# 5.8. Integration¶

The following parameters are used to steer the integration:

## 5.8.1. INTEGRATION_ERROR¶

Specifies the relative integration error target.

## 5.8.2. INTEGRATOR¶

Specifies the integrator. The possible integrator types depend on the
matrix element generator. In general users should rely on the default
value and otherwise seek the help of the authors, see Authors.
Within AMEGIC++ the options ```
AMEGIC: {INTEGRATOR: <type>,
RS_INTEGRATOR: <type>}
```

can be used to steer the behaviour of the
default integrator.

`4`

: building up the channels is achieved through respecting the peak structure given by the propagators. The algorithm works recursively starting from the initial state.`5`

: this is an extension of option 4. In the case of competing peaks (e.g. a Higgs boson decaying into W+W-, which further decay), additional channels are produced to account for all kinematical configurations where one of the propagating particles is produced on its mass shell.`6`

: in contrast to option 4 the algorithm now starts from the final state. The extra channels described in option 5 are produced as well. This is the default integrator if both beams are hadronic.`7`

: Same as option`4`

but with tweaked exponents. Optimised for the integration of real-subtracted matrix-elements. This is the default integrator when at least one of the beams is not hadronic.

In addition, a few ME-generator independent integrators have been implemented for specific processes:

`Rambo`

: RAMBO [KSE86]. Generates isotropic final states.`VHAAG`

: Vegas-improved HAAG integrator [vHP02].`VHAAG_res`

: is an integrator for a final state of a weak boson, decaying into two particles plus two or more jets based on HAAG [vHP02]. This integrator can be further configured using`VHAAG`

sub-settings, i.e.`VHAAG: {<sub-setting>: <value>`

}. The following sub-settings are available.`RES_KF`

specifies the kf-code of the weak boson, the default is W (`24`

).`RES_D1`

and`RES_D2`

define the positions of the Boson decay products within the internal naming scheme, where`2`

is the position of the first outgoing particle. The defaults are`2`

and`3`

, respectively, which is the correct choice for all processes where the decay products are the only not strongly interacting final state particles.

## 5.8.3. VEGAS_MODE¶

Specifies the mode of the Vegas adaptive integration. `0`

disables
Vegas, `2`

enables it (default).

## 5.8.4. FINISH_OPTIMIZATION¶

Specifies whether the full Vegas optimization is to be carried out.
The two possible options are `true`

(default) and `false`

.

## 5.8.5. PSI¶

The sub-settings for the phase space integrator can be customised as follows:

```
PSI:
<sub-setting>: <value>
# more PSI settings ...
```

The following sub-settings exist:

`ITMIN`

The minimum number of points used for every optimisation cycle. Please note that it might be increased automatically for complicated processes.

`ITMAX`

The maximum number of points used for every optimisation cycle. Please note that for complicated processes the number given might be insufficient for a meaningful optimisation.

`NPOWER`

The power of two, by which the number of points increases with every step of the optmization.

`NOPT`

The number of optimization cycles.

`MAXOPT`

The minimal number of integration cycles after the optimization is done.

`STOPOPT`

The maximal number of additional cycles in the integration performed to reach the integration error goal.

`ITMIN_BY_NODE`

Same as

`ITMIN`

, but specified per node to allow tuning of integration performance in large-scale MPI runs.`ITMAX_BY_NODE`

Same as

`ITMAX`

, but specified per node to allow tuning of integration performance in large-scale MPI runs.