When total width smaller than partial width

Hi,

if you study H > t t~, without any production, then the matrix-element is a constant over the phase-space and does not actually depend of the width. Obviously the amount of distribution that you can do for such decay is limited since you have only two degree of freedom which is the direction of decay.

If you study a realy process with production and decay, you then have a propagator in (some?) of the amplitude and the propagator does depend on the value of the width.
If that width is wrong, this will impact both the cross-section and the shape of differential cross-section.
Now if the width is small, you can use the narrow width approximation to know how much biased is the cross-section when you use a wrong width.

For distribution, this is obviously more complex and depend on the observable. If you look at the invariant mass of the decay then at theory level the curve will not have the correct shape, but at experimental level it sometimes can be ok if you are dominated by resolution effect. In general this can be ok if you are in a case where narrow width approximation is valid and if you look at observables which are not too sensitive...
In other word, you will need to check.

Cheers,

Olivier