TLorentzVector is a general four-vector class, which can be used either for the description of position and time (x,y,z,t) or momentum and energy (px,py,pz,E).
Declaration
TLorentzVector has been implemented as a set a TVector3 and a Double_t variable. By default all components are initialized by zero.
For backward compatibility there are two constructors from an Double_t and Float_t C array.
Access to the components
There are two sets of access functions to the components of a LorentzVector: X(), Y(), Z(), T() and Px(), Py(), Pz() and E(). Both sets return the same values but the first set is more relevant for use where TLorentzVector describes a combination of position and time and the second set is more relevant where TLorentzVector describes momentum and energy:
Double_t xx =v.X();
...
Double_t tt = v.T();
Double_t px = v.Px();
...
Double_t ee = v.E();
The components of TLorentzVector can also accessed by index:
You can use the Vect() member function to get the vector component of TLorentzVector:
For setting components also two sets of member functions can be used:
v.SetX(1.); or v.SetPx(1.);
... ...
v.SetT(1.); v.SetE(1.);
To set more the one component by one call you can use the SetVect() function for the TVector3 part or SetXYZT(), SetPxPyPzE(). For convenience there is
also a SetXYZM():
v.SetPxPyPzE(px,py,pz,e);
Vector components in non-cartesian coordinate systems
There are a couple of member functions to get and set the TVector3 part of the parameters in spherical coordinate systems:
Double_t
m, theta, cost, phi, pp, pp2, ppv2, pp2v2;
m = v.Rho();
t = v.Theta();
cost = v.CosTheta();
phi = v.Phi();
v.SetRho(10.);
or get information about the r-coordinate in cylindrical systems:
Double_t pp, pp2, ppv2, pp2v2;
pp = v.Perp();
pp2 = v.Perp2();
ppv2 = v.Perp(v1);
pp2v2 = v.Perp(v1);
for convenience there are two more set functions SetPtEtaPhiE(pt,eta,phi,e); and SetPtEtaPhiM(pt,eta,phi,m);
Arithmetic and comparison operators
The TLorentzVector class provides operators to add, subtract or compare four-vectors:
v3 = -v1;
v1 = v2+v3;
v1+= v3;
v1 = v2 + v3;
v1-= v3;
if (v1 == v2) {...}
if(v1 != v3) {...}
Magnitude/Invariant mass, beta, gamma, scalar product
The scalar product of two four-vectors is calculated with the (-,-,-,+) metric,
i.e. s = v1*v2 = t1*t2-x1*x2-y1*y2-z1*z2 The magnitude squared mag2 of a four-vector is therefore:
mag2 = v*v = t*t-x*x-y*y-
z*
z It mag2 is negative mag = -Sqrt(-mag*mag). The member functions are:
Double_t s, s2;
s = v1*v2;
s2 = v.
Mag2(); or s2 = v.M2();
s = v.Mag(); s = v.M();
Since in case of momentum and energy the magnitude has the meaning of invariant mass TLorentzVector provides the more meaningful aliases M2() and M(); The member functions Beta() and Gamma() returns beta and gamma = 1/Sqrt(1-beta*beta).
Lorentz boost
A boost in a general direction can be parameterised with three parameters which can be taken as the components of a three vector b = (bx,by,bz). With x = (x,y,z) and gamma = 1/Sqrt(1-beta*beta) (beta being the module of vector b), an arbitrary active Lorentz boost transformation (from the rod frame to the original frame) can be written as:
x = x
' + (gamma-1)/(beta*beta) * (b*x') * b +
gamma * t
' * bt = gamma (t'+ b*x').
The member function Boost() performs a boost transformation from the rod frame to the original frame. BoostVector() returns a TVector3 of the spatial components divided by the time component:
v.Boost(bx,by,bz);
v.Boost(b);
b = v.BoostVector();
Rotations
There are four sets of functions to rotate the TVector3 component of a TLorentzVector:
rotation around axes
v.RotateY(.5);
v.RotateZ(.99);
rotation around an arbitrary axis
v.Rotate(TMath::Pi()/4., v1); // rotation around v1
transformation from rotated frame
Misc
Angle between two vectors
Double_t a = v1.
Angle(v2.Vect());
Light-cone components
Member functions Plus() and Minus() return the positive and negative light-cone components:
Double_t pcone = v.Plus();
Double_t mcone = v.Minus();
CAVEAT: The values returned are T{+,-}Z. It is known that some authors find it easier to define these components as (T{+,-}Z)/sqrt(2). Thus check what definition is used in the physics you're working in and adapt your code accordingly.
A general Lorentz transformation see class TLorentzRotation can be used by the Transform() member function, the *= or operator of the TLorentzRotation class:
Definition at line 32 of file TLorentzVector.h.
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| | TLorentzVector () |
| |
| | TLorentzVector (Double_t x, Double_t y, Double_t z, Double_t t) |
| |
| | TLorentzVector (const Double_t *carray) |
| |
| | TLorentzVector (const Float_t *carray) |
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| | TLorentzVector (const TVector3 &vector3, Double_t t) |
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| | TLorentzVector (const TLorentzVector &lorentzvector) |
| |
| virtual | ~TLorentzVector () |
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| Double_t | Angle (const TVector3 &v) const |
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| Double_t | Beta () const |
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| void | Boost (Double_t, Double_t, Double_t) |
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| void | Boost (const TVector3 &) |
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| TVector3 | BoostVector () const |
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| Double_t | CosTheta () const |
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| Double_t | DeltaPhi (const TLorentzVector &) const |
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| Double_t | DeltaR (const TLorentzVector &) const |
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| Double_t | Dot (const TLorentzVector &) const |
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| Double_t | DrEtaPhi (const TLorentzVector &) const |
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| Double_t | E () const |
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| Double_t | Energy () const |
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| Double_t | Et () const |
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| Double_t | Et (const TVector3 &) const |
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| Double_t | Et2 () const |
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| Double_t | Et2 (const TVector3 &) const |
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| Double_t | Eta () const |
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| TVector2 | EtaPhiVector () |
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| Double_t | Gamma () const |
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| void | GetXYZT (Double_t *carray) const |
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| void | GetXYZT (Float_t *carray) const |
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| Double_t | M () const |
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| Double_t | M2 () const |
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| Double_t | Mag () const |
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| Double_t | Mag2 () const |
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| Double_t | Minus () const |
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| Double_t | Mt () const |
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| Double_t | Mt2 () const |
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| Bool_t | operator!= (const TLorentzVector &) const |
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| Double_t | operator() (int i) const |
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| Double_t & | operator() (int i) |
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| TLorentzVector | operator* (Double_t a) const |
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| Double_t | operator* (const TLorentzVector &) const |
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| TLorentzVector & | operator*= (Double_t a) |
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| TLorentzVector & | operator*= (const TRotation &) |
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| TLorentzVector & | operator*= (const TLorentzRotation &) |
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| TLorentzVector | operator+ (const TLorentzVector &) const |
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| TLorentzVector & | operator+= (const TLorentzVector &) |
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| TLorentzVector | operator- (const TLorentzVector &) const |
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| TLorentzVector | operator- () const |
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| TLorentzVector & | operator-= (const TLorentzVector &) |
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| TLorentzVector & | operator= (const TLorentzVector &) |
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| Bool_t | operator== (const TLorentzVector &) const |
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| Double_t | operator[] (int i) const |
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| Double_t & | operator[] (int i) |
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| Double_t | P () const |
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| Double_t | Perp () const |
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| Double_t | Perp (const TVector3 &v) const |
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| Double_t | Perp2 () const |
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| Double_t | Perp2 (const TVector3 &v) const |
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| Double_t | Phi () const |
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| Double_t | Plus () const |
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| virtual void | Print (Option_t *option="") const |
| | Print the TLorentz vector components as (x,y,z,t) and (P,eta,phi,E) representations. More...
|
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| Double_t | PseudoRapidity () const |
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| Double_t | Pt () const |
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| Double_t | Pt (const TVector3 &v) const |
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| Double_t | Px () const |
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| Double_t | Py () const |
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| Double_t | Pz () const |
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| Double_t | Rapidity () const |
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| Double_t | Rho () const |
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| void | Rotate (Double_t, const TVector3 &) |
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| void | RotateUz (TVector3 &newUzVector) |
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| void | RotateX (Double_t angle) |
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| void | RotateY (Double_t angle) |
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| void | RotateZ (Double_t angle) |
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| void | SetE (Double_t a) |
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| void | SetPerp (Double_t) |
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| void | SetPhi (Double_t phi) |
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| void | SetPtEtaPhiE (Double_t pt, Double_t eta, Double_t phi, Double_t e) |
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| void | SetPtEtaPhiM (Double_t pt, Double_t eta, Double_t phi, Double_t m) |
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| void | SetPx (Double_t a) |
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| void | SetPxPyPzE (Double_t px, Double_t py, Double_t pz, Double_t e) |
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| void | SetPy (Double_t a) |
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| void | SetPz (Double_t a) |
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| void | SetRho (Double_t rho) |
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| void | SetT (Double_t a) |
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| void | SetTheta (Double_t theta) |
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| void | SetVect (const TVector3 &vect3) |
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| void | SetVectM (const TVector3 &spatial, Double_t mass) |
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| void | SetVectMag (const TVector3 &spatial, Double_t magnitude) |
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| void | SetX (Double_t a) |
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| void | SetXYZM (Double_t x, Double_t y, Double_t z, Double_t m) |
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| void | SetXYZT (Double_t x, Double_t y, Double_t z, Double_t t) |
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| void | SetY (Double_t a) |
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| void | SetZ (Double_t a) |
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| Double_t | T () const |
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| Double_t | Theta () const |
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| TLorentzVector & | Transform (const TRotation &) |
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| TLorentzVector & | Transform (const TLorentzRotation &) |
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| TVector3 | Vect () const |
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| Double_t | X () const |
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| Double_t | Y () const |
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| Double_t | Z () const |
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ROOT 6.13/01 - Reference Guide Generated on Sun Jan 7 2018 01:05:53 (GVA Time) using Doxygen 1.8.13.