Main User Routines

For each event a number of phase spaces is generated, each of these phase spaces can have several contributions. The main idea is to calculate your observables once for each phase space iphasno and add all weights of the corresponding contributions to the event weight. The calculation of the observables is done in disphase and the summing is done in discontr. The user has to take care, that the observables are saved in a common block and are available when discontr is called. It is sufficient to allocate space for up to 30 different phase spaces.

In addition to the actual event sampling, some programs perform an adaptation loop to adapt the phase space to the region that is actually used. In this additional loop disphase is called only. The adaptation is then done according to the return value.

The syntax is

      function disphase (iphasno, npar, ps, iadapt)

      double precision disphase
      integer          iphasno, npar, iadapt
      double precision ps(4,10)

and

      subroutine discontr (iphasno, ntype, nalp, nalps, n2pi,
     +   ilognf, jmin, jmax, weight )
      
      integer          iphasno, ntype, nalp, nalps, n2pi
      integer          ilognf, jmin, jmax 
      double precision weight(-13:11)

where the arguments have the following meaning :

• iphasno gives the number of the phase space.
• npar is the number of outgoing particles (excluding the scattered lepton)
• ntype is the type of the contribution

  ntype = -1

  unknown

  ntype = 0

  tree level

  ntype = 1

  subtraction counterterm

  ntype = 2

  finite virtual term

  ntype = 3

  finite collinear term

  ntype = 4

  renormalization term

• nalp and nalps are the orders of $\alpha_{\mbox{\scriptsize elm}}^{}$ and $\alpha_{s}^{}$, respectively. n2pi gives the power of an additional factor of $${1\over 2\pi}$$.
• ilognf selects one of the following factors :

  ilognf=0 :

  $\lambda$ = 1

  ilognf=1 :

  $${\lambda=\log\left( {\mu_r^2\over Q^2}\right)}$$

  ilognf=2 :

  $${\lambda=N_f\log\left( {\mu_r^2\over Q^2}\right)}$$

  ilognf=3 :

  $${\lambda=\log\left( {\mu_f^2\over Q^2}\right)}$$

  ilognf=4 :

  $${\lambda=N_f\log\left( {\mu_f^2\over Q^2}\right)}$$

• ps(i, j) defines the phase space. The array contains several particles distinguished by the second index j.

  j = 1  :

  incoming proton

  j = 2  :

  incoming lepton

  j = 3  :

  boson

  j = 4  :

  outgoing lepton

  j = 5  :

  outgoing proton remnant

  j = 6  :

  incoming parton

  j = 7,..., 10  :

  outgoing partons

  The first index gives the 4-vector components, where i = 1 corresponds to the energy, and i = 2, 3, 4 to the x, y, and z components of the momentum, respectively.
• iadapt is set to 1 during the adaptation loop. The value returned by disphase is used to adapt the integration and sampling phase space. If a negative is returned, a default adaptation calculation is used.
• weight is an array containing several weights. For each contribution only a specific range in this array, defined by jmin and jmax is valid. Each weight has to be multiplied by a factor $\rho_{i}^{}$ and then all weights have to be summed. The factor $\rho_{i}^{}$ for the weight i depends on the particle density functions f_$\alpha$ for the different flavours $\alpha$ and is calculated by :

  i = - 8... - 13  :

  f_{$\bar{\alpha}$} with $\alpha$ = u(- 8), d, s, c, b, t(- 13).

  i = - 7  :

  f_g

  i = - 1... - 6  :

  f_$\alpha$ with $\alpha$ = u(- 6), d, s, c, b, t(- 1).

  i = 0  :

  1

  i = 1, 4  :

  $$\sum_{\alpha=1}^{N_f}$$Q_$\alpha$²f_$\alpha$

  i = 2, 5  :

  $$\sum_{\alpha=1}^{N_f}$$Q_$\alpha$²f_{$\bar{\alpha}$}

  i = 3  :

  $$\sum_{\alpha=1}^{N_f}$$Q_$\alpha$²f_g

  i = 6  :

  (1-N_f)$$\sum_{\alpha=1}^{N_f}$$Q_$\alpha$²f_$\alpha$

  i = 7  :

  (1-N_f)$$\sum_{\alpha=1}^{N_f}$$Q_$\alpha$²f_{$\bar{\alpha}$}

  i = 8  :

  $$\sum_{\alpha=1}^{N_f}$$f_$\alpha$$$\sum_{\beta=1,\beta\ne\alpha}^{N_f}$$Q_$\beta$²

  i = 9  :

  $$\sum_{\alpha=1}^{N_f}$$f_{$\bar{\alpha}$}$$\sum_{\beta=1,\beta\ne\alpha}^{N_f}$$Q_$\beta$²

  i = 10  :

  $$\sum_{\alpha=1}^{N_f}$$f_$\alpha$Q_$\alpha$$$\sum_{\beta=1,\beta\ne\alpha}^{N_f}$$Q_$\beta$

  i = 11  :

  $$\sum_{\alpha=1}^{N_f}$$f_$\alpha$Q_{$\bar{\alpha}$}$$\sum_{\beta=1,\beta\ne\alpha}^{N_f}$$Q_$\beta$

The full weight of one contribution is then

w_contribution = $$\lambda$$$$\alpha_{s}^{\mbox{\scriptsize\tt ialps}}$$$$\alpha_{\mbox{\scriptsize elm}}^{\mbox{\scriptsize\tt ialp}}$$$$\left(\vphantom{{1\over 2\pi}}\right.$$$${1\over 2\pi}$$ $$\left.\vphantom{{1\over 2\pi}}\right)^{\mbox{\scriptsize\tt n2pi}}_{}$$$$\sum_{i= \mbox{\scriptsize\tt jmin}}^{\mbox{\scriptsize\tt jmax}}$$$$\tt weight$$(i)$$\rho_{i}^{}$$

This somewhat complicated procedure can be performed by a library function double wsum (nord, nalp, nalps, n2pi, ilognf, jmin, jmax, weight,
fscale, rscale, alphas). See section the web version [5] for an example. nord selects the leading or higher order particle density function (see steering card values PDFL and PDFH). fscale and rscale are the inputs for the factorization and renormalization scale, respectively. alphas is an output parameter returning the value of $\alpha_{s}^{}$ at this phase space point.

Additional information for experienced users : For DISASTER++ all phase spaces for one event are generated at the beginning of the event and the disphase routine is called for each phase space, before the first call to discontr is made. The ntype information is 0 for tree level and -1 otherwise. In DISENT the sequence is different, for each contribution disphase and discontr are called right after each other. The ntype information is fully available. The adaptation loop is performed in DISASTER++, only.