off shell cross section

Asked by Wang Daohan on 2020-04-06

I have a problem with on shell and off shell cross sections. maybe it's naive, but I am confused for a long time. Take a SM example.
I generate p p > t t~ > b b~ w- j j, let's call it process 1. this process contain t and w+ off shell and on shell contributions. But the cross section is smaller than this process p p > t t~, t > w+ > b j j, t~ > b~ w- which only contain on shell contribution, let's call it process2.
But when I generate p p > t t~ > b b~ w+ w- in madgraph and write the decay in madspin. Let's call it process 3. The corresponding cross section then is larger than this process p p > t t~, t > w+ > b j j, t~ > b~ w-.
I want to know why the cross section of process 1 is smaller than process 2 and why the cross section of process 3 is larger than process 2.
I hope you can help me with it.
Thank you very much!
Dorhand

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Olivier Mattelaer
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2020-04-06
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2020-04-06
2020-04-06
 Olivier Mattelaer (olivier-mattelaer) said on 2020-04-06: #1

Hi,

Did you look at the FAQ that I just linked?
I believe that what you observe is just related to different cut (and in particular to the variable cut_decays set to False in your case)

Cheers,

Olivier

FAQ #2442: “why production and decay cross-section didn't agree.”.

 Wang Daohan (dorhand) said on 2020-04-06: #3

Thanks very much for your reply. The variable cut_decays defaulted setting is False. But my question is still there. Why the cross section of this process p p > t t~ > b b~ w- j j is larger than p p > t t~, t > w+ > b j j, t~ > b~ w- ? The only difference is the latter t tbar is forced to be on shell. I really hope you can give me some hints.

 Olivier Mattelaer (olivier-mattelaer) said on 2020-04-06: #4

Hi,

When i run:
> p p > t t~ > b b~ w- j j

INFO: #***************************************************************************
#
# original cross-section: 241.955420632
# scale variation: +30.5% -21.9%
# central scheme variation: +5.02% -26.1%
# PDF variation: +4.38% -4.38%
#
# dynamical scheme # 1 : 202.875 +28.6% -21% # \sum ET
# dynamical scheme # 2 : 197.925 +28.4% -20.8% # \sum\sqrt{m^2+pt^2}
# dynamical scheme # 3 : 254.094 +30.9% -22.1% # 0.5 \sum\sqrt{m^2+pt^2}
# dynamical scheme # 4 : 178.787 +27.3% -20.3% # \sqrt{\hat s}
#***************************************************************************

When I run
> p p > t t~, t > w+ > b j j, t~ > b~ w-

(with cut_decays=True)
INFO: #***************************************************************************
#
# original cross-section: 237.297817773
# scale variation: +30.3% -21.7%
# central scheme variation: +4.91% -26%
# PDF variation: +4.29% -4.29%
#
# dynamical scheme # 1 : 199.166 +28.4% -20.8% # \sum ET
# dynamical scheme # 2 : 194.22 +28.2% -20.7% # \sum\sqrt{m^2+pt^2}
# dynamical scheme # 3 : 248.939 +30.7% -22% # 0.5 \sum\sqrt{m^2+pt^2}
# dynamical scheme # 4 : 175.718 +27.1% -20.1% # \sqrt{\hat s}
#***************************************************************************

So the difference is quite small (4pb) and you can see that the theoretical uncertainty is much bigger than that (30% of the corss-section). The fact is that the default dynamical scale depends of the exact syntax that you use and therefore can lead to difference in term of prediction which are within theoretical uncertainty.

Now if I run for HT/2 as the central dynamical scale (which does not depend of the syntax used)
> p p > t t~ > b b~ w- j j

INFO: #***************************************************************************
#
# original cross-section: 261.413583767
# scale variation: +30.9% -22%
# central scheme variation: + 0% -29.6%
# PDF variation: +4.31% -4.31%
#
# dynamical scheme # 1 : 208.918 +28.5% -20.9% # \sum ET
# dynamical scheme # 2 : 203.786 +28.3% -20.8% # \sum\sqrt{m^2+pt^2}
# dynamical scheme # 3 : 261.414 +30.9% -22% # 0.5 \sum\sqrt{m^2+pt^2}
# dynamical scheme # 4 : 184.028 +27.2% -20.2% # \sqrt{\hat s}
#***************************************************************************

When I run
> p p > t t~, t > w+ > b j j, t~ > b~ w-

(with cut_decays=True)
INFO: #***************************************************************************
#
# original cross-section: 250.52584976
# scale variation: +30.7% -22%
# central scheme variation: +9.78e-09% -29.3%
# PDF variation: +4.28% -4.28%
#
# dynamical scheme # 1 : 200.41 +28.4% -20.8% # \sum ET
# dynamical scheme # 2 : 195.454 +28.2% -20.7% # \sum\sqrt{m^2+pt^2}
# dynamical scheme # 3 : 250.526 +30.7% -22% # 0.5 \sum\sqrt{m^2+pt^2}
# dynamical scheme # 4 : 177.001 +27.1% -20.2% # \sqrt{\hat s}
#***************************************************************************

Finally If I try to remove the onshell requirement with this syntax (in order to match the above result) by setting bwcutoff to 1e9, I get:
INFO: #***************************************************************************
#
# original cross-section: 261.589530988
# scale variation: +30.8% -22%
# central scheme variation: +2.96e-09% -29.4%
# PDF variation: +4.26% -4.26%
#
# dynamical scheme # 1 : 209.256 +28.5% -20.9% # \sum ET
# dynamical scheme # 2 : 204.063 +28.2% -20.7% # \sum\sqrt{m^2+pt^2}
# dynamical scheme # 3 : 261.59 +30.8% -22% # 0.5 \sum\sqrt{m^2+pt^2}
# dynamical scheme # 4 : 184.723 +27.1% -20.2% # \sqrt{\hat s}
#***************************************************************************

This being said, using
> p p > t t~ > b b~ w- j j
or
> p p > t t~, t > w+ > b j j, t~ > b~ w-
with very large bwcutoff are both impacted by another source of theoretical error due to the fact that you neglect interference with other type of diagrams and by the handling of the width (which is using here a fix value, i.e no running).
Note that you can use complex mass scheme in madgraph (but this requires that you also decay the W for that scheme to make sense).

Cheers,

Olivier

> On 6 Apr 2020, at 09:22, Wang Daohan <email address hidden> wrote:
>
> Question #689732 on MadGraph5_aMC@NLO changed:
>
> Wang Daohan gave more information on the question:
> Thanks very much for your reply. The variable cut_decays defaulted
> setting is False. But my question is still there. Why the cross section
> of this process p p > t t~ > b b~ w- j j is larger than p p > t t~, t >
> w+ > b j j, t~ > b~ w- ? The only difference is the latter t tbar is
> forced to be on shell. I really hope you can give me some hints.
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

 Wang Daohan (dorhand) said on 2020-04-06: #5

Thank you very much !

 Wang Daohan (dorhand) said on 2020-04-06: #6

Thanks Olivier Mattelaer, that solved my question.

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