The order of Diagrams and sqaured amplitude

Asked by Feng

Dear MadGraph author,
Recently I was calculating the contribution of higgs cubic coupling to e+ e- > z h h process in the SM model.

Let me denote the amplitude as
M = M1 + M2
M1 contains the cubic higgs coupling, while M2 not.
M^2 = M1^2 + 2 Re( M1 M2*) + M2 ^2

What I want to do is to generate event sample containing only M1^2 + 2 Re( M1 M2*) . (What I did is follow your suggestion)
I tried to follow the suggestion on https://answers.launchpad.net/mg5amcnlo/+question/248683, defining a new order NP, and replacing the higgs cubic vertex QED order with NP order. And then I generate the process with the following commands

(1) generate e+ e- > z h h NP^2==0
(2)generate e+ e- > z h h NP^2>0
(3)generate e+ e- > z h h NP^2<=5

It displays that there are 4 diagrams in case (2) and (3) while only 3 diagrams in case (1). Case (1) do not involve the higgs coupling. And the sum of the cross section of (1) and (2) is equal to the cross section of (3).

I would say that (1) corresponds to M2^2 and (2) corresponds to M1^2 + 2 Re( M1 M2*). Am I right?

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Valentin Hirschi
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Best Valentin Hirschi (valentin-hirschi) said :
#1

You are exactly correct. (2) is the results you are looking for, namely the "signal" (feat. the Higgs cubic coupling) squared and its interference with the "background" (without a Higgs cubic coupling).

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Feng (chizukuangben) said :
#2

Thank you very much! @Valentin Hirschi (valentin-hirschi)

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Feng (chizukuangben) said :
#3

Thanks Valentin Hirschi, that solved my question.