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2.2 Decay distributions

The decay width is given by

and the total rate is the integral over this for the case . For the case the integral has to be divided by the factor 2 for two identical particles in the final state.

We first consider the case where and introduce the dimensionless variables

Then one obtains, after integrating over and at fixed [20],

 

This result allows one to evaluate, e.g., the distribution of produced pairs rather easily. The kinematically allowed region is

with

The case is slightly more elaborate. We feel that it does not make sense to display the term because it is of considerable complexity in the general case when all the form factors , and are and dependent. The expression together with the Monte Carlo program to do the phase space integrals is available on request from the authors.



Carlos E.Piedrafita