MadGraph5_aMC@NLO

Widths off-shell

Asked by Matthew Low

Dear MadGraph team,

I was wondering how MadGraph handles particle widths for very off-shell propagators? I've looked at e+e- > resonance > mu+mu- and it follows a relativistic breit-wigner with the replacement Width -> (sqrt(s)/m) Width, which is only relevant off-shell. If I look at the same process with an ISR photon (for a very narrow resonance) then is the replacement Width -> (sqrt(s)/m) Width made or is it done event-by-event and would use the s-hat value for the incoming e+e- (which is less than s because of the radiated photon)?

Thanks,
- Matthew

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Olivier Mattelaer
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Olivier Mattelaer (olivier-mattelaer) said : 		#1

Dear Matthew,

I’m confuse about your question.

> I’ve looked at e+e- > resonance > mu+mu- and it follows a relativistic breit-wigner

Since typically e+ e- beam have a fix energy, I do no see how you can have a breit-wigner.
The curve that you observe is just likely to be due to the numerical accuracy.

Cheers,

Olivier

On 30 Dec 2014, at 10:51, Matthew Low <email address hidden> wrote:

> New question #259886 on MadGraph5_aMC@NLO:
> https://answers.launchpad.net/mg5amcnlo/+question/259886
>
> Dear MadGraph team,
>
> I was wondering how MadGraph handles particle widths for very off-shell propagators? I've looked at e+e- > resonance > mu+mu- and it follows a relativistic breit-wigner with the replacement Width -> (sqrt(s)/m) Width, which is only relevant off-shell. If I look at the same process with an ISR photon (for a very narrow resonance) then is the replacement Width -> (sqrt(s)/m) Width made or is it done event-by-event and would use the s-hat value for the incoming e+e- (which is less than s because of the radiated photon)?
>
> Thanks,
> - Matthew
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

Revision history for this message
Matthew Low (mattlow) said : 		#2

Hi Olivier,

I mean if I scan over the center of mass energy, a Breit-Wigner (near resonance) would be:
\sigma(s) = c \Gamma^2 / ((s-m^2)^2 + m^2 \Gamma^2)

where c accounts for spin factors and branching ratios. When I do this scan I find:
\sigma(s) = c (s/m^2) \Gamma^2 / ((s-m^2)^2 + s \Gamma^2)

fits the curve, but the first equation does not. So I assume that MadGraph is using the second equation, which you get from making the replacement \Gamma -> \sqrt(s)/m \Gamma in the first equation (the first equation is the "normal" Breit-Wigner).

My question is if I look at the same process with an ISR photon, now s-hat != s. For the Breit-Wigner subprocess does MadGraph use s or s-hat?

Thanks,
- Matthew

Revision history for this message
Best Olivier Mattelaer (olivier-mattelaer) said : 		#3

Dear Matthew,

MadGraph do not performed any special treatment for the width.
The dependence in the width is just part of the propagator definition.
No event by event or other “weird” operation is applied.

> I mean if I scan over the center of mass energy, a Breit-Wigner (near resonance) would be:
> \sigma(s) = c \Gamma^2 / ((s-m^2)^2 + m^2 \Gamma^2)
>
> where c accounts for spin factors and branching ratios. When I do this scan I find:
> \sigma(s) = c (s/m^2) \Gamma^2 / ((s-m^2)^2 + s \Gamma^2)

I guess that the difference between the two curve are very small and that the reason why the first curve does not fit can be explained by other factor like
- flux
- phase-space opening
- influence of cut
-…

> My question is if I look at the same process with an ISR photon, now
> s-hat != s. For the Breit-Wigner subprocess does MadGraph use s or
> s-hat?

We use the invariant mass of the particle.
In presence of ISR, this is generated via our random number generator.

Cheers,

Olivier

PS: If you use a old MG4 model, then the propagator definition comes from the HELAS library where some treatment where done in order to have the propagator definition closer of the complex-mass scheme mode.

On 03 Jan 2015, at 18:46, Matthew Low <email address hidden> wrote:

> Question #259886 on MadGraph5_aMC@NLO changed:
> https://answers.launchpad.net/mg5amcnlo/+question/259886
>
> Status: Answered => Open
>
> Matthew Low is still having a problem:
> Hi Olivier,
>
> I mean if I scan over the center of mass energy, a Breit-Wigner (near resonance) would be:
> \sigma(s) = c \Gamma^2 / ((s-m^2)^2 + m^2 \Gamma^2)
>
> where c accounts for spin factors and branching ratios. When I do this scan I find:
> \sigma(s) = c (s/m^2) \Gamma^2 / ((s-m^2)^2 + s \Gamma^2)
>
> fits the curve, but the first equation does not. So I assume that
> MadGraph is using the second equation, which you get from making the
> replacement \Gamma -> \sqrt(s)/m \Gamma in the first equation (the first
> equation is the "normal" Breit-Wigner).
>
> My question is if I look at the same process with an ISR photon, now
> s-hat != s. For the Breit-Wigner subprocess does MadGraph use s or
> s-hat?
>
> Thanks,
> - Matthew
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

Revision history for this message
Matthew Low (mattlow) said : 		#4

Thanks Olivier Mattelaer, that solved my question.