MadGraph5_aMC@NLO

Independent simulation of EFT terms don't match the cross sections of full process

Asked by xiao jie

Dear authors,

I have generated same-sign WW process as following:
generate p p > l+ l+ vl vl j j QCD=0 SMHLOOP=0 @1
add process p p > l- l- vl~ vl~ j j QCD=0 SMHLOOP=0 @2

The model I used is:
SMEFTsim_A_U35_MwScheme_UFO
https://feynrules.irmp.ucl.ac.be/wiki/SMEFT

When I tested operators whose Wilson coefficients are cqq3, cqq31, cqq1, cqq11. Those operators are all four-quark operators.
I generated processes with only one of those coefficients are 1. I used following settings:
1. Independent simulation:
simulate interference terms and quadratic terms by adding "NP=1 NP^2==1", "NP=1 NP^2==2"seperately. Then the total cross sections are xs_sm+xs_interference+xs_quadratic
2. Full process:
Just set "NP=1", the cross sections are xs_full

Then I got the cross sections of all the processes:
a. For cqq3
    xs_sm+xs_interference+xs_quadratic: 0.16799 pb
    xs_full: 0.1898 pb
b. For cqq31
    xs_sm+xs_interference+xs_quadratic: 0.17921 pb
    xs_full: 0.2017 pb
c. For cqq1
    xs_sm+xs_interference+xs_quadratic: 0.07978 pb
    xs_full: 0.08374 pb
d. For cqq11
    xs_sm+xs_interference+xs_quadratic: 0.076795 pb
    xs_full: 0.08261 pb

So I found the total cross sections are all small than full processes, and those operators' quadratic term cross sections are large than SM cross sections.

Also the variables distributions are different. For example, for cqq3, you can find the mjj distributions here: http://jixiao.web.cern.ch/jixiao/polar_gen/eft/mjj_cqq3_shape.png

But except those four operators, other operators have good agreement.

Do you know why such four-quark operators are not consistent? And what kind of settings we should trust, independent simulation or full process.

Thanks,
Jie

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Olivier Mattelaer (olivier-mattelaer) said : 		#1

Hi,

The first point to check is that you are using the same run_card for each simulation.
Indeed the interference term in particular has a different default setting by default (in particular since the default dynamical scale choice is not relevant for that case). The agreement should be done within scale uncertainty (i.e. around 50% precision).

In the same spirit, if you set the dynamical_scale_choice to -1 for all 4 computation (which is default for the other ones) , you are still expected difference within scale uncertainty since that mode is based on the relative importance of Feynman diagram and since all four computation will have a different relative importance of each contribution the scale definition will also differ.

Therefore my suggestion is to use dynamical_scale_choice to "3" (HT/2) which is the default for the interference in that case (at least for the validation after that you can use back -1 if you think this is better for your computation).

Finally, note that MG5aMC does not have a dedicated phase-space integrator for interference ONLY. It is advise to either integrate that part together with a square matrix-element or to carefully check that the phase-space integration converges as expected. You can find in launchpad a huge list of case where the integration of interference alone does not converge correctly.

Cheers,

Olivier

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