MadGraph5_aMC@NLO

Goldstone boson equivalence theorem

Asked by Taegyu Lee

Hello,

I was running madgraph to check the Goldstone boson equivalence theorem (GBET) using the "sm-full" model file.

From my understanding of GBET assures that cross section for goldstone boson production should be equal to cross section for longitudinal gauge boson up to the (mass/energy).

I found that for many cases, this does not work in madgraph.

For example, using "sm-full",
I calculated cross section for
c c~ > g0 g0
c c~ > z{0} z{0}
which gave me different result for both 13 TeV proton proton collision and 13 TeV No PDF.

I am not sure where I missed. I ran for many different processes with different final and initial state.
I found it works for mu mu > g0g0 and mu mu > z{0} z{0}, but somehow for quarks it does not work in many cases.

Thanks!

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Launchpad Janitor (janitor) said : 		#1

This question was expired because it remained in the 'Open' state without activity for the last 15 days.

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Taegyu Lee (taegyulee) said : 		#2

I still need an answer

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Olivier Mattelaer (olivier-mattelaer) said : 		#3

Hi,

I have run the following:
import model sm-full
generate c c~ > g0 g0
output
launch
set lpp 0
set ebeam 100k

this returns:
     Cross-section : 5.001e-13 +- 1.258e-15 pb
     Nb of events : 10000

and then i did run
import model sm-full
generate c c~ > z{0} z{0}
output
launch
set lpp 0
set ebeam 100k

this returns:
     Cross-section : 5.014e-13 +- 1.264e-15 pb
     Nb of events : 10000

Based on that, I do not know what I can answer to you...

Cheers,

Olivier

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Taegyu Lee (taegyulee) said (last edit ): 		#4

Hi Olivier,

Thanks for your answer!
I ran the same code you suggested with very large energy and my result agreed with yours.

I also tried lpp=1

import model sm-full
generate c c~ > g0 g0
output
launch
set lpp 1

gave me result

Cross-section : 4.771e-06 +- 9.775e-09 pb
     Nb of events : 10000

While

import model sm-full
generate c c~ > z{0} z{0}
output
launch
set lpp 1

gave me

     Cross-section : 0.008132 +- 2.031e-05 pb
     Nb of events : 10000

Do you think this is just an artifact of less energy transfer and PDF compared to your case?

By the way, I get

import model sm-full
generate c c~ > g0 g0
output
launch
set lpp 0

     Cross-section : 8.912e-11 +- 1.691e-13 pb
     Nb of events : 10000

import model sm-full
generate c c~ > z{0} z{0}
output
launch
set lpp 0

     Cross-section : 1.494e-10 +- 2.862e-13 pb
     Nb of events : 10000

Both with CME = 14 TeV.

Thank you very much for your time!

Best,
Taegyu

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Olivier Mattelaer (olivier-mattelaer) said : 		#5

Hi,

The PDF are large at small x, this typically means that the energy of the collision prefer to be small (i.e. close to threshold).
In that area you obviously do not expect the approximation to hold. (Now you can use MA5 to plot the actuall energy of the collision if my guess is correct/wrong.

Now at 14 TeV without PDF, it is what it is. I do not know the exact form of the correction term that you expect and how large they are suppose to be and when to be able to comment more.

Cheers,

Olivier

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Taegyu Lee (taegyulee) said : 		#6

Hi,

Thanks, I think I get it.

Thanks for your help!

Best,
Taegyu