Modules
	4-vector comparison functions (for sorting)

Functions
template<typename V4TYPE , typename std::enable_if< HasXYZT< V4TYPE >::value, int >::type DUMMY = 0>
	Rivet::FourVector::FourVector (const V4TYPE &other)

	Rivet::FourVector::FourVector (const Vector< 4 > &other)

	Rivet::FourVector::FourVector (const double t, const double x, const double y, const double z)

double	Rivet::FourVector::t () const

double	Rivet::FourVector::t2 () const

FourVector &	Rivet::FourVector::setT (const double t)

double	Rivet::FourVector::x () const

double	Rivet::FourVector::x2 () const

FourVector &	Rivet::FourVector::setX (const double x)

double	Rivet::FourVector::y () const

double	Rivet::FourVector::y2 () const

FourVector &	Rivet::FourVector::setY (const double y)

double	Rivet::FourVector::z () const

double	Rivet::FourVector::z2 () const

FourVector &	Rivet::FourVector::setZ (const double z)

double	Rivet::FourVector::invariant () const

bool	Rivet::FourVector::isNull () const

double	Rivet::FourVector::angle (const FourVector &v) const
	Angle between this vector and another.

double	Rivet::FourVector::angle (const Vector3 &v3) const
	Angle between this vector and another (3-vector)

double	Rivet::FourVector::polarRadius2 () const
	Mod-square of the projection of the 3-vector on to the \( x-y \) plane This is a more efficient function than `polarRadius`, as it avoids the square root. Use it if you only need the squared value, or e.g. an ordering by magnitude.

double	Rivet::FourVector::perp2 () const
	Synonym for polarRadius2.

double	Rivet::FourVector::rho2 () const
	Synonym for polarRadius2.

double	Rivet::FourVector::polarRadius () const
	Magnitude of projection of 3-vector on to the \( x-y \) plane.

double	Rivet::FourVector::perp () const
	Synonym for polarRadius.

double	Rivet::FourVector::rho () const
	Synonym for polarRadius.

Vector3	Rivet::FourVector::polarVec () const
	Projection of 3-vector on to the \( x-y \) plane.

Vector3	Rivet::FourVector::perpVec () const
	Synonym for polarVec.

Vector3	Rivet::FourVector::rhoVec () const
	Synonym for polarVec.

double	Rivet::FourVector::azimuthalAngle (const PhiMapping mapping=ZERO_2PI) const
	Angle subtended by the 3-vector's projection in x-y and the x-axis.

double	Rivet::FourVector::phi (const PhiMapping mapping=ZERO_2PI) const
	Synonym for azimuthalAngle.

double	Rivet::FourVector::polarAngle () const
	Angle subtended by the 3-vector and the z-axis.

double	Rivet::FourVector::theta () const
	Synonym for polarAngle.

double	Rivet::FourVector::pseudorapidity () const
	Pseudorapidity (defined purely by the 3-vector components)

double	Rivet::FourVector::eta () const
	Synonym for pseudorapidity.

double	Rivet::FourVector::abspseudorapidity () const
	Get the \( \|\eta\| \) directly.

double	Rivet::FourVector::abseta () const
	Get the \( \|\eta\| \) directly (alias).

Vector3	Rivet::FourVector::vector3 () const
	Get the spatial part of the 4-vector as a 3-vector.

	Rivet::FourVector::operator Vector3 () const
	Implicit cast to a 3-vector.

double	Rivet::FourVector::contract (const FourVector &v) const
	Contract two 4-vectors, with metric signature (+ - - -).

double	Rivet::FourVector::dot (const FourVector &v) const
	Contract two 4-vectors, with metric signature (+ - - -).

double	Rivet::FourVector::operator* (const FourVector &v) const
	Contract two 4-vectors, with metric signature (+ - - -).

FourVector &	*Rivet::FourVector::operator=** (double a)
	Multiply by a scalar.

FourVector &	Rivet::FourVector::operator/= (double a)
	Divide by a scalar.

FourVector &	Rivet::FourVector::operator+= (const FourVector &v)
	Add to this 4-vector.

FourVector &	Rivet::FourVector::operator-= (const FourVector &v)
	Subtract from this 4-vector. NB time as well as space components are subtracted.

FourVector	Rivet::FourVector::operator- () const
	Multiply all components (space and time) by -1.

FourVector	Rivet::FourVector::reverse () const
	Multiply space components only by -1.

template<typename V4TYPE , typename std::enable_if< HasXYZT< V4TYPE >::value, int >::type DUMMY = 0>
	Rivet::FourMomentum::FourMomentum (const V4TYPE &other)

	Rivet::FourMomentum::FourMomentum (const Vector< 4 > &other)

	Rivet::FourMomentum::FourMomentum (const double E, const double px, const double py, const double pz)

Friends
FourVector	Rivet::FourVector::multiply (const double a, const FourVector &v)

FourVector	Rivet::FourVector::multiply (const FourVector &v, const double a)

FourVector	Rivet::FourVector::add (const FourVector &a, const FourVector &b)

FourVector	Rivet::FourVector::transform (const LorentzTransform &lt, const FourVector &v4)

FourMomentum	Rivet::FourMomentum::multiply (const double a, const FourMomentum &v)

FourMomentum	Rivet::FourMomentum::multiply (const FourMomentum &v, const double a)

FourMomentum	Rivet::FourMomentum::add (const FourMomentum &a, const FourMomentum &b)

FourMomentum	Rivet::FourMomentum::transform (const LorentzTransform &lt, const FourMomentum &v4)

Coordinate setters
FourMomentum &	Rivet::FourMomentum::setE (double E)
	Set energy \( E \) (time component of momentum).

FourMomentum &	Rivet::FourMomentum::setPx (double px)
	Set x-component of momentum \( p_x \).

FourMomentum &	Rivet::FourMomentum::setPy (double py)
	Set y-component of momentum \( p_y \).

FourMomentum &	Rivet::FourMomentum::setPz (double pz)
	Set z-component of momentum \( p_z \).

FourMomentum &	Rivet::FourMomentum::setPE (double px, double py, double pz, double E)
	Set the p coordinates and energy simultaneously.

FourMomentum &	Rivet::FourMomentum::setXYZE (double px, double py, double pz, double E)
	Alias for setPE.

FourMomentum &	Rivet::FourMomentum::setPM (double px, double py, double pz, double mass)
	Set the p coordinates and mass simultaneously.

FourMomentum &	Rivet::FourMomentum::setXYZM (double px, double py, double pz, double mass)
	Alias for setPM.

FourMomentum &	Rivet::FourMomentum::setEtaPhiME (double eta, double phi, double mass, double E)

FourMomentum &	Rivet::FourMomentum::setEtaPhiMPt (double eta, double phi, double mass, double pt)

FourMomentum &	Rivet::FourMomentum::setRapPhiME (double y, double phi, double mass, double E)

FourMomentum &	Rivet::FourMomentum::setRapPhiMPt (double y, double phi, double mass, double pt)

FourMomentum &	Rivet::FourMomentum::setThetaPhiME (double theta, double phi, double mass, double E)

FourMomentum &	Rivet::FourMomentum::setThetaPhiMPt (double theta, double phi, double mass, double pt)

FourMomentum &	Rivet::FourMomentum::setPtPhiME (double pt, double phi, double mass, double E)

Accessors
double	Rivet::FourMomentum::E () const
	Get energy \( E \) (time component of momentum).

double	Rivet::FourMomentum::E2 () const
	Get energy-squared \( E^2 \).

double	Rivet::FourMomentum::px () const
	Get x-component of momentum \( p_x \).

double	Rivet::FourMomentum::px2 () const
	Get x-squared \( p_x^2 \).

double	Rivet::FourMomentum::py () const
	Get y-component of momentum \( p_y \).

double	Rivet::FourMomentum::py2 () const
	Get y-squared \( p_y^2 \).

double	Rivet::FourMomentum::pz () const
	Get z-component of momentum \( p_z \).

double	Rivet::FourMomentum::pz2 () const
	Get z-squared \( p_z^2 \).

double	Rivet::FourMomentum::mass () const
	Get the mass \( m = \sqrt{E^2 - p^2} \) (the Lorentz self-invariant). More...

double	Rivet::FourMomentum::mass2 () const
	Get the squared mass \( m^2 = E^2 - p^2 \) (the Lorentz self-invariant).

Vector3	Rivet::FourMomentum::p3 () const
	Get 3-momentum part, \( p \).

double	Rivet::FourMomentum::p () const
	Get the modulus of the 3-momentum.

double	Rivet::FourMomentum::p2 () const
	Get the modulus-squared of the 3-momentum.

double	Rivet::FourMomentum::rapidity () const
	Calculate the rapidity.

double	Rivet::FourMomentum::rap () const
	Alias for rapidity.

double	Rivet::FourMomentum::absrapidity () const
	Absolute rapidity.

double	Rivet::FourMomentum::absrap () const
	Absolute rapidity.

Vector3	Rivet::FourMomentum::pTvec () const
	Calculate the transverse momentum vector \( \vec{p}_T \).

Vector3	Rivet::FourMomentum::ptvec () const
	Synonym for pTvec.

double	Rivet::FourMomentum::pT2 () const
	Calculate the squared transverse momentum \( p_T^2 \).

double	Rivet::FourMomentum::pt2 () const
	Calculate the squared transverse momentum \( p_T^2 \).

double	Rivet::FourMomentum::pT () const
	Calculate the transverse momentum \( p_T \).

double	Rivet::FourMomentum::pt () const
	Calculate the transverse momentum \( p_T \).

double	Rivet::FourMomentum::Et2 () const
	Calculate the transverse energy \( E_T^2 = E^2 \sin^2{\theta} \).

double	Rivet::FourMomentum::Et () const
	Calculate the transverse energy \( E_T = E \sin{\theta} \).

Lorentz boost factors and vectors
double	Rivet::FourMomentum::gamma () const

Vector3	Rivet::FourMomentum::gammaVec () const

double	Rivet::FourMomentum::beta () const

Vector3	Rivet::FourMomentum::betaVec () const

Arithmetic operators
FourMomentum &	*Rivet::FourMomentum::operator=** (double a)
	Multiply by a scalar.

FourMomentum &	Rivet::FourMomentum::operator/= (double a)
	Divide by a scalar.

FourMomentum &	Rivet::FourMomentum::operator+= (const FourMomentum &v)
	Add to this 4-vector. NB time as well as space components are added.

FourMomentum &	Rivet::FourMomentum::operator-= (const FourMomentum &v)
	Subtract from this 4-vector. NB time as well as space components are subtracted.

FourMomentum	Rivet::FourMomentum::operator- () const
	Multiply all components (time and space) by -1.

FourMomentum	Rivet::FourMomentum::reverse () const
	Multiply space components only by -1.

Factory functions
static FourMomentum	Rivet::FourMomentum::mkXYZE (double px, double py, double pz, double E)
	Make a vector from (px,py,pz,E) coordinates.

static FourMomentum	Rivet::FourMomentum::mkXYZM (double px, double py, double pz, double mass)
	Make a vector from (px,py,pz) coordinates and the mass.

static FourMomentum	Rivet::FourMomentum::mkEtaPhiME (double eta, double phi, double mass, double E)
	Make a vector from (eta,phi,energy) coordinates and the mass.

static FourMomentum	Rivet::FourMomentum::mkEtaPhiMPt (double eta, double phi, double mass, double pt)
	Make a vector from (eta,phi,pT) coordinates and the mass.

static FourMomentum	Rivet::FourMomentum::mkRapPhiME (double y, double phi, double mass, double E)
	Make a vector from (y,phi,energy) coordinates and the mass.

static FourMomentum	Rivet::FourMomentum::mkRapPhiMPt (double y, double phi, double mass, double pt)
	Make a vector from (y,phi,pT) coordinates and the mass.

static FourMomentum	Rivet::FourMomentum::mkThetaPhiME (double theta, double phi, double mass, double E)
	Make a vector from (theta,phi,energy) coordinates and the mass.

static FourMomentum	Rivet::FourMomentum::mkThetaPhiMPt (double theta, double phi, double mass, double pt)
	Make a vector from (theta,phi,pT) coordinates and the mass.

static FourMomentum	Rivet::FourMomentum::mkPtPhiME (double pt, double phi, double mass, double E)
	Make a vector from (pT,phi,energy) coordinates and the mass.

Detailed Description

Function Documentation

◆ beta()

double Rivet::FourMomentum::beta ( ) const

inline

Calculate the boost factor \( \beta \).

Note: \( \beta = pc/E \) so we rely on the c=1 convention

References Rivet::FourMomentum::E(), and Rivet::FourMomentum::p().

◆ betaVec()

Vector3 Rivet::FourMomentum::betaVec ( ) const

inline

Calculate the boost vector \( \vec{\beta} \).

Note: \( \beta = pc/E \) so we rely on the c=1 convention

References Rivet::FourMomentum::E(), and Rivet::FourMomentum::p3().

Referenced by Rivet::LorentzTransform::mkFrameTransform(), and Rivet::LorentzTransform::mkObjTransform().

◆ gamma()

double Rivet::FourMomentum::gamma ( ) const

inline

Calculate the boost factor \( \gamma \).

Note: \( \gamma = E/mc^2 \) so we rely on the c=1 convention

References Rivet::FourMomentum::E2(), and Rivet::FourMomentum::mass2().

Referenced by Rivet::FourMomentum::gammaVec().

◆ gammaVec()

Vector3 Rivet::FourMomentum::gammaVec ( ) const

inline

Calculate the boost vector \( \vec{\gamma} \).

Note: \( \gamma = E/mc^2 \) so we rely on the c=1 convention

References Rivet::FourMomentum::gamma(), Rivet::FourMomentum::p3(), and Rivet::Vector3::unit().

◆ mass()

double Rivet::FourMomentum::mass ( ) const

inline

Get the mass \( m = \sqrt{E^2 - p^2} \) (the Lorentz self-invariant).

For spacelike momenta, the mass will be -sqrt(|mass2|).

References Rivet::FourMomentum::mass2(), and Rivet::sign().

◆ setEtaPhiME()

FourMomentum & Rivet::FourMomentum::setEtaPhiME	(	double	eta,
		double	phi,
		double	mass,
		double	E
	)

inline

Set the vector state from (eta,phi,energy) coordinates and the mass

eta = -ln(tan(theta/2)) -> theta = 2 atan(exp(-eta))

References Rivet::FourMomentum::E(), Rivet::FourVector::eta(), Rivet::FourMomentum::mass(), Rivet::FourVector::phi(), Rivet::FourMomentum::setThetaPhiME(), and Rivet::FourVector::theta().

Referenced by Rivet::FourMomentum::mkEtaPhiME().

◆ setEtaPhiMPt()

FourMomentum & Rivet::FourMomentum::setEtaPhiMPt	(	double	eta,
		double	phi,
		double	mass,
		double	pt
	)

inline

Set the vector state from (eta,phi,pT) coordinates and the mass

eta = -ln(tan(theta/2)) -> theta = 2 atan(exp(-eta))

References Rivet::FourMomentum::E(), Rivet::FourVector::eta(), Rivet::FourMomentum::mass(), Rivet::FourMomentum::p(), Rivet::FourVector::phi(), Rivet::FourMomentum::pt(), Rivet::FourMomentum::setThetaPhiME(), Rivet::sqr(), and Rivet::FourVector::theta().

Referenced by Rivet::FourMomentum::mkEtaPhiMPt().

◆ setPtPhiME()

FourMomentum & Rivet::FourMomentum::setPtPhiME	(	double	pt,
		double	phi,
		double	mass,
		double	E
	)

inline

Set the vector state from (pT,phi,energy) coordinates and the mass

pz = sqrt(E^2 - mass^2 - pt^2)

References Rivet::FourMomentum::E(), Rivet::FourMomentum::mass(), Rivet::FourVector::phi(), Rivet::FourMomentum::pt(), Rivet::FourMomentum::px(), Rivet::FourMomentum::py(), Rivet::FourMomentum::pz(), Rivet::FourMomentum::setPE(), and Rivet::sqr().

Referenced by Rivet::FourMomentum::mkPtPhiME().

◆ setRapPhiME()

FourMomentum & Rivet::FourMomentum::setRapPhiME	(	double	y,
		double	phi,
		double	mass,
		double	E
	)

inline

Set the vector state from (y,phi,energy) coordinates and the mass

y = 0.5 * ln((E+pz)/(E-pz)) -> (E^2 - pz^2) exp(2y) = (E+pz)^2 & (E^2 - pz^2) exp(-2y) = (E-pz)^2 -> E = sqrt(pt^2 + m^2) cosh(y) -> pz = sqrt(pt^2 + m^2) sinh(y) -> sqrt(pt^2 + m^2) = E / cosh(y)

References Rivet::FourMomentum::E(), Rivet::FourMomentum::mass(), Rivet::FourVector::phi(), Rivet::FourMomentum::pt(), Rivet::FourMomentum::px(), Rivet::FourMomentum::py(), Rivet::FourMomentum::pz(), Rivet::FourMomentum::setPE(), and Rivet::sqr().

Referenced by Rivet::FourMomentum::mkRapPhiME(), and Rivet::FourMomentum::setRapPhiMPt().