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Regularization

In general case a squared matrix element is too singular for direct Monte Carlo integration. Singularities of the matrix element are caused by poles of virtual particle propagators and can have one of the following forms

$$1/(p^2 - m^2)$$ (2)

$$1/(p^2 - m^2)^2$$ (3)

$$1/( (p^2-m^2)^2 + (m\cdot\Gamma)^2)$$ (4)

where $m$, $\Gamma$, and $p$ are the mass, width, and momentum of virtual particle.

The Regularization menu function allows the user to point out dangerous denominators for automatic smoothing the sharp peaks of the squared matrix element. The regularization table contains four fields: momenta, mass, width and power.

Momentum of virtual particle is a sum of momenta of incoming and outgoing particles. Just type the ordering numbers of these momenta in the Momentum field. The sign is substituted automatically. For example, for a collision process 12 is treated as $(p1+p2)$ and 134 is treated as $(p1-p3-p4)$.

Mass and Width describe a position of the pole. In the case of Fortran  program the corresponding numerical values must be written down in these fields. In the case of C program the user can write down some algebraic expressions which contain the identifiers enumerated in the Model parameters menu. For t-channel propagators (both incoming and outgoing momenta contribute to $P$) only a zero value in the Width field is permitted because CompHEP  ignores particle width term for such propagators.

The Power field defines an exponent of the propagator. Acceptable values are 1 and 2. Of course, in a squared matrix element any propagator appears to the power of 2. But sometimes as a result of gauge cancellations the exponent can be efficiently decreased to 1. If the Width field is not equal to 0 such a cancellation is not expected and CompHEP  will use value 2 for the exponent ignoring the user input.

The work of regularization program is sensitive to the S and M types of cuts (see Section ) and is not sensitive to other ones. Consequently, if you would like to smooth some singularity due to the pole inside the phase space, you should apply the S or M cut to exclude the pole point from the consideration.

The algorithm of regularization is explained in Section .