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Kinematics

Methods

Constructor

Kinematics(Double_t enEleBeam, Double_t enIonBeam, Double_t crossAng);
  • requires beam energies and crossing angle, set by Analysis (at the macro level)
  • sets the following hard-coded settings:
    • mainFrame: the Lorentz frame in which calculations are performed, when there is ambiguity which frame to use
      • in general, we try to use Lorentz invariant formulas where possible
      • for frame-dependent formulas, we have these options (defined as mainFrame):
        • lab frame
        • head-on frame (default)
    • qComponentsMethod: how to obtain the virtual photon 4-momentum components, for some of the reconstruction methods (e.g., JB, DA)
      • see GetQWNu_* auxiliary methods below for details
      • options:
        • quadratic (default)
        • hadronic
        • electronic
  • sets beam momenta and boosts
  • sets other miscellaneous variables, such as default spin and polarization

Preparation

For DIS Calculators

For each event, to prepare an instance of Kinematics for calculations, set the following:

  • vecElectron: scattered electron 4-momentum
  • vecEleBeam and vecIonBeam: beam 4-momenta (if taking into account beam effects (generator level))
  • Hadronic Final State (HFS)
    • for Delphes, call GetHFS for reconstructed or GetTrueHFS for generated; both require several objects (see code)
      • note: GetHFS uses getTrackPID for smeared PID
    • for DD4hep/Juggler, use AddToHFS in particle loop, then at the end call SubtractElectronFromHFS to omit the scattered electron
      • don't forget to call ResetHFS() beforehand
    • HFS variables sigmah, Pxh, and Pyh, are needed for reconstruction methods that require the HFS

For SIDIS Single-Hadron Calculators

For each hadron, set vecHadron, the hadron 4-momentum

  • note that CalculateDIS should be called beforehand

For Jets

Currently implemented in AnalysisDelphes only!

  • call GetJets, which does the work
  • added flags to choose jet algorithm, jet radius, and minimum jet pT
  • alternatively, call GetBreitFrameJets (requires Centauro)

Calculators

Calculate DIS Kinematics

Bool_t CalculateDIS(TString recmethod);

This is the main method for calculating the DIS kinematics

  • boosts beams to head-on frame (used only as needed)
  • calls CalculateDISby* to do the calculations according to recmethod, which specifies the reconstruction method; this choice is set by Analysis (at the macro level); see below
    • required inputs depend on choice of reconstruction method (see below)
    • calculated quantities:
      • Q2
      • x
      • y
      • W
      • Nu
      • virtual photon 4-momentum vecQ
      • 4-momentum for W (vecW)
  • calculate additional boosts
    • C.O.M. frame of virtual photon and ion
    • ion rest frame
  • calculate depolarization factors (and epsilon and gamma)
Reconstruction Methods

One of the following methods will be called by CalculateDIS:

void CalculateDISbyElectron();
  • Electron method
  • requires electron 4-momentum
  • calls auxiliary method GetQWNu_electronic() to obtain vecQ, vecW, W, and Nu
  • calculates Q2, x, y
void CalculateDISbyJB();
  • Jacquet-Blondel method
  • requires HFS variables
    • also requires electron 4-momentum, if using GetQWNu_electronic()
  • calculates y, Q2, and x; the calculation of y depends on mainFrame since it involves the electron beam momentum
  • calculates vecQ, vecW, W, and Nu, depending on qComponentsMethod
void CalculateDISbyDA();
  • Double Angle method
  • requires HFS variables and electron 4-momentum
  • calculates Q2, x, and y, which depend on mainFrame
  • calculates vecQ, vecW, W, and Nu, depending on qComponentsMethod
void CalculateDISbyMixed();
  • Mixed Variables method
  • requires HFS variables and electron 4-momentum
  • calculates vecQ, vecW, W, and Nu, using GetQWNu_electronic()
  • calculate Q2
  • calculate y and x, which depend on mainFrame, since they require the electron beam momentum
void CalculateDISbySigma();
  • Sigma method
  • requires HFS variables and electron 4-momentum
  • calculates y, Q2, and x, which depend on mainFrame, since they require the scattered electron momentum
  • calculates vecQ, vecW, W, and Nu, depending on qComponentsMethod
void CalculateDISbyeSigma();
  • eSigma method
  • first calls CalculateDISbySigma()
  • calculate vecQ using scattered electron, followed by Q2
  • uses x from the Sigma method
  • calculates y from this Q2 and x
  • finally, calculates vecQ, vecW, W, and Nu, depending on qComponentsMethod
Auxiliary Methods
  • These methods calculate vecQ, vecW, W, and Nu; one of these will be called from CalculateDISby* methods, depending on the choice of qComponentsMethod:
void GetQWNu_electronic();
  • requires electron momentum
  • calculates 4-momenta vecQ and vecW by subtracting the scattered electron momenta from beam momenta
  • calculates W and Nu
void GetQWNu_hadronic();
  • requires HFS
  • calculates vecQ and vecW by the HFS 4-momentum and subtracting the ion beam (for vecQ)
  • calculates W and Nu
void GetQWNu_quadratic();
  • requires HFS, along with Q2 and y
  • solves quadratic equation for vecQ, vecW, W and Nu

Calculate Single-Hadron SIDIS Kinematics

void CalculateHadronKinematics();
  • requires DIS kinematics and vecHadron
  • calculates:
    • z
    • mX (missing mass)
    • xF
    • phiH
    • phiS (requires spin-up reference, set in constructor)
    • pT
    • qT

Calculate Jet Kinematics

void CalculateJetKinematics(fastjet::PseudoJet jet);
void CalculateBreitJetKinematics(fastjet::PseudoJet jet);
  • requires Jets (from GetJets or GetBreitFrameJets)
  • calculates:
    • qTjet
    • pTjet
    • zjet
    • jperp
    • ...

Find Truth Jets Matching Reco Jets

void CalculateJetResolution(fastjet::PseudoJet jet);
  • requires that GetJets and CalculateJetKinematics has run
  • for the input reconstructed jet, find the closest truth level jet
  • pass the kinematics of the matched truth level jet

Boosts

Several boost methods are available. For all of these, the first TLorentzVector parameter is copied to a new TLorentzVector; this copy is then boosted, and passed by reference as the second TLorentzVector parameter.

// boost from Lab frame Lvec to photon+ion C.o.m. frame Cvec
void BoostToComFrame(TLorentzVector Lvec, TLorentzVector &Cvec);

// boost from Lab frame Lvec to Ion rest frame Ivec
void BoostToIonFrame(TLorentzVector Lvec, TLorentzVector &Ivec);

// boost from Lab frame Lvec to ion+electron Beam c.o.m. frame Bvec
void BoostToBeamComFrame(TLorentzVector Lvec, TLorentzVector &Bvec);

// tranform from Lab frame Lvec to Head-on frame Hvec
void TransformToHeadOnFrame(TLorentzVector Lvec, TLorentzVector &Hvec);

// transform from Head-on frame Hvec back to Lab frame Lvec
void TransformBackToLabFrame(TLorentzVector Hvec, TLorentzVector &Lvec);
// tests and validation
void ValidateHeadOnFrame(); // test head-on frame boost

Miscellaneous Methods

// convert energy,mass to momentum
static Double_t EMtoP(Double_t energy, Double_t mass);

// vector projection: returns vA projected onto vB
static TVector3 Project(TVector3 vA, TVector3 vB);

// vector rejection: returns vC projected onto plane transverse to vD
static TVector3 Reject(TVector3 vC, TVector3 vD);

// calculate angle between two planes, spanned by vectors (e.g., phiH)
static Double_t PlaneAngle(TVector3 vA, TVector3 vB, TVector3 vC, TVector3 vD);

// shift angle to the range [-PI,+PI]
static Double_t AdjAngle(Double_t ang);

// particle masses
static Double_t ElectronMass() { return 0.000511; };
static Double_t ProtonMass()   { return 0.938272; };
static Double_t KaonMass()     { return 0.493677; };
static Double_t PionMass()     { return 0.139570; };

Variables

Most of these variables are public to allow for easy access

  • many calculator methods will modify / determine them; because of this, you need to understand which calculations calculate what, and what variables each calculation depends on
  • be careful not to 'accidentally' modify them!
// DIS
Double_t W, Q2, Nu, x, y, s;

// Single-hadron SIDIS
Double_t pLab, pTlab, phiLab, etaLab, z, pT, qT, mX, xF, phiH, phiS;

// HFS variables
Double_t sigmah, Pxh, Pyh;
TLorentzVector hadronSumVec;

// depolarization
Double_t gamma,epsilon;
// - factors A,B,C,V,W from [hep-ph/0611265] using notation from [1408.5721]
Double_t depolA, depolB, depolC, depolV, depolW;
// - ratios of factors, following notation of [1807.10606] eq. 2.3 (cf. eqs. 2.2a,b)
Double_t depolP1; // for A_UT*sin(phiH+phiS) (collins), A_UT*sin(3phiH-phiS) (pretzelosity)
Double_t depolP2; // for A_LL*const
Double_t depolP3; // for twist-3 A_UT
Double_t depolP4; // for A_LL*cos(phiH)

// lab-frame 4-vectors for beams, electron, hadron
TLorentzVector vecEleBeam, vecIonBeam;
TLorentzVector vecElectron, vecW, vecQ;
TLorentzVector vecHadron;

// jet objects
int jetAlgo;
double jetRad, jetMinPt; 

std::vector<fastjet::PseudoJet> jetsRec, jetsTrue;
std::vector<fastjet::PseudoJet> breitJetsRec, breitJetsTrue;
std::map<double, int> jetConstituents;
fastjet::ClusterSequence csRec;
fastjet::ClusterSequence csTrue;

// jet variables
Double_t zjet, pTjet, qTjet, mTjet, etajet, phijet, mjet, ejet;
Double_t deltaRjet;
int matchStatusjet;
Double_t pTmtjet, mTmtjet, etamtjet, phimtjet, mmtjet, emtjet;
std::vector<double> jperp;
std::vector<double> zhad_jet;
Double_t quarkpT; // struck quark information

Constants, set in constructor (they are not actually const, just generally treated as such):

// nucleon transverse spin; if you set this externally,
// it must be done before calculating phiS
Int_t tSpin; // should be +1 or -1
Int_t lSpin; // should be +1 or -1

// beam polarization
Double_t polT;
Double_t polL;
Double_t polBeam;