# Higgs branching fraction to b\bar{b} using compute_widths

Dear Authors,

I was trying to compute Higgs decay width using "compute_widths h". After the run, in models/sm/param_card.dat, the branching fraction of h to b\bar{b} can found to be 83% instead of 58%. Can you tell me why this is happening?

Thanks
Debashis

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Olivier Mattelaer
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2021-03-14
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2021-03-07
 Olivier Mattelaer (olivier-mattelaer) said on 2021-03-04: #1

The compute-width is know to not work for the Higgs in the SM since the Higgs has loop-induced decay which are not included in the auto width mode.

> On 4 Mar 2021, at 06:10, Debashis <email address hidden> wrote:
>
> New question #695855 on MadGraph5_aMC@NLO:
>
> Dear Authors,
>
> I was trying to compute Higgs decay width using "compute_widths h". After the run, in models/sm/param_card.dat, the branching fraction of h to b\bar{b} can found to be 83% instead of 58%. Can you tell me why this is happening?
>
> Thanks
> Debashis
>
> --

 Debashis (deba672) said on 2021-03-04: #2

Does that mean if we decay a final state Higgs to b\bar{b} in madgraph, it will give wrong results?

For example consider the following process:
p p > h j j, h > b b~

set DECAY 25 auto

Thanks
Debashis

 Olivier Mattelaer (olivier-mattelaer) said on 2021-03-04: #3

Hi,

This technically depends of the model in heft this will be fine obviously.
But yes if you use the "sm" model the total-width will be under-estimated and the cross-section will be over-estimated accordingly.
Now the shape of all distributions will be basically the same.

This is one of the limitation of the auto mode describe in the paper describing that feature: 1402.1178

Cheers,

Olivier

 Debashis (deba672) said on 2021-03-07: #4

Dear Olivier,

I was going through some of the other threads related to Higgs decay. Reading those, it seems that to get correct branching for h -> b b~, there are only two options. Either by modifying total width or by modifying the Yukawa coupling in param_card.dat. One can easily see what value one needs to use, as param_card.dat file has partial width information after width is calculated by using either "compute_widths" or "set DECAY 25 auto".

Although in principle one may want to change branching ratio directly, but as madgraph does not use narrow width approximation, rather uses directly Breit-Wigner propagator(mass of Higgs and total width) and Yukawa coupling, the partial width can be effectively modified on the fly by modifying Yukawa coupling or mass. OR keeping partial width same (by keeping Yukawa coupling and mass same), one can modify total width to effectively change the branching ratio.

You have mentioned the shape of all distributions will be basically the same even for underestimated total width. I think changing the branching ratio indirectly by changing Yukawa coupling will give the same distribution as that obtained with modified total width, as these are just overall factors for very small total decay width. Right? I suppose the same apply for W and Z also, where the width is comparatively large, but still very small with respect their masses.

Thanks,
Debashis

 Olivier Mattelaer (olivier-mattelaer) said on 2021-03-07: #5

The width for the Z/W are much larger than the width of the Higgs.
CMS is actually not using a breit-wigner shape for the higgs decay but that effect is taken into account for W and Z.

Cheers,

Olivier

 Debashis (deba672) said on 2021-03-14: #6

Thanks Olivier Mattelaer, that solved my question.