MadGraph5_aMC@NLO

cross-section of subprocess larger than total cross-section

Asked by Alberto Gascón

Hi,

running some simple tests I ended up comparing 4 top final states in the following two ways:

generate g g > t t~ t t~

to

generate g g > t t~ all, (all > t t~)

with orders set to their default value (so "all" in only gluons in the second case)

As far as I understand, the second process is a subprocess of the first one. This is, all diagrams in the second process are included in the first one. In fact, the first process has 72 diagrams while the second one has 16. However, the cross-section for the first process is ~8 fb but ~25 fb for the second. At first sight that does not make sense to me, but I think there's something basic I'm not understanding.

Cheers,
   Alberto

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Olivier Mattelaer
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Madalina Stanescu-Bellu (madalina-stanescu-bellu) said : 		#1

I think you should add as well that you used import sm and that you didn't change the default value for "all", but you left it at default value , and you observed that in the end the only diagrams produced for generate g g > t t~ all, (all > t t~) are g g > t t~ g, (g > t t~) , right ? and you also observed that these g g > t t~ g, (g > t t~) diagrams are all included in the g g > t t~ t t~ diagrams , right ?

Cheers,
Madalina

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Alberto Gascón (albergascon) said : 		#2

Thanks Madalina for making my question more accurate. Both thing
are right: using all as an intermediate I only found g g > t t~ g, (g > t t~) diagrams,
and g g > t t~ t t~ contains all diagrams in g g > t t~ g, (g > t t~), plus additional diagrams.

Alberto

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Best Olivier Mattelaer (olivier-mattelaer) said : 		#3

Hi Alberto, Madalina,

The syntax
> g g > t t~ g, (g > t t~)

means generate a gluon on shell and then decay the on shell particles to t t~…. not very physical

Actually the cross-section of
g g > t t~ ALL, ALL > t t~
is not expected to be equal to
g g > t t t~ t~
exactly because the first syntax force the particle “ALL” to be on shell which is not the case of the second syntax.
The first syntax should only be use when Narrow width approximation is valid.
Therefore I would encourage to NOT use multi-particle label with decay chain syntax.

Since the syntax “g g > t t~ g, (g > t t~) “ is meaningless, I have no idea (and do not care) how madgraph succeeds to returned a number to it.
The actual number that I would expect madgraph to returns for the above syntax is 0 due to the restriction of the gluon to be on shell.
What probably happens is that MG discard the condition of the gluon to be on shell. But even if that assumptions is correct and even if MG does it in a fully sensible way.
You result is still meaningless since you break gauge invariance, meaning that your cross-section has no physical meaning (your cross-section is likely to be boost dependent, i.e. not lorentz invariant).

The reason of this breaking of gauge invariance and lorentz invariant is that you are discarding important set of Feynman diagram, diagram which interferes strongly with the one that you kept.
You can see that even from your number. Your cross-section is likely to be bigger simply because you discard Feynman diagram which interferes negatively with the Feynman diagram that you kept.

Cheers,

Olivier

On 24 Mar 2015, at 20:36, Alberto Gascón <email address hidden> wrote:

> Question #264109 on MadGraph5_aMC@NLO changed:
> https://answers.launchpad.net/mg5amcnlo/+question/264109
>
> Alberto Gascón posted a new comment:
> Thanks Madalina for making my question more accurate. Both thing
> are right: using all as an intermediate I only found g g > t t~ g, (g > t t~) diagrams,
> and g g > t t~ t t~ contains all diagrams in g g > t t~ g, (g > t t~), plus additional diagrams.
>
> Alberto
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

Revision history for this message
Alberto Gascón (albergascon) said : 		#4

Thanks Olivier Mattelaer, that solved my question.

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Madalina Stanescu-Bellu (madalina-stanescu-bellu) said : 		#5

Dear Olivier,

Thanks for the explanations. Regarding:

> Therefore I would encourage to NOT use multi-particle label with decay chain syntax.

What about this decay chain syntax ?

define l+ = e+ mu+ ta+
define l- = e- mu- ta-
define p = g u c d s u~ c~ d~ s~ b b~
define j = p

generate g g > t t~, ( t > b w+, w+ > l+ vl), ( t~ > b~ w-, w- > j j) @1

That's the syntax I've been always running in my interference studies the last year ...

Cheers,
Madalina

Revision history for this message
Olivier Mattelaer (olivier-mattelaer) said : 		#6

> generate g g > t t~, ( t > b w+, w+ > l+ vl), ( t~ > b~ w-, w- > j j) @1

That’s a perfectly valid syntax, where the particle request to be on shell are t t~ w+ w- so no multi-particle and for each of them the Narrow width approximation is a relatively good approximation.

Cheers,

Olivier

On 24 Mar 2015, at 23:01, Madalina Stanescu-Bellu <email address hidden> wrote:

> Question #264109 on MadGraph5_aMC@NLO changed:
> https://answers.launchpad.net/mg5amcnlo/+question/264109
>
> Madalina Stanescu-Bellu posted a new comment:
> Dear Olivier,
>
> Thanks for the explanations. Regarding:
>
>> Therefore I would encourage to NOT use multi-particle label with decay
> chain syntax.
>
> What about this decay chain syntax ?
>
> define l+ = e+ mu+ ta+
> define l- = e- mu- ta-
> define p = g u c d s u~ c~ d~ s~ b b~
> define j = p
>
> generate g g > t t~, ( t > b w+, w+ > l+ vl), ( t~ > b~ w-, w- > j j) @1
>
> That's the syntax I've been always running in my interference studies
> the last year ...
>
> Cheers,
> Madalina
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.