Subroutines

CALL GLOREN (BETA,PA,PB*) GLOREN transforms the momentum and the energy from one Lorentz frame (A) to another (B). It uses the following input and output:

BETA(4)

( REAL) velocity components in light units of frame B in frame A, BETA(1$...$ 3) $=\beta$ , BETA(4)$=(1-\beta 2)-1/2=\; \gamma$ ;

PA(4)

( REAL) momentum components in the frame (A);

PB(4)

( REAL) momentum components in the frame (B).

GLOREN is called from the routine GDECAY. The momentum $p$_A and energy $E$_A in reference frame A are transformed into the momentum $p$_B and energy $E$_B in reference frame B which translates with velocity $\beta$ with respect to A:

$E$B	$=$	$\gamma (E$A- βpA)
$p$B	$=$	$p$A+γβ({ γβpAγ+1}- EA)

CALL GDROT (P*,COSTH,SINTH,COSPH,SINPH) GDROT rotates a vector from one reference system to another.

P(3)

( REAL) vector to rotate, overwritten on output;

COSTH

( REAL) cosine of the polar angle;

SINTH

( REAL) sine of the polar angle;

COSPH

( REAL) cosine of the azimuthal angle;

SINPH

( REAL) sine of the azimuthal angle;

GDROT is called from several routines to rotate a particle from in the center-of-mass system to the GEANT (laboratory) system. The following rotation matrix is used:

$($

$cos\theta cos\phi$	$-sin\phi$	$sin\theta cos\phi$
$cos\theta sin\phi$	$cos\phi$	$sin\theta sin\phi$
$-\; sin\theta$	$0$	$cos\theta$

$)=($

$cos\phi$	$-sin\phi$	$0$
$sin\phi$	$cos\phi$	$0$
$0$	$0$	$1$

$)$_Rφ(

$cos\theta$	$0$	$sin\theta$
$0$	$1$	$0$
$-sin\theta$	$0$	$cos\theta$

$)$_Rθ

$R$_θ is a counterclockwise rotation around axis y by an angle $\theta$ , and $R$_φ is a counterclockwise rotation around axis $z\text{'}$ (rotated by an angle $\theta$ from the initial position) by an angle $\phi$ .

CALL GFANG (P,COSTH*,SINTH*,COSPH*,SINPH*,ROTATE*)

P(3)

( REAL) input direction;

COSTH

( REAL) cosine of the polar angle;

SINTH

( REAL) sine of the polar angle;

COSPH

( REAL) cosine of the azimuthal angle;

SINPH

( REAL) sine of the azimuthal angle;

ROTATE

( LOGICAL) rotation flag, the rotation matrix is the unit matrix if ROTATE=.FALSE., i.e. no rotation is needed;

Find the sine and cosine of the polar and azimuthal angle of the direction defined by the vector P. If P is along the z axis, ROTATE=.FALSE..

CALL GVROT (DCOSIN,PART*)

PART(3)

( REAL) direction to be rotated, overwritten on output;

DCOSIN(3)

( REAL) direction of the new z axis;

Given the direction PART in a system of reference O, it returns the same direction in the system of reference where the z axis of O is along DCOSIN. This routine is very useful when the $\theta$

angle of a secondary particle is sampled in a reference frame where the parent particle moves along the z axis. Then the direction of the secondary product in the MRS is returned by GVROT if DCOSIN is the direction of the parent particle.

A call to GVROT is equivalent to the following code:

      DIMENSION PART(3), DCOSIN(3)
      LOGICAL ROTATE
      .
      .
      .
      CALL GFANG(DCOSIN,COSTH,SINTH,COSPH,SINPH,ROTATE)
      IF(ROTATE) CALL GDROT(PART,COSTH,SINTH,COSPH,SINPH)

with the advantage that inside GVROT all calculations are performed in double precision.

PHYS430