# why production and decay cross-section didn't agree.

- Keywords:
- bzcutoff narrow width approximations

- Last updated by:
- Olivier Mattelaer on

One regular question is why the following process (or similar) didn't have the same cross-section in MG:

p p > t t~

and

p p > t t~, t > w+ b, t~ > w- b~

A lot of people expect both to have the same cross-section since the Brancing ratio of top in b w is 1.

They are multiples reasons why the two numbers didn't agree

1) The cut on the final state are not the same between both generation (since the final state is not the same).

One way to prevent (most of) this problem is to set cut_decays on False on the run_card.

2) When a particle is decayed, MG associates to this particles an invariant mass cut. (bwcutoff in the run_card).

More explanation on this cut is available on Madgraph tutorial:

https:/

But in short, this cut is there to prevent the generation of very off-shell particles, in area of the phase-space where the interference with other diagrams are not negligeable. This cut will obviously reduce the cross-section of the decay and should be remove when you perform such comparisons.

3) The multiplication of the production cross-section by the branching ratio is the formula that you obtain in the narrow-width approximations. As his name stated, this is an approximation and has therefore an intrinsic precision (Gamma/M). MadGraph didn't use the Narrow-Width Approximation for the computation and it is therefore expected to have deviation between the corect computation performed by MG and the quick estimation provided by the Narrow width approximation.

4) If you use width computed at NLO, then it also introduce a (small) shift compare to the NWA.

Remember that if you change the value of the mass, you always have to change the width in a coherent way.

5) If your width is much too small (less than 10^-12*mass) then you can be sensitive to numerical precision issue. In such case, the advised method is to artificially run with a larger width and correct the total-cross section by the appropriate factor (i.e. the ratio of the width)

6) if you use the dynamical scale choice "-1" then the various syntax used can lead to a different choice in the scale selected. In that case comparison should be done within scale uncertainty (which are typically quite large)