MadGraph5_aMC@NLO

bwcutoff in top pair gluon gluon/ e+ e- production and decay

Asked by sara diglio

Dear MadGraph Team,
I have a question concerning the bwcutoff dependence of the cross section for the following SM processes:

g g > t t~, t > w+ b, t~ > w- b~
e+ e- > t t~, t > w+ b, t~ > w- b~

compared to g g > t t~ and e+ e- > t t~, respectively.

I already read the two posts concerning the top pair productions in proton proton collisions
https://answers.launchpad.net/mg5amcnlo/+faq/2442
https://answers.launchpad.net/mg5amcnlo/+question/236617
but I still have a question concerning the above cases.

My understanding from the previous posts was that increasing the value of bwcutoff would have increased the value of the cross section such that the two cross sections obtained by specifying or not the two top decays tend to agree (apart from the uncertainty related to the NWA), is this correct?
I verified that this is the case for the proton proton collisions, for which I got (removing all cuts)
@14TeV
p p > t t~ (bwcutoff independent)
xsec : 596.5 +- 0.8166 pb

p p > t t~ , t > w+ b, t~ > w- b~ (bwcutoff 15)
xsec: 570.6 +- 1.212 pb
p p > t t~ , t > w+ b, t~ > w- b~ (bwcutoff 1500)
xsec : 593.6 +- 1.257 pb
p p > t t~ , t > w+ b, t~ > w- b~ (bwcutoff 15E+37)
xsec : 594.4 +- 1.235 pb

If indeed when I tried the gluon gluon or the e+ e- productions I got results that I do not understand.
In order to choose either gluon gluon or e+ e- as initial states, I changed the param_card.dat by setting
#*********************************************************************
# Collider type and energy *
# lpp: 0=No PDF, 1=proton, -1=antiproton, 2=photon from proton, *
# 3=photon from electron *
#*********************************************************************
        0 = lpp1 ! beam 1 type
        0 = lpp2 ! beam 2 type
      1200 = ebeam1 ! beam 1 total energy in GeV
      1200 = ebeam2 ! beam 2 total energy in GeV

All the other cuts are removed, and here what I got

@2.4TeV
g g > t t~ (bwcutoff independent)
xsec : 4.852 +- 0.002349 pb

g g > t t~ , t > w+ b, t~ > w- b~ (bwcutoff 15)
xsec: 4.664 +- 0.003242 pb
g g > t t~ , t > w+ b, t~ > w- b~ (bwcutoff 1500)
xsec : 6.601 +- 0.01622 pb
g g > t t~ , t > w+ b, t~ > w- b~ (bwcutoff 15E+37)
xsec : 6.614 +- 0.01082 pb

@2.4TeV
e+ e- > t t~ (bwcutoff independent)
xsec : 0.02984 +- 2.621e-05 pb

e+ e- > t t~ , t > w+ b, t~ > w- b~ (bwcutoff 15)
xsec: 0.02865 +- 2.86e-05 pb
e+ e- > t t~ , t > w+ b, t~ > w- b~ (bwcutoff 1500)
xsec : 0.0399 +- 8.208e-05 pb
e+ e- > t t~ , t > w+ b, t~ > w- b~ (bwcutoff 15E+37)
xsec : 0.03983 +- 7.534e-05 pb

What the reason for having such trend? How comes that the cross sections where the two top decays are specified may be larger than the top pair production one? Are there large far off shell effects that are playing a role for such large center of mass energies and large bwcutoff?

Thanks a lot in advance for the clarification
Cheers
Sara

Question information

Language:
English Edit question
Status:
Answered
For:
MadGraph5_aMC@NLO Edit question
Assignee:
FabioMaltoni Edit question
Last query:
Last reply:
Revision history for this message
Rikkert Frederix (frederix) said : 		#1

Dear Sara,

Sorry for the late reply.

In fact, the NWA is only a "correct" approximation if the intermediate resonance is exactly on-shell. Away from on-shell, the results will, in general, not be gauge invariant or unitary. Indeed, if you plot the invariant mass of the w+ b (or w- b~), for a fixed collider energy, you see that this distribution shows the top resonance, but a large increasing tail at larger masses. Indeed, these are contributions that are not correctly modelled and for which the NWA is not a valid approximation. In that case, it is more correct to directly generate the e+ e- > w+ w- b b~ process.

Note that this effect is highly suppressed in the case of LHC (or hadron collision in general), due to the fact that the parton luminosities being much smaller at large w+ b (or w- b~) invariant masses.

best regards,
Rikkert

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