How does Madgraph calculate the width of a particle when we set the particle width to auto

Hi,

For all the details on the automatic computation of the width when using auto.
The best is to read the associated paper: 1402.1178 <https://arxiv.org/abs/1402.1178>

> But I am confused about the automatic computation of the width is only valid in narrow-width approximation .

Yes indeed such computation assumes that narrow-width approximation is valid.
If this is not the case then I do not know how to compute such width reliably.

> For example if I generate e e > z > T t ，(T >ｗｂ), that T represents a BSM particle with a large width(Γ_T/m_T=0.5, m_T=3000GeV).

so here you have two issues:
1) if you use auto and get a 50% ratio, then you can not trust the value of the width (since NWA is clearly no valid)
2) you can not use such syntax (the use of the "," to distinguish production and decay) since again such syntax is assuming NWA

what you need to use is
> generate e e > z > t ｗｂ

which will include other diagrams and importantly the interference with those diagrams.
(but also the importance of the exact value of the width will decrease)

> I confused if the cross section calculated by NWA is valid for this width.

Likely not.

> In presence of resonances, the width control how large is the cross-section. So they have huge impact on the cross-section. Does this resonance refer to the Breit-Wigner resonance? Whether the width of T controls the scattering cross section of the above process?

Yes resonances refers to the Breit-Wigner.

> Whether the width of T controls the scattering cross section of the above process?

In narrow-width approximation the cross-section is proportional to 1/width
but this assumes that M >> width and that the matrix-element is flat on the phase-space region enhanced by the Breit-Wigner.

With width at 50% of the mass, the "enhanced" correspond to basically full phase-space and assuming
a flat matrix-element is certainly a bad approximation.

Another way to see the problem is that the narrow-width approximation is associated to a theoretical error of
width/mass so using the NWA approximation for such mass/width is at best associated to an additional 50% theoretical uncertainty and I would even bet that you under-estimate such error by using such formula.

So in this case since you use twice the NWA (once for the computation of the width and once for the computation of the cross-section) your theoretical error is likely of the order of 100%.

Now if you drop the NWA, the total cross-section should start to have a decreased sensitity to the exact value of the (large) width.

Cheers,

Olivier

> On 30 Nov 2021, at 13:05, 王世钰 <email address hidden> wrote:
>
> New question #699682 on MadGraph5_aMC@NLO:
> https://answers.launchpad.net/mg5amcnlo/+question/699682
>
> Hi, I am a new user of MadGraph. I have read the question https://answers.launchpad.net/mg5amcnlo/+question/698447
>
> But I am confused about the automatic computation of the width is only valid in narrow-width approximation .
>
> For example if I generate e e > z > T t ，(T >ｗｂ), that T represents a BSM particle with a large width(Γ_T/m_T=0.5, m_T=3000GeV).
> I confused if the cross section calculated by NWA is valid for this width.
> and other confused:
> In presence of resonances, the width control how large is the cross-section. So they have huge impact on the cross-section. Does this resonance refer to the Breit-Wigner resonance? Whether the width of T controls the scattering cross section of the above process?
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

First of all, you have resolved a lot of my confusion, and I would like to express my sincere thanks.
I would like to continue to ask a few questions:
>So in this case since you use twice the NWA (once for the >computation of the width and once for the computation of the cross->section) your theoretical error is likely of the order of 100%.
Shouldn’t the calculation of the width be irrelevant to the process, if so, what does “once for the computation of the width” here represent?

Cheers,

Wsy

I'm not 100% sure here.

If you take the case where width >> mass,
then the propagator effectivelly act as an effective coupling which is proportional to 1/(width*mass)
and therefore if you do not have any other diagram in your process that interefere with that diagram/contribute (a big if obviously), the cross-section should scale as 1/(width*mass)^2
So the width is still an important parameter for the cross-section even in the large width limit.
Now in practise, this term will likely start to be very small and therefore interference term might be more relevant than this amplitude square term (as we often see when we take a full theory and explore the EFT regime)

Cheers,

Olivier

> On 30 Nov 2021, at 13:55, 王世钰 <email address hidden> wrote:
>
> Question #699682 on MadGraph5_aMC@NLO changed:
> https://answers.launchpad.net/mg5amcnlo/+question/699682
>
> Status: Answered => Open
>
> 王世钰 is still having a problem:
> First of all, you have resolved a lot of my confusion, and I would like to express my sincere thanks.
> I would like to continue to ask a few questions:
>> So in this case since you use twice the NWA (once for the >computation of the width and once for the computation of the cross->section) your theoretical error is likely of the order of 100%.
> Shouldn’t the calculation of the width be irrelevant to the process, if so, what does “once for the computation of the width” here represent?
>
> Cheers,
>
> Wsy
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

Hello, my last question may not be clear; my confusion is whether the width automatically calculated by madgraph is related to the process I input (ee> z> T t, (T> wb)), regardless of the large width Or the case of NWA.
I have another confusion: If the width of the particle can really reach 0.5*m, then we give the particle width instead of the automatic calculation of madgraph, and then use> generate ee> z> t wb instead of generate ee> z> T t , (T> wb), then is this approach reliable？

Hi,

No the width computed does not depend on the production process.

> then is this approach reliable？

Like this you avoid the issue with the Narrow Width Approximation.
So you should be fine in that direction, now I can not speak for the model validity and other source of theoretical error.

Cheers,

Olivier

> On 1 Dec 2021, at 06:05, 王世钰 <email address hidden> wrote:
>
> Question #699682 on MadGraph5_aMC@NLO changed:
> https://answers.launchpad.net/mg5amcnlo/+question/699682
>
> Status: Answered => Open
>
> 王世钰 is still having a problem:
> Hello, my last question may not be clear; my confusion is whether the width automatically calculated by madgraph is related to the process I input (ee> z> T t, (T> wb)), regardless of the large width Or the case of NWA.
> I have another confusion: If the width of the particle can really reach 0.5*m, then we give the particle width instead of the automatic calculation of madgraph, and then use> generate ee> z> t wb instead of generate ee> z> T t , (T> wb), then is this approach reliable？
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

Dear Olivier
Thank you very much!
Do you mean that whatever process I set, the result of the width is not influenced when set to auto?
I have another doubt: how to calculate the scattering cross section madgraph of this process (ee> z> t wb); write down the scattering amplitude of this 2 to 3 process, and then do a three-body phase space integration; or Calculate the (ee> z> tT) scattering cross section of this process according to the breit-wigner resonance formula, and then multiply it by the decay branch ratio (T> wb); This question is asked because I am very interested in madgraph's automatic calculation of scattering amplitude and giving numerical results. I hope to know more about madgraph.

Hi,

> Do you mean that whatever process I set, the result of the width is not influenced when set to auto?

Correct

Actually the "auto" is just a convenient way to call the package defined in the paper mentioned above.
When you read that paper you will see that we never mention any production process.
Also within that paper you will learn that they are other way to call that code.
and will you see that those other method do not have any process defined at all.

The width is a property of the particle, and this is independent of on how such particle is produced.

> I have another doubt: how to calculate the scattering cross section madgraph of this process (ee> z> t wb); write down the scattering amplitude of this 2 to 3 process, and then do a three-body phase space integration; or Calculate the (ee> z> tT) scattering cross section of this process according to the breit-wigner resonance formula, and then multiply it by the decay branch ratio (T> wb); This question is asked because I am very interested in madgraph's automatic calculation of scattering amplitude and giving numerical results. I hope to know more about madgraph.

Using the branching ratio is certainly wrong since the concept of branching ratio is based on the narrow width approximation. So here you have to use a three body phase-space integrator.

Cheers,

Olivier

> On 1 Dec 2021, at 12:50, 王世钰 <email address hidden> wrote:
>
> Question #699682 on MadGraph5_aMC@NLO changed:
> https://answers.launchpad.net/mg5amcnlo/+question/699682
>
> Status: Answered => Open
>
> 王世钰 is still having a problem:
> Dear Olivier
> Thank you very much!
> Do you mean that whatever process I set, the result of the width is not influenced when set to auto?
> I have another doubt: how to calculate the scattering cross section madgraph of this process (ee> z> t wb); write down the scattering amplitude of this 2 to 3 process, and then do a three-body phase space integration; or Calculate the (ee> z> tT) scattering cross section of this process according to the breit-wigner resonance formula, and then multiply it by the decay branch ratio (T> wb); This question is asked because I am very interested in madgraph's automatic calculation of scattering amplitude and giving numerical results. I hope to know more about madgraph.
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

Thank you very much for your answers, and I will continue to pay attention to your articles. Fortunately, our conversation allowed me to learn so much about madgraph