We have now covered the simple case. In a
process, the integral is absent, and the differential
cross section
is replaced by
. The cross section may now be written as

The structure is thus exactly the same, but the -related pieces are absent, and the rôle of the dimensionless cross section is played by .

If the range of allowed decay angles of the resonance is restricted,
e.g. by requiring the decay products to have a minimum transverse
momentum, effectively this translates into constraints on the
variable of the process. The
difference is that the angular dependence of a resonance decay is
trivial, and that therefore the -dependent factor can be easily
evaluated. For a spin-0 resonance, which decays isotropically, the
relevant weight is simply
.
For a transversely polarized spin-1 resonance the expression is,
instead,

(101) |

For processes where either of the final-state
particles is a resonance, or both, an additional choice has to
be made for
each resonance mass, eq. (). Since the allowed
, and ranges depend on and ,
the selection of masses have to precede the choice of the other
phase-space variables. Just as for the other variables, masses
are not selected uniformly over the allowed range, but are rather
distributed according to a function
, with a
compensating factor in the Jacobian. The functional
form picked is normally

The fourth term is only used for processes involving production, where the propagator guarantees that the cross section does have a significant secondary peak for . Therefore here the choice is , , and .

A few special tricks have been included to improve efficiency when the allowed mass range of resonances is constrained by kinematics or by user cuts. For instance, if a pair of equal or charge-conjugate resonances are produced, such as in , use is made of the constraint that the lighter of the two has to have a mass smaller than half the c.m. energy.