let’s visualize the separation by plotting the signal and background for several track features that may be important.

Number of secondary vertices
Maximum relative secondary vertex \(p_T\)
Maximum relative secondary vertex mass

ROC Curves¶

ROC curves can tell us how well each of these features discriminates betweeen signal and background.

from sklearn.metrics import roc_curve, auc
disc = np.nan_to_num(ak.num(track_features['track_pt'], axis=-1).to_numpy(allow_missing=True))

fpr, tpr, threshold = roc_curve(label_Hbb, disc)
# plot ROC curve
plt.figure()
plt.plot(fpr, tpr, lw=2.5, label="AUC = {:.1f}%".format(auc(fpr,tpr)*100))
plt.xlabel(r'False positive rate')
plt.ylabel(r'True positive rate')
#plt.semilogy()
plt.ylim(0,1)
plt.xlim(0,1)
plt.plot([0, 1], [0, 1], lw=2.5, label='Random, AUC = 50.0%')
plt.grid(True)
plt.legend(loc='upper left')
plt.show()

Other engineered features¶

To read more about the features read this: http://opendata.cern.ch/record/12102

Here is a selection:

Data variable	Type	Description
`event_no`	UInt_t	Event number
`npv`	Float_t	Number of reconstructed primary vertices (PVs)
`ntrueInt`	Float_t	True mean number of the poisson distribution for this event from which the number of interactions in each bunch crossing has been sampled
`rho`	Float_t	Median density (in GeV/A) of pile-up contamination per event; computed from all PF candidates of the event
`sample_isQCD`	Int_t	Boolean that is 1 if the simulated sample corresponds to QCD multijet production
`label_H_bb`	Int_t	Boolean that is 1 if a Higgs boson is matched and at least two b quarks are found within the AK8 jet
`label_QCD_bb`	Int_t	Boolean that is 1 if no resonances are matched and at least two b quarks are found within the AK8 jet
`label_QCD_b`	Int_t	Boolean that is 1 if no resonances are matched and only one b quark is found within the AK8 jet
`label_QCD_cc`	Int_t	Boolean that is 1 if no resonances are matched and at least two c quarks are found within the AK8 jet
`label_QCD_c`	Int_t	Boolean that is 1 if no resonances are matched and only one c quark is found within the AK8 jet
`label_QCD_others`	Int_t	Boolean that is 1 if no resonances are matched and no b or c quarks are found within the AK8 jet
`fj_doubleb`	Float_t	Double-b tagging discriminant based on a boosted decision tree calculated for the AK8 jet (see CMS-BTV-16-002)
`fj_eta`	Float_t	Pseudorapidity η of the AK8 jet
`fj_gen_eta`	Float_t	Pseudorapidity η of the generator-level, matched heavy particle: H, W, Z, top, etc. (default = -999)
`fj_gen_pt`	Float_t	Transverse momentum of the generator-level, geometrically matched heavy particle: H, W, Z, t, etc. (default = -999)
`fj_isBB`	Int_t	Boolean that is 1 if two or more b hadrons are clustered within the AK8 jet (see SWGuideBTagMCTools)
`fj_isNonBB`	Int_t	Boolean that is 1 if fewer than two b hadrons are clustered within the AK8 jet (see SWGuideBTagMCTools)
`fj_nbHadrons`	Int_t	Number of b hadrons that are clustered within the AK8 jet (see SWGuideBTagMCTools)
`fj_ncHadrons`	Int_t	Number of c hadrons that are clustered within the AK8 jet (see SWGuideBTagMCTools)
`fj_isH`	Int_t	Boolean that is 1 if a generator-level Higgs boson and its daughters are geometrically matched to the AK8 jet
`fj_isTop`	Int_t	Boolean that is 1 if a generator-level top quark and its daughters are geometrically matched to the AK8 jet
`fj_isW`	Int_t	Boolean that is 1 if a generator-level W boson and its daughters are geometrically matched to the AK8 jet
`fj_isZ`	Int_t	Boolean that is 1 if a generator-level Z boson and its daughters are geometrically matched to the AK8 jet
`fj_isQCD`	Int_t	Boolean that is 1 if none of the above matching criteria are satisfied (H, top, W, Z)
`fj_label`	Int_t	Integer label: `Invalid=0, Top_all=10, Top_bcq=11, Top_bqq=12, Top_bc=13, Top_bq=14, W_all=20, W_cq=21, W_qq=22, Z_all=30, Z_bb=31, Z_cc=32, Z_qq=33, H_all=40, H_bb=41, H_cc=42, H_qqqq=43, QCD_all=50, QCD_bb=51, QCD_cc=52, QCD_b=53, QCD_c=54, QCD_others=55`
`fj_labelJMAR`	Int_t	Alternative integer label from the CMS Jet/MET and Resolution (JMAR) group: `Default=0, Top=1, W=2, Z=3, H=4`
`fj_labelLegacy`	Int_t	Alternative (legacy) integer label: `Default=0, Top=1, W=2, Z=3, H=4`
`fj_jetNTracks`	Float_t	Number of tracks associated with the AK8 jet
`fj_nSV`	Float_t	Number of SVs associated with the AK8 jet (∆R < 0.7)
`fj_n_sdsubjets`	Float_t	Number of soft drop subjets in the AK8 jet (up to 2)
`fj_mass`	Float_t	Ungroomed mass of the AK8 jet
`fj_phi`	Float_t	Azimuthal angle ϕ of the AK8 jet
`fj_pt`	Float_t	Transverse momentum of the AK8 jet
`fj_tau1`	Float_t	N-subjettiness variable for a 1-prong jet hypothesis
`fj_tau2`	Float_t	N-subjettiness variable for a 2-prong jet hypothesis
`fj_tau3`	Float_t	N-subjettiness variable for a 3-prong jet hypothesis
`fj_tau21`	Float_t	N-subjettiness variable for 2-prong vs 1-prong jet discrimination (`fj_tau2/fj_tau1`)
`fj_tau32`	Float_t	N-subjettiness variable for 3-prong vs 2-prong jet discrimination (`fj_tau3/fj_tau2`)
`fj_sdmass`	Float_t	Soft drop mass of the AK8 jet
`fj_ptDR`	Float_t	Transverse momentum times the ΔR between the two soft drop subjets
`fj_relptdiff`	Float_t	Absolute relative difference between the transverse momenta of the two softdrop subjets
`fj_sdn2`	Float_t	Fraction of second subjet transverse momentum times ∆R squared
`fj_sdsj1_axis1`	Float_t	First axis of the first subjet
`fj_sdsj1_axis2`	Float_t	Second axis of the first subjet
`fj_sdsj1_csv`	Float_t	Combined secondary vertex (CSV) b-tagging discriminant for the first subjet
`fj_sdsj1_eta`	Float_t	Pseudorapidity η of the first subjet
`fj_sdsj1_mass`	Float_t	Mass of the first subjet
`fj_sdsj1_mult`	Float_t	Particle multiplicity of the first subjet
`fj_sdsj1_phi`	Float_t	Azimuthal angle ϕ of the first subjet
`fj_sdsj1_pt`	Float_t	Transverse momentum of the first subjet
`fj_sdsj1_ptD`	Float_t	ptD variable, defined as the square root of the sum in quadrature of the transverse momentum of the subjet constituents divided by the scalar sum of the transverse momentum of the subjet constituents, for the first subjet (see CMS-PAS-JME-13-002)
`fj_sdsj2_axis1`	Float_t	First axis of the first subjet
`fj_sdsj2_axis2`	Float_t	Second axis of the first subjet
`fj_sdsj2_csv`	Float_t	Combined secondary vertex (CSV) b-tagging discriminant for the first subject
`fj_sdsj2_eta`	Float_t	Pseudorapidity η of the second subjet
`fj_sdsj2_mass`	Float_t	Mass of the second subjet
`fj_sdsj2_mult`	Float_t	Particle multiplicity of the second subjet
`fj_sdsj2_phi`	Float_t	Azimuthal angle ϕ of the second subjet
`fj_sdsj2_pt`	Float_t	Transverse momentum of the second subjet
`fj_sdsj2_ptD`	Float_t	ptD variable, defined as the square root of the sum in quadrature of the transverse momentum of the subjet constituents divided by the scalar sum of the transverse momentum of the subjet constituents, for the second subjet (see CMS-PAS-JME-13-002)
`fj_z_ratio`	Float_t	z ratio variable as defined in CMS-BTV-16-002
`fj_trackSipdSig_0`	Float_t	First largest track 3D signed impact parameter significance (see CMS-BTV-16-002 )
`fj_trackSipdSig_1`	Float_t	Second largest track 3D signed impact parameter significance (see CMS-BTV-16-002 )
`fj_trackSipdSig_2`	Float_t	Third largest track 3D signed impact parameter significance (see CMS-BTV-16-002 )
`fj_trackSipdSig_3`	Float_t	Fourth largest track 3D signed impact parameter significance (see CMS-BTV-16-002 )
`fj_trackSipdSig_0_0`	Float_t	First largest track 3D signed impact parameter significance associated to the first N-subjettiness axis
`fj_trackSipdSig_0_1`	Float_t	Second largest track 3D signed impact parameter significance associated to the first N-subjettiness axis
`fj_trackSipdSig_1_0`	Float_t	First largest track 3D signed impact parameter significance associated to the second N-subjettiness axis
`fj_trackSipdSig_1_1`	Float_t	Second largest track 3D signed impact parameter significance associated to the second N-subjettiness axis
`fj_trackSip2dSigAboveCharm_0`	Float_t	Track 2D signed impact parameter significance of the first track lifting the combined invariant mass of the tracks above the c hadron threshold mass (1.5 GeV)
`fj_trackSip2dSigAboveBottom_0`	Float_t	Track 2D signed impact parameter significance of the first track lifting the combined invariant mass of the tracks above b hadron threshold mass (5.2 GeV)
`fj_trackSip2dSigAboveBottom_1`	Float_t	Track 2D signed impact parameter significance of the second track lifting the combined invariant mass of the tracks above b hadron threshold mass (5.2 GeV)
`fj_tau0_trackEtaRel_0`	Float_t	Smallest track pseudorapidity ∆η, relative to the jet axis, associated to the first N-subjettiness axis
`fj_tau0_trackEtaRel_1`	Float_t	Second smallest track pseudorapidity ∆η, relative to the jet axis, associated to the first N-subjettiness axis
`fj_tau0_trackEtaRel_2`	Float_t	Third smallest track pseudorapidity ∆η, relative to the jet axis, associated to the first N-subjettiness axis
`fj_tau1_trackEtaRel_0`	Float_t	Smallest track pseudorapidity ∆η, relative to the jet axis, associated to the second N-subjettiness axis
`fj_tau1_trackEtaRel_1`	Float_t	Second smallest track pseudorapidity ∆η, relative to the jet axis, associated to the second N-subjettiness axis
`fj_tau1_trackEtaRel_2`	Float_t	Third smallest track pseudorapidity ∆η, relative to the jet axis, associated to the second N-subjettiness axis
`fj_tau_vertexMass_0`	Float_t	Total SV mass for the first N-subjettiness axis, defined as the invariant mass of all tracks from SVs associated with the first N-subjettiness axis
`fj_tau_vertexMass_1`	Float_t	Total SV mass for the second N-subjettiness axis, defined as the invariant mass of all tracks from SVs associated with the second N-subjettiness axis
`fj_tau_vertexEnergyRatio_0`	Float_t	SV vertex energy ratio for the first N-subjettiness axis, defined as the total energy of all SVs associated with the first N-subjettiness axis divided by the total energy of all the tracks associated with the AK8 jet that are consistent with the PV
`fj_tau_vertexEnergyRatio_1`	Float_t	SV energy ratio for the second N-subjettiness axis, defined as the total energy of all SVs associated with the first N-subjettiness axis divided by the total energy of all the tracks associated with the AK8 jet that are consistent with the PV
`fj_tau_flightDistance2dSig_0`	Float_t	Transverse (2D) flight distance significance between the PV and the SV with the smallest uncertainty on the 3D flight distance associated to the first N-subjettiness axis
`fj_tau_flightDistance2dSig_1`	Float_t	Transverse (2D) flight distance significance between the PV and the SV with the smallest uncertainty on the 3D flight distance associated to the second N-subjettiness axis
`fj_tau_vertexDeltaR_0`	Float_t	Pseudoangular distance ∆R between the first N-subjettiness axis and SV direction
`n_pfcands`	Int_t	Number of particle flow (PF) candidates associated to the AK8 jet with transverse momentum greater than 0.95 GeV
`npfcands`	Float_t	Number of particle flow (PF) candidates associated to the AK8 jet with transverse momentum greater than 0.95 GeV
`pfcand_VTX_ass`	Int_t	PV association quality for the PF candiate: `UsedInFitTight=7`, the track is used in the PV fit and the weight is above 0.5; `UsedInFitLoose=6`, the track is used in the PV fit and the weight is below 0.5; `CompatibilityDz=5` the track is not used in fit but is very close in `dz` to the PV (`dzsig` < 5 or `dz` < 300 um); `CompatibilityBTag=4`, the track is not compatible with the PV but it is close to the nearest jet axis starting from the PV (distance to jet axis < 700 um); `NotReconstructedPrimary=0`, the track is not associated to any PV and is compatible with the beam spot hence it is likely to be originating from an interaction for which we did not reconstruct the PV (beam spot compatibility: `dxysig` < 2 and `dxy` < 200 um); `OtherDeltaZ=1`, none of the above criteria is satisfied, hence the closest in `dz` vertex is associated)
`pfcand_charge`	Float_t	Electric charge of the PF candidate
`pfcand_deltaR`	Float_t	Pseudoangular distance ∆R between the PF candidate and the AK8 jet axis
`pfcand_drminsv`	Float_t	Minimum pseudoangular distance ∆R between the associated SVs and the PF candidate
`pfcand_drsubjet1`	Float_t	Pseudoangular distance ∆R between the PF candidate and the first soft drop subjet
`pfcand_drsubjet2`	Float_t	Pseudoangular distance ∆R between the PF candidate and the second soft drop subjet
`pfcand_dxy`	Float_t	Transverse (2D) impact paramater of the PF candidate, defined as the distance of closest approach of the PF candidate trajectory to the beam line in the transverse plane to the beam
`pfcand_dxysig`	Float_t	Transverse (2D) impact paramater significance of the PF candidate
`pfcand_dz`	Float_t	Longitudinal impact parameter, defined as the distance of closest approach of the PF candidate trajectory to the PV projected on to the z direction
`pfcand_dzsig`	Float_t	Longitudinal impact parameter significance of the PF candidate
`pfcand_erel`	Float_t	Energy of the PF candidate divided by the energy of the AK8 jet
`pfcand_etarel`	Float_t	Pseudorapidity of the PF candidate relative to the AK8 jet axis
`pfcand_phirel`	Float_t	Azimuthal angular distance ∆ϕ between the PF candidate and the AK8 jet axis
`pfcand_ptrel`	Float_t	Transverse momentum of the PF candidate divided by the transverse momentum of the AK8 jet
`pfcand_fromPV`	Float_t	Integer indicating whether the PF candidate is consistent with the PV: `PVUsedInFit=3`, if the track is used in the PV fit; `PVTight=2` if the track is not used in the fit of any of the other PVs and is closest in z to the PV, `PVLoose=1` if the track is closest in z to a PV other then the PV; `NoPV=0` if the track is used in the fit of another PV
`pfcand_hcalFrac`	Float_t	Fraction of energy of the PF candidate deposited in the hadron calorimeter
`pfcand_isChargedHad`	Float_t	Boolean that is 1 if the PF candidate is classified as a charged hadron
`pfcand_isEl`	Float_t	Boolean that is 1 if the PF candidate is classified as an electron
`pfcand_isGamma`	Float_t	Boolean that is 1 if the PF candidate is classified as an photon
`pfcand_isMu`	Float_t	Boolean that is 1 if the PF candidate is classified as an muon
`pfcand_isNeutralHad`	Float_t	Boolean that is 1 if the PF candidate is classified as a neutral hadron
`pfcand_lostInnerHits`	Float_t	Integer with information related to inner silicon tracker hits for the PF candidate: `validHitInFirstPixelBarrelLayer=-1`, if the track has a valid hit in the first pixel barrel layer; `noLostInnerHits=0` if it does not have such hit because of geometrical or detector inefficiencies (i.e. the hit wasn’t expected to be there); `oneLostHit=1`, if the track extrapolation towards the beam line crosses an active detector but no hit is found there; `moreLostHits=2` if there are at least two missing expected inner hits
`pfcand_mass`	Float_t	Mass of the PF candidate
`pfcand_puppiw`	Float_t	Pileup per-particle identification (PUPPI) weight indicating whether the PF candidate is pileup-like (0) or not (1)
`n_tracks`	Int_t	Number of tracks associated with the AK8 jet
`ntracks`	Float_t	Number of tracks associated with the AK8 jet
`trackBTag_DeltaR`	Float_t	Pseudoangular distance ∆R between the track and the AK8 jet axis
`trackBTag_Eta`	Float_t	Pseudorapidity η of the track
`trackBTag_EtaRel`	Float_t	Pseudorapidity ∆η of the track relative the AK8 jet axis
`trackBTag_JetDistVal`	Float_t	Minimum track approach distance to the AK8 jet axis
`trackBTag_Momentum`	Float_t	Momentum of the track
`trackBTag_PPar`	Float_t	Component of track momentum parallel to the AK8 jet axis
`trackBTag_PParRatio`	Float_t	Component of track momentum parallel to the AK8 jet axis, normalized to the track momentum
`trackBTag_PtRatio`	Float_t	Component of track momentum perpendicular to the AK8 jet axis, normalized to the track momentum
`trackBTag_PtRel`	Float_t	Component of track momentum perpendicular to the AK8 jet axis
`trackBTag_Sip2dVal`	Float_t	Transverse (2D) signed impact paramater of the track
`trackBTag_Sip2dSig`	Float_t	Transverse (2D) signed impact paramater significance of the track
`trackBTag_Sip3dSig`	Float_t	3D signed impact parameter significance of the track
`trackBTag_Sip3dVal`	Float_t	3D signed impact parameter of the track
`track_VTX_ass`	Float_t	PV association quality for the track: `UsedInFitTight=7`, the track is used in the PV fit and the weight is above 0.5; `UsedInFitLoose=6`, the track is used in the PV fit and the weight is below 0.5; `CompatibilityDz=5` the track is not used in fit but is very close in `dz` to the PV (`dzsig` < 5 or `dz` < 300 um); `CompatibilityBTag=4`, the track is not compatible with the PV but it is close to the nearest jet axis starting from the PV (distance to jet axis < 700 um); `NotReconstructedPrimary=0`, the track is not associated to any PV and is compatible with the BeamSpot hence it is likely to be originating from an interaction for which we did not reconstruct the PV (beam spot compatibility: `dxysig` < 2 and `dxy` < 200 um); `OtherDeltaZ=1`, none of the above criteria is satisfied, hence the closest in dZ vertex is associated)
`track_charge`	Float_t	Electric charge of the charged PF candidate
`track_deltaR`	Float_t	Pseudoangular distance (∆R) between the charged PF candidate and the AK8 jet axis
`track_detadeta`	Float_t	Track covariance matrix entry (eta, eta)
`track_dlambdadz`	Float_t	Track covariance matrix entry (lambda, dz)
`track_dphidphi`	Float_t	Track covariance matrix entry (phi, phi)
`track_dphidxy`	Float_t	Track covariance matrix entry (phi, xy)
`track_dptdpt`	Float_t	Track covariance matrix entry (pT, pT)
`track_dxydxy`	Float_t	Track covariance matrix entry (dxy, dxy)
`track_dxydz`	Float_t	Track covariance matrix entry (dxy, dz)
`track_dzdz`	Float_t	Track covariance matrix entry (dz, dz)
`track_drminsv`	Float_t	Minimum pseudoangular distance ∆R between the associated SVs and the charged PF candidate
`track_drsubjet1`	Float_t	Pseudoangular distance ∆R between the charged PF candidate and the first soft drop subjet
`track_drsubjet2`	Float_t	Pseudoangular distance ∆R between the charged PF candidate and the second soft drop subjet
`track_dxy`	Float_t	Transverse (2D) impact parameter of the track, defined as the distance of closest approach of the track trajectory to the beam line in the transverse plane to the beam
`track_dxysig`	Float_t	Transverse (2D) impact parameter significance of the track
`track_dz`	Float_t	Longitudinal impact parameter, defined as the distance of closest approach of the track trajectory to the PV projected on to the z direction
`track_dzsig`	Float_t	Longitudinal impact parameter significance of the track
`track_erel`	Float_t	Energy of the charged PF candidate divided by the energy of the AK8 jet
`track_etarel`	Float_t	Pseudorapidity ∆η of the track relative to the jet axis
`track_fromPV`	Float_t	Integer indicating whether the charged PF candidate is consistent with the PV: `PVUsedInFit=3`, if the track is used in the PV fit; `PVTight=2` if the track is not used in the fit of any of the other PVs and is closest in z to the PV, `PVLoose=1` if the track is closest in z to a PV other then the PV; `NoPV=0` if the track is used in the fit of another PV
`track_isChargedHad`	Float_t	Boolean that is 1 if the charged PF candidate is classified as a charged hadron
`track_isEl`	Float_t	Boolean that is 1 if the charged PF candidate is classified as an electron
`track_isMu`	Float_t	Boolean that is 1 if the charged PF candidate is classified as a muon
`track_lostInnerHits`	Float_t	Integer with information related to inner silicon tracker hits for the track: `validHitInFirstPixelBarrelLayer=-1`, if the track has a valid hit in the first pixel barrel layer; `noLostInnerHits=0` if it does not have such hit because of geometrical or detector inefficiencies (i.e. the hit wasn’t expected to be there); `oneLostHit=1`, if the track extrapolation towards the beam line crosses an active detector but no hit is found there; `moreLostHits=2` if there are at least two missing expected inner hits
`track_mass`	Float_t	Mass of the charged PF candidate
`track_normchi2`	Float_t	Normalized χ2 of the track fit
`track_phirel`	Float_t	Azimuthal angular distance ∆ϕ between the charged PF candidate and the AK8 jet axis
`track_pt`	Float_t	Transverse momentum of the charged PF candidate
`track_ptrel`	Float_t	Transverse momentum of the charged PF candidate divided by the transverse momentum of the AK8 jet
`track_puppiw`	Float_t	Pileup per-particle identification (PUPPI) weight indicating whether the PF candidate is pileup-like (0) or not (1)
`track_quality`	Float_t	Track quality: `undefQuality=-1`; `loose=0`; `tight=1`; `highPurity=2`; `confirmed=3`, if track found by more than one iteration; `looseSetWithPV=5`; `highPuritySetWithPV=6`, `discarded=7` if a better track found; `qualitySize=8`
`n_sv`	Int_t	Number of secondary vertices (SV) associated with the AK8 jet (∆R < 0.8)
`nsv`	Float_t	Number of secondary vertices (SV) associated with the AK8 jet (∆R < 0.8)
`sv_chi2`	Float_t	χ2 of the vertex fit
`sv_ndf`	Float_t	number of degrees of freedom of the vertex fit
`sv_normchi2`	Float_t	χ2 divided by the number of degrees of freedom for the vertex fit
`sv_costhetasvpv`	Float_t	Cosine of the angle cos(θ) between the SV and the PV
`sv_d3d`	Float_t	3D flight distance of the SV
`sv_d3derr`	Float_t	3D flight distance uncertainty of the SV
`sv_d3dsig`	Float_t	3D flight distance significance of the SV
`sv_dxy`	Float_t	Transverse (2D) flight distance of the SV
`sv_dxyerr`	Float_t	Transverse (2D) flight distance uncertainty of the SV
`sv_dxysig`	Float_t	Transverse (2D) flight distance significance of the SV
`sv_deltaR`	Float_t	Pseudoangular distance ∆R between the SV and the AK8 jet
`sv_erel`	Float_t	Energy of the SV divided by the energy of the AK8 jet
`sv_etarel`	Float_t	Pseudorapidity ∆η of the SV relative to the AK8 jet axis
`sv_mass`	Float_t	Mass of the SV
`sv_ntracks`	Float_t	Number of tracks associated with the SV
`sv_phirel`	Float_t	Azimuthal angular distance ∆ϕ of the SV relative to the jet axis
`sv_pt`	Float_t	Transverse momentum of the SV
`sv_ptrel`	Float_t	Transverse momentum of the SV divided by the transverse momentum of the AK8 jet

Particle Physics and Machine Learning