SUBROUTINE QIGPAR - Find the incoming partons in the strings of (outgoing) partons

In this subroutine, one of the $n_g+1$ gluons in the $n_f$ $[\,q \ldots \overline{q}\,]$ strings of partons participating in the instanton subprocess, set up in the subroutine QIGPAR, is randomly chosen and marked as incoming. Furthermore, the anti-parton corresponding to the virtual quark $q^\prime$ is found in above strings and marked as incoming.

Example: Suppose we have the following instanton-induced subprocess,

$$g+s\Rightarrow 3\,g's + d + \overline{d} + u + \overline{u} + s \, .$$ (1)

Then the subroutines QIGLST and QIGPAR might produce the following strings,

$$[\,d\; {\bf g}\;\overline{\bf u}\,]\hspace{5ex} [\,u\;g\;g\;... ...line{\bf s}\,] \hspace{5ex} [\,s\;g\;{\bf\overline{d}}\,]\, ,$$ (2)

where the boldface entries denote the partons marked as incoming.

The idea above is realized in the subroutine QIGPAR as follows:

The routine searches for the entries (JLP,ILP) of the array of (outgoing) partons corresponding to (the particle data group identities of) the incoming parton $q^\prime$ and incoming on-shell gluon $g$. These data are stored and the entries are marked as incoming (see Table 1). In detail:

• It gets the particle data group identity of the incoming virtual parton $q^\prime$ set in QIHGEN, QIPINC(1,3).
  • If $q^\prime$ is an antiquark, i.e. for $-7 < {\rm QIPINC(1,3)} \leq -1$, it treats it as a quark in the array of (outgoing) partons set in QIGLST: The row number JLP of the corresponding quark is stored as ${\rm QIPINC(1,1)}=1$ and the column number is stored as ${\rm QIPINC(1,2)}=\mid {\rm QIPINC(1,3)}\mid$. The corresponding entry is marked as incoming, ${\rm QIPINF(QIPINC(1,1)},\mid {\rm QIPINC(1,3)}\mid)={\rm .TRUE.}$.
  • If $q^\prime$ is a quark, i.e. for $1\leq {\rm QIPINC(1,3)}< 7$, it treats it as an antiquark in the array of (outgoing) partons set in QIGLST: It loops over the columns (i.e. over ILP) in the array of (outgoing) partons. In each column (i.e. for each ILP) it looks at the last non-zero entry on the bottom (i.e. the QINLIS(ILP)'th entry from above) to find the antiquark (with particle data group identity -QIPINC(1,3)) and stores the corresponding ILP in QIPINC(1,2) and the corresponding JLP in QIPINC(1,1). The entry is marked as incoming, ${\rm QIPINF(QIPINC(1,1)},{\rm QIPINC(1,2)})={\rm .TRUE.}$.
• It gets the particle data group identity of the incoming on-shell gluon $g$ set in QIHGEN, QIPINC(2,3). It picks one of the gluon entries (JLP,ILP) in the array of (outgoing) partons QIPTYP(JLP,ILP) at random and stores the corresponding JLP in QIPINC(2,1) and the corresponding ILP in QIPINC(2,2). The entry is marked as incoming, ${\rm QIPINF(QIPINC(2,1)},{\rm QIPINC(2,2)})={\rm .TRUE.}$.

Table 1: Variables (re-)set in QIGPAR.

Name	Description
QIPINC(1,1)	JLP of quark/antiquark in array
	of (outgoing) partons corresponding to
	incoming virtual quark/antiquark $q^\prime$
QIPINC(1,2)	ILP of quark/antiquark in array
	of (outgoing) partons corresponding to
	incoming virtual $q^\prime$
QIPINC(2,1)	JLP of gluon in array
	of (outgoing) partons corresponding to
	incoming on-shell gluon $g$
QIPINC(2,2)	ILP of gluon in array
	of (outgoing) partons corresponding to
	incoming on-shell gluon $g$
QIPINF(QIPINC(IPART,1),QIPINC(IPART,2))	Mark entry as incoming
=.TRUE.