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Kinematics Class Reference

Kinematics is a utility class to calculate and transform kinematic variables. More...

 #include "Kinematics.h"

Public Member Functions

Detailed Description

The Kinematics class consists of a rich set of static methods that allows one to calculate kinematic variables common in DIS. These methods are heavily used in Sartre but are also quite useful for the user. All calculation are conducted in the most precise way, i.e. without neglecting the nucleon mass or even the electron mass. We strongly recommend to use these methods. If an error occurs (e.g. invalid range) an internal error flag is set that can be checked using Kinematics::error().

Public Member Function Documentation

static double xprobe(double Q2, double W2, double vmM)

For vector meson production, the gluon density is typically evaluated at x = x_BJ(1 + M_V²/Q²). Here we use the (for our purposes) slightly more robust equivalent expression x = (Q²+ M_V²)/(W² - m_p² + Q²). If x < 0 or x > 1 the error flag is set.

static TLorentzVector electronBeam(double eE)

Returns Lorentz vector of the electron beam for given beam energy eE. Note that p_x=p_y=0 and _z<0 (Sartre conventions).

static TLorentzVector hadronBeam(double eH)

Returns Lorentz vector of the hadron beam for given beam energy eH. Note that p_x=p_y=0 and p_z > 0 (Sartre conventions).
Note that the units are always per nucleon.

static double s(const TLorentzVector& e, const TLorentzVector& p)

Returns the center-of-mass energy squared for electron beam e, and hadron beam 4-vector p.

static double s(double eE, double hE)

Overloaded function. Same as s(Kinematics::electronBeam(eE), Kinematics::hadronBeam(eH)).

static double x(double Q2, double W2)

Returns Bjorken x for given Q² and W² values.

static double y(double Q2, double x, double s)

Returns inelasticity for given Q², W², and s.

static double ymin(double s, double vmM)

Returns smallest allowed inelasticity value (kinematic limit) for given s and vector meson mass vmM.

static double ymax(double s, double vmM)

Returns largest allowed inelasticity value (kinematic limit) for given s and vector meson mass vmM.

static double W2(double Q2, double x)

Returns W² for given Q² and Bjorken x.

static double W2(double Q2, double xprobe, double vmM)

Returns W² for given Q², x_probe and vector meson mass vmM. For x_probe see xprobe().

static double W2min(double vmM)

Returns smallest allowed W² value (kinematic limit) for vector meson mass vmM.

static double W2max(double s)

Returns largest allowed W² value (kinematic limit) for given s.

static double Q2min(double y)

Returns smallest allowed Q² value (kinematic limit) for given inelasticity y.

static double Q2max(double s)

Returns largest allowed Q² value (kinematic limit) for given s.

static double xpomeron(double t, double Q2, double W2, double vmM)

Returns x_IP for given t, Q², W²,and vector meson mass M_V.

static double tmax(double xpom)

Returns largest kinematically allowed t for a given x_IP. Note that this value is incorrectly often referred to as t_min ignoring the fact that t < 0. See also notes at the second version of tmax().

static double tmax(double t, double Q2, double W2, double vmM)

Returns largest kinematically allowed t for given values of t, Q², W², and vector meson mass vmM. At a first glance this looks strange since t_max depends on t. The definition for t_max we use is t_max = - M_p² x_IP² / (1 - x_IP). Unfortunately x_IP depends on t if no approximations are included. For all practical purposes setting t=0 is a good approximation.

Note that the returned value is incorrectly often referred to as t_min ignoring the fact that t < 0.

static double tmin(double hE)

Returns largest kinematically allowed |t| for a given hadron beam energy, hE.

static bool valid(double s, double t, double Q2, double W2, double vmMass, bool useTrueXp, bool verbose)

Returns true if the set of kinematic variables (s, t, Q², W² and M_p) are kinematically valid. Flag useTrueXp controls whether the exact calculation of x_IP should be used (i.e., not neglecting t) or if the approximation for x_IP with t=0 is to be used. If the verbose flag is on the method will print out the first encountered reason why the set of kinematic variables is not valid.

static bool error()

Returns the error flag of the last call. If true an error has occurred and the result cannot be trusted.