SUBROUTINE QIKGAM - Generate 4-momentum of virtual photon $q$

In this subroutine the 4-momentum of the virtual photon, $q$, with $q^2=-Sx_{\rm Bj}y_{\rm Bj}\equiv -Q^2$, is generated. It assumes $e^2=0$ and that $e=(e_t,0,0,e_z)$ with $e_z >0$ (i.e. incoming $e$ goes in $+z$ direction).

According to a Sudakov decomposition, the 4-momentum of the virtual photon is expressed as

$$q_t = y_{\rm Bj}\,e_t-\frac{Sx_{\rm Bj}y_{\rm Bj}}{4\,e_t},$$ (1)

$$q_x = -\sqrt{Sx_{\rm Bj}y_{\rm Bj}(1-y_{\rm Bj})}\,\cos\phi_q ,$$ (2)

$$q_y = -\sqrt{Sx_{\rm Bj}y_{\rm Bj}(1-y_{\rm Bj})}\,\sin\phi_q ,$$ (3)

$$q_z = y_{\rm Bj}\,e_t+\frac{S x_{\rm Bj}y_{\rm Bj}}{4\,e_t}.$$ (4)

The azimuthal angle $\phi_q$, $-\pi\leq \phi_q \leq +\pi$, is randomly generated for default setting of the control flags. Otherwise, $\phi_q$ is fixed at zero, i.e. $e^\prime$ (the 4-momentum of the scattered $e^\pm$) and $q$ are lying in the $x-z$ plane.

Table 1: Variables set in QIKGAM.

Name	Description
QIPGAM(1)	$q_x$
QIPGAM(2)	$q_y$
QIPGAM(3)	$q_z$
QIPGAM(4)	$q_t$