# Effects of Narrow Width Approximation with and without decay

Hello,

I am trying to evaluate the effects of the NWA in the calculation of the production cross-section as a function of a coupling parameter in the VLQ UFO model I am using, which affects the width of the VLQ. I have read the FAQ (#2442) that explains why one expects a discrepancy in the production cross-section with and without decays adding up to BR=1. However, I would like to ask for some clarifications. Apologies if I am not understanding something trivial.

On the example of FAQ #2442, should I understand that this directive

p p > t t~

(without any decays) uses or has the same effect as the NWA, whereas the directive

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

does not use the approximation? Also, in the former case, do the BR defined by the model play any role?

Regards,
Nik

## Question information

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Olivier Mattelaer
Solved:
2018-02-26
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2018-02-26
2018-02-21
 Olivier Mattelaer (olivier-mattelaer) said on 2018-02-20: #1

Hi,

p p > t t~ without any decay. Does not use the Narrow width approximation.
However, since we are using the S-matrix formalism (the diffusion theory) we assume that both top are in an infinite asymptotic state (i.e. that they are stable and onshell).
For that computation, the width does not play any role (as long as no decay occurs).

In order to speak of narrow width approximation, you need to include a decay. Since the narrow-width approximation is a way to factorise the amplitude containing a decay of an onshell particle.

For
p p > t t~, t > w+ b, t~ > w- b~
we use the full amplitude and therefore do not use the narrow-width approximation. However, this syntax does not include all the possible Feynman diagram leading to the same final state. The justification for discarding such diagrams are either due to experimental cuts and/or to the fact that such contributions are negligible compared to the onshell contribution (and then you are back to the motivation of the NWA)

Cheers,

Olivier

 sawtoothx (sawtoothx) said on 2018-02-21: #2

Dear Olivier,

thanks for your reply. I understand better now, after your reply, that, as is also stated in the FAQ above, that the cross-sections are going to be different NOT due to the NWA, but only due to cuts.

If I may ask, if I would disable the cut_decays function and put a very large bwcutoff, would I recover the same cross-section? I guess I could try this anyway.

More importantly, do you then think that there is a way I could use MadGraph to estimate the effects of using the NWA for a given model? I understand now that comparing the cross-sections obtained using these two syntaxes is not an appropriate measure.

Regards.
Nik

 Olivier Mattelaer (olivier-mattelaer) said on 2018-02-21: #3

if you compare

p p > b b~ w+ w-
to
p p > t t~
+ decay of the top via madspin with options "spinmode=none"

then you can compare the distribution and see the effect of the NWA

Cheers,

Olivier

> On 21 Feb 2018, at 09:47, sawtoothx <email address hidden> wrote:
>
> Question #664698 on MadGraph5_aMC@NLO changed:
>
>
> sawtoothx is still having a problem:
> Dear Olivier,
>
> as is also stated in the FAQ above, that the cross-sections are going to
> be different NOT due to the NWA, but only due to cuts.
>
> If I may ask, if I would disable the cut_decays function and put a very
> large bwcutoff, would I recover the same cross-section? I guess I could
> try this anyway.
>
> More importantly, do you then think that there is a way I could use
> MadGraph to estimate the effects of using the NWA for a given model? I
> understand now that comparing the cross-sections obtained using these
> two syntaxes is not an appropriate measure.
>
> Regards.
> Nik
>
> --

 sawtoothx (sawtoothx) said on 2018-02-21: #4

Thanks Olivier,

I actually want to study the production cross-section of a VLQ, so in the VLQ_UFO model, I wanted to try for various coupling parameters to do the following:

define VLQ = tp tp~
define bb = b b~
generate p p > j bb VLQ

It is interesting to see the use of madspin. However, I am interested primarily on the differences in the cross-section calculation for large VLQ width with and without the NWA. As I understand madspin would not help me in this case, correct? If not, I think I will have to compare the cross-section values to ones obtained from a different method.

Regards,
Nik

 Olivier Mattelaer (olivier-mattelaer) said on 2018-02-21: #5

Hi,

If you are only interested in the effect in the cross-section, then you do not need MadSpin since you know that the cross-section
is simply the production one time the BR. (As long as you do not have any cut obviously)

Cheers,

Olivier

> On 21 Feb 2018, at 15:52, sawtoothx <email address hidden> wrote:
>
> Question #664698 on MadGraph5_aMC@NLO changed:
>
>
> sawtoothx is still having a problem:
> Thanks Olivier,
>
>
> I actually want to study the production cross-section of a VLQ, so in the VLQ_UFO model, I wanted to try for various coupling parameters to do the following:
>
> define VLQ = tp tp~
> define bb = b b~
> generate p p > j bb VLQ
>
>
> It is interesting to see the use of madspin. However, I am interested primarily on the differences in the cross-section calculation for large VLQ width with and without the NWA. As I understand madspin would not help me in this case, correct? If not, I think I will have to compare the cross-section values to ones obtained from a different method.
>
> Regards,
> Nik
>
> --