SUBROUTINE HWEPRO - When NEVHEP=0, chooses $x$ values and finds weight for process IPROC; otherwise, chooses and loads all variables for hard process

Routine from HERWIG [1]; not included in QCDINS package.

In this subroutine a hard process routine is called twice. The first call, with the variable GENEV set to .FALSE., requests for the generation of an event weight by the hard process routine. The second call, with GENEV now .TRUE., asks for event generation to be completed and the event record to be written into the standard HEPDATA common block.

In the context of QCDINS this proceeds as follows:

In the first call the following steps are performed:

• The variable GENEV (generate full event) is set to .FALSE..
• The initial state ($eP$) is set up.
• The HERWIG routine HWEGAM, which nominally generates an incoming photon from the incoming $e^\pm$, is called. Within QCDINS, however, the photon is generated in a later stage in the subroutine QIKGAM. Thus, the HERWIG routine HWEGAM has been modified to immediately return for IPRO=76.
• The (modified¹) HERWIG subroutine HVHBVI is called which in turn calls the subroutine QIHGEN. Within the latter, the Bjorken variables $(Q^{\prime 2},x^\prime$, $z,x_{\rm Bj},y_{\rm Bj})$ of the instanton-induced $\gamma^\ast P$ scattering process are generated and a Monte Carlo weight $W_{eP}^{(I)}$ (EVWGT) corresponding to the instanton-induced total cross section,
  

  $$\sigma_{eP}^{(I)}({\rm Cuts}) \simeq \frac{2\,\pi\,\alpha^2}{S}\,\sum\limits_{q^\prime} e_{q^\prime}^2... ...^\prime}\, \,\frac{\sigma^{(I)}_{q^\prime g}(x^\prime ,Q^{\prime 2})}{x^\prime}$$

  $$\times \int\limits_{{\rm max}\left(\frac{Q^{\prime 2}}{Sx^\prime ... ...rm Bj\,max}-\frac{Q^{\prime 2}}{Sx^\prime z}}} \frac{dx_{\rm Bj}}{x_{\rm Bj}}\,$$ (1)

  $$\times \int\limits_{{\rm max}\left( \frac{Q^{\prime 2}}{Sx^\prime... ..._{\rm min})\, \frac{1+(1-y_{\rm Bj})^2}{y_{\rm Bj}}\ P_{q^\prime}^{{ (I)}}\ ,$$

  
  
  is calculated. Here $\sigma^{(I)}_{q^\prime g}$ denotes the instanton-induced $q^\prime g$ total cross section from Ref. [2], $f_g$ is the gluon distribution, and $P_{q^\prime}^{{ (I)}}$ accounts for the flux of virtual (anti-)quarks $q^\prime$ (with e.m. coupling $\alpha\, e^2_{q^\prime}$) in the $I$-background entering the $I$-induced $q^\prime p$-subprocess from the photon side [2,3].

• For standard settings of the contrôl flags in the HERWIG [1] routine HWIGIN (NOWGT=.TRUE.), the rejection method is applied to end up with unweighted events: The generated total event weight $W_{eP}^{(I)}$ is compared with a random number $r\in (0,1)$ times the previously determined maximum weight $W_{\rm max}$ (see description of the subroutine QCLOOP). Only ``events'', i.e. generated values of $(Q^{\prime 2},x^\prime ,z,x_{\rm Bj},y_{\rm Bj})$, for which
  

  $$W_{eP}^{(I)} > r\,\cdot W_{\rm max}$$ (2)

  
  
  are accepted: For these events the variable GENEV is set to .TRUE.. Furthermore, to each accepted event an event weight equal to the total cross section (1) is associated. It is clear that the accepted events are then distributed according to the differential cross section
  

  $$\frac{1}{\sigma_{eP}^{(I)}}\ \frac{d^5\sigma_{eP}^{(I)}} {dQ^{\prime 2}\,dx^\prime\, dz\, dx_{\rm Bj}\, dy_{\rm Bj}} \, ,$$ (3)

  
  
  whose explicit expression can be easily read off from Eq. (1).

If the event is accepted, i.e. if GENEV is now .TRUE., the following steps are performed in HWEPRO:

• The routine loops back to call again the subroutine HVHBVI.
• The latter, for GENEV=.TRUE., completes the event generation, by calling again QIHGEN.

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

Name	Description
GENEV	Flag for event generation
GAMWT	Weight from photon generation
EVWGT	Event weight corresponding to the cross section (1)
NWGTS	Number of event weights
WGTSUM	Sum of event weights according
WSQSUM	Sum of squared event weights