SUBROUTINE QIKGSP - Generate 4-momenta of virtual quark $q^\prime$ and current quark $q^{\prime\prime}$

In this subroutine the 4-momenta of the virtual quark, $q^\prime$, with $q^{\prime 2}=-Q^{\prime 2}$, where $Q^{\prime 2}$ is the virtuality generated in QIHINS, and of the outgoing, on-shell current quark $q^{\prime\prime}$, with $\sqrt{q^{\prime\prime\, 2}}=m_{q^{\prime\prime}}$, are generated. The incoming $P$ is assumed to go into the $-z$ direction, the incoming $e$ in the $+z$ direction.

Using a Sudakov decomposition, the 4-momentum of the virtual quark $q^\prime$ is generated in this subroutine as

$$q^\prime_t = -2\, D\, \left( \cos\phi_{q^\prime}\cos\phi_q +\sin\phi_{q^\prime... ...(1-y_{\rm Bj})} \frac{P_t}{S y_{\rm Bj}}+ e_t \frac{Q^{\prime 2}}{S x^\prime z}$$ (1)

$$+ P_t \left( \frac{Q^{\prime 2}}{Sx^\prime z\, y_{\rm Bj}}\left(x... ...m Bj})\right) -x_{\rm Bj} -\frac{m^2_{q^{\prime\prime}}}{Sy_{\rm Bj}} \right) ,$$

$$q^\prime_x = D\,\cos\phi_{q^\prime}-\frac{Q^{\prime 2}}{Sx^\prime z\, y_{\rm Bj}}\,\sqrt{Sx_{\rm Bj}y_{\rm Bj}(1-y_{\rm Bj})}\,\cos\phi_q ,$$ (2)

$$q^\prime_y = D\,\sin\phi_{q^\prime}-\frac{Q^{\prime 2}}{Sx^\prime z\, y_{\rm Bj}}\,\sqrt{Sx_{\rm Bj}y_{\rm Bj}(1-y_{\rm Bj})}\,\sin\phi_q ,$$ (3)

$$q^\prime_z = 2\, D\, \left( \cos\phi_{q^\prime}\cos\phi_q +\sin\phi_{q^\prime}... ...(1-y_{\rm Bj})} \frac{P_t}{S y_{\rm Bj}}+ e_t \frac{Q^{\prime 2}}{S x^\prime z}$$ (4)

$$- P_t \left( \frac{Q^{\prime 2}}{Sx^\prime z\, y_{\rm Bj}}\left(x... ...m Bj})\right) -x_{\rm Bj} -\frac{m^2_{q^{\prime\prime}}}{Sy_{\rm Bj}} \right) ,$$

with

$$D=\sqrt{S x_{\rm Bj}y_{\rm Bj} \frac{Q^{\prime 2}}{Sx^\prime... ...prime 2}}{Sx^\prime z\, y_{\rm Bj}}m^2_{q^{\prime\prime}}}\,.$$ (5)

The azimuthal angle $\phi_{q^\prime}$, $-\pi\leq\phi_{q^\prime}\leq +\pi$, is generated randomly. The 4-momentum of the current quark is then calculated via

$$q^{\prime\prime} = q - q^\prime .$$ (6)

Table 1: Variables set in QIKGSP.

Name	Description
QIQGAM(1,2)	$q^\prime_x$
QIQGAM(2,2)	$q^\prime_y$
QIQGAM(3,2)	$q^\prime_z$
QIQGAM(4,2)	$q^\prime_t$
QIQGAM(1,1)	$q^{\prime\prime}_x$
QIQGAM(2,1)	$q^{\prime\prime}_y$
QIQGAM(3,1)	$q^{\prime\prime}_z$
QIQGAM(4,1)	$q^{\prime\prime}_t$