A width is calculated perturbatively for those resonances which appear in the PYTHIA hard process generation machinery. The width is used to select masses in hard processes according to a relativistic Breit-Wigner shape. In many processes the width is allowed to be -dependent, see section .
Other particle masses, as discussed so far, have been fixed at their nominal value. We now have to consider the mass broadening for short-lived particles such as , or . Compared to the , it is much more difficult to describe the resonance shape, since nonperturbative and threshold effects act to distort the naïve shape. Thus the mass is limited from below by its decay , but also from above, e.g. in the decay . Normally thus the allowed mass range is set by the most constraining decay chains. Some rare decay modes, specifically and , are not allowed to have full impact, however. Instead one accepts an imperfect rendering of the branching ratio, as some low-mass decays of the above kind are rejected in favour of other decay channels. In some decay chains, several mass choices are coupled, like in , where also the has a non-negligible width. Finally, there are some extreme cases, like the , which has a nominal mass below the threshold, but a tail extending beyond that threshold, and therefore a non-negligible branching ratio to the channel.
In view of examples like these, no attempt is made to provide a
full description. Instead a simplified description is used, which
should be enough to give the general smearing of events due to
mass broadening, but maybe not sufficient for detailed studies of
a specific resonance. By default, hadrons are therefore given a
mass distribution according to a non-relativistic Breit-Wigner
The problem has been `solved' by shifting the mass to be slightly above the threshold and have vanishing width. Then kinematics in decays is reasonably well modelled. The mass is too large in the channel, but this does not really matter, since one anyway is far above threshold here.