SUBROUTINE QIPSGN - Generate 4-momenta of outgoing partons

• Using the MAMBO [1] algorithm¹ , the momenta $p_i$ of the $n=2n_f-1+n_g$ outgoing partons in the instanton subprocess CMS are generated uniformly in phase space,
  

  $$\int \prod_{i=1}^{n} \left\{ d^4p_i\,\delta \left( p_i^2-m... ...i \right)\, \delta \left( W_i - \sum_{i=1}^n p_i^t\right) .$$ (1)

  
  
  The masses $m_i$ have been set in the subroutine QIPLST.
• For default setting of the contrôl flags in QIINIT, the routine calls the subroutine QIPSWT to generate the momenta $p_i$ finally uniformly in energy-weighted phase space,
  

  $${\int \prod_{q=1}^{2n_f-1} \left\{ d^4p_q\,\delta \left( p_q^2-m_... ...k=1}^{n_g} \left\{ d^4p_k\,\delta \left( p_k^2-m_g^2\right) p^{t\,2}_k\right\}}$$

  $$\times \, \delta^{(3)}\left( \sum_{q=1}^{2n_f-1} \vec{p}_q+ \sum_... ...\delta \left( W_i - \sum_{q=1}^{2n_f-1} p_q^t - \sum_{k=1}^{n_g} p_k^t\right) ,$$

  
  
  corresponding to the leading-order matrix elements [3] with different energy weights for gluons and quarks.

Table 1: Variables set in QIPLST.

Name	Description
QIPHEP(1,IHEP)	$x$-component of the momentum of the
	IHEP'th outgoing parton from instanton subprocess
QIPHEP(2,IHEP)	$y$-component of the momentum of the
	IHEP'th outgoing parton from instanton subprocess
QIPHEP(3,IHEP)	$z$-component of the momentum of the
	IHEP'th outgoing parton from instanton subprocess
QIPHEP(4,IHEP)	$t$-component of the momentum of the
	IHEP'th outgoing parton from instanton subprocess