| 8 | | The motivation for using a bias function typically falls in one of the following two categories: |
| 9 | | * a) Producing smoother distributions for the tail of a particular observable. This means that physical results obtained in presence of the bias will be identical but sampled differently. One can also use this mode if something specific must be done with each event, independently of the integration (for instance: on-the-flight plotting). |
| 10 | | * b) One wants to modify the integrand so as to really impact the physical results. This can be useful for a plethora of applications: ad-hoc unitarisation of the matrix elements, merging weights, inclusion of higher order contributions, implementation of customized cuts, etc.. |
| | 8 | The motivation for applying a bias function falls in either of the following two categories: |
| | 9 | |
| | 10 | * a) |
| | 11 | |
| | 12 | It can be employed in order to produce smoother distributions for the tail of a particular observable. I that case the bias function should not impact the physical results obtained, but rather only affect the distribution of the events generated or, in other words, the phase-space sampling. |
| | 13 | In this case the events will be first generated and unweighted in presence of this biasing weight. MG5aMC will then reweight these unweighted events by their corresponding bias weight, so as to restore the original physical distributions. |
| | 14 | The resulting events made available to the user will therefore be weighted in this case, and distributed in a manner that enhances the statistics in the desired region of phase-space. |
| | 15 | |
| | 16 | Notice that one can also use the bias function in this way and with a bias weight equal to unity, if something specific must be done with each event, for example on-the-flight plotting. |
| | 17 | |
| | 18 | * b) |
| | 19 | |
| | 20 | It can be used when one wants to modify the integrand so as to really impact the physical results. In this case MG5aMC will generate and unweight events in presence of the bias function, and the resulting unweighted events will be handed over to the user as such. |
| | 21 | Consequently, the produced events remain unweighted, with a physical distribution impacted by the bias. In this case, the bias function should be understood as a direct modification of the underlying matrix element weight. |
| | 22 | |
| | 23 | This category of bias can be useful for a plethora of applications: ad-hoc unitarisation, accounting for additional merging weights, inclusion of higher order contributions, implementation of non-trivial cuts depending not only on kinematics, etc.. |
