SUBROUTINE QIGLST - Generate strings of outgoing partons given total numbers

In this subroutine, $n_f$ $[\,q \ldots \overline{q}\,]$ - ``strings'' of partons are set up whose entries identify the particle types of the $(n_g+1)$ gluons and $2n_f$ quarks participating in the instanton subprocess. Each string begins with a quark, followed by a random number of gluons and ending with an anti-quark of randomly chosen flavour. There are $n_g+1$ gluons in total and all $n_f$ flavours occur precisely once. All partons in these lists are marked by logical flags to be outgoing.

A simple example for $n_f=3$ and $n_g=3$ outgoing gluons may provide some illustration:

$$[\,d\; g\;\overline{u}\,]\hspace{5ex} [\,u\;g\;g\;\overline{s}\,] \hspace{5ex} [\,s\;g\;\overline{d}\,]\, .$$ (1)

In practice, the above idea is realized in the subroutine QIGLST as follows:

• One starts by building a $30\times 30$ array¹ with all entries equal to zero.
• The quarks, identified by their particle data group identities (IDPDG), $1,\ldots ,n_f$, are then inserted consecutively at the top of the first $n_f$ columns (``strings''). As an example, one has, for $n_f=3$,
  

  $$\begin{array}{cc\vert cccccc} & & \multicolumn{6}{\vert c}... ...IS(ILP)} & & 1 & 1 & 1 & 0 & \ldots & 0 \\ \end{array} \, .$$ (2)

  
  

• Now, the antiquarks, identified by their IDPDG's, $-1,\ldots,-n_f$, are inserted randomly in the second entry of the first $n_f$ columns, e.g.
  

  $$\begin{array}{cc\vert cccccc} & & \multicolumn{6}{\vert c}... ...m QINLIS(ILP)} & & 2 & 2 & 2 & 0 & \ldots & 0 \\ \end{array}$$ (3)

  
  
  plus all permutations of $-1,-2,-3$.
• Finally, the $n_g+1$ gluons participating in the instanton subprocess, identified by the particle data group identity 21, are distributed randomly over the first $n_f$ columns. This is done, for each of the gluons, by picking one of the first $n_f$ columns at random, moving the antiquark in this column one entry further down and inserting the gluon at the previous position of the antiquark. A possible outcome of this procedure for the example above and the case of $n_g=3$ is
  

  $$\begin{array}{cc\vert cccccc} & & \multicolumn{6}{\vert c}... ...S(ILP)} & & 3 & 4 & 3 & 0 & \ldots & 0 \\ \end{array} \, .$$ (4)

  
  

The integer variable QIPTYP(JLP,ILP) set in QIGLST denotes the JLP'th entry in the ILP'th column (``string'') of the array constructed above. The integer variable QINLIS(ILP) gives the number of non-zero entries, i.e. the number of partons, of the ILP'th column (``string'') of the array.

Table 1: Variables set in QIGLST.

Name	Description
QIPTYP(JLP,ILP)	Array of parton identification labels (IDPDG's)
QINLIS(ILP)	Number of partons in column of the array
	of parton identification labels
QIPINF(JLP,ILP)	Array of logical flags to mark entries as incoming.
	All entries are set to .FALSE. in QIGLST