SUBROUTINE QCLOOP - Loop over required number of events

• An elementary process is initialized by calling the HERWIG [1] subroutine HWEINI. Within HWEINI the following steps are performed:
  • For default setting of input parameters in HWIGIN (e.g. NOWGT=.TRUE. ...generate unweighted events), first an initial search for the maximum weight is started with 2000 shots by calling HWEPRO.
  • After the initial search is finished, the HERWIG subroutine HWEFIN is called, which provides terminal calculations on the elementary process and prints out the quantities listed in Table 1.

    
    

    Table 1: Output from HWEFIN.

    Name	Description
    NEVHEP	Number of events
    NWGTS	Number of weights
    AVWGT	Mean weight (cross section in nb)
    SPWGT	RMS spread of weight
    WBIGST	Actual maximum weight
    WGTMAX	Assumed maximum weight
    IPROC	Process code
    1000.*AVWGT	Cross section (in pb)
    1000.*ERWGT	Error in cross section (in pb)
    100.*AVWGT/WGTMAX	Efficiency (in % )

    
    

    The cross section (in nb) for instanton-induced events in DIS is given by the quantity AVWGT which corresponds, for default settings of the input parameters in QIINIT, to
    

    $$\sigma_{eP}^{(I)}({\rm Cuts}) \simeq \frac{2\,\pi\,\alpha^2}{S}\,\sum\limits_{q^\prime} e_{q^\prime}^2... ...^\prime}\, \,\frac{\sigma^{(I)}_{q^\prime g}(x^\prime ,Q^{\prime 2})}{x^\prime}$$ (1)

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

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

    
    
    in concordance with Ref. [2]. Here the sum extends over all quarks and anti-quarks of all $n_f$ flavours. $\sigma^{(I)}_{q^\prime g}$ denotes the instanton-induced $q^\prime g$ total cross section from Ref. [2], $f_g$ is the gluon distribution in the proton, 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] (c.f. Fig. 1).

  

• Then, within a loop from N=1 to N=MAXEV (the required number of events), the subroutines QCDGEN (generation of one event) and HWANAL (user's routine to analyze data from event) are called.
• Finally, the elementary process is terminated by calling the HERWIG subroutine HWEFIN which produces the final output according to Table 1.