Excluding exchange diagrams

Asked by Feyza Baspehlivan

Dear experts,

I have a BSM model with new heavy leptons (vlm) which have mixings with only leptons via bosons. I am generating the process:

> generate mu+ mu- > vlm+ vlm-

and 5 diagrams we have for this process:

- Z and photon and Higgs s-channel
- Z and Higgs t-channel (exchange diagram).

I want to keep only Z and photon s-channel diagrams but I couldn't find a way to do this. Could you inform me about this?

I know that by the command

> generate mu+ mu- > vlm+ vlm- /h

I can get rid of all Higgs diagrams and by the command

> generate mu+ mu- > vlm+ vlm- $z

I can get rid of only Z on-shell diagram but these do not solve my problem.

Thank you in advance,

Feyza

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Olivier Mattelaer (olivier-mattelaer) said :
#1

Can this syntax is what you want?
generate mu+ mu- > Z | a > vlm+ vlm-

Carefully that such syntax is likely not gauge invariant
(also note that for not gauge invariant amplitude our result are also not lorentz invariant).
And therefore result can be surprising (and arbitrary)

Cheers,

Olivier

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Feyza Baspehlivan (feyzabaspehlivan) said :
#2

Hello again,

This helps, thanks a lot and the results do not seem peculiar. But still, I wonder why this syntax is unlikely to be gauge invariant, is it because of the infrastructure of MadGraph or because of its physics?

Best regards,

Feyza

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Olivier Mattelaer (olivier-mattelaer) said :
#3

Just physics, not all subset of diagram are gauge invariant.

Now the fact that breaking gauge invariance, breaks lorentz invariance in MG5aMC is specific to our code (since the gauge choice are done differently in different frame).

Cheers,

Olivier

PS: you can use the command "check mu+ mu- > Z | a > vlm+ vlm-" to check on a couple phase-space point if the result is lorentz/gauge invariant (and other sanity check). If such test fails then I would certainly not use such syntax.
(I would not say that such command is strong enough to aleviate any doubt but it is a good start)

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Feyza Baspehlivan (feyzabaspehlivan) said (last edit ):
#4

Thank you for your helpful reply. I checked the gauge invariance by the code you have given:

MG5_aMC>check mu+ mu- > Z | a > vlm+ vlm-
check: Samurai not available on your system; it will be skipped.
check: Ninja not available on your system; it will be skipped.
INFO: Checking crossings of process mu+ mu- > z|a > vlm+ vlm-
INFO: Testing permutation: [1, 2, 4, 3]
INFO: Testing permutation: [1, 3, 2, 4]
INFO: Testing permutation: [1, 3, 4, 2]
INFO: Testing permutation: [1, 4, 2, 3]
INFO: Testing permutation: [2, 1, 3, 4]
INFO: Testing permutation: [2, 3, 1, 4]
INFO: Testing permutation: [2, 3, 4, 1]
INFO: Testing permutation: [3, 1, 2, 4]
INFO: Testing permutation: [4, 1, 2, 3]
INFO: Set All width to zero for non complex mass scheme checks
INFO: Checking lorentz transformations for process mu+ mu- > z|a > vlm+ vlm-
INFO: Set All width to zero for non complex mass scheme checks
INFO: No ward identity for process: mu+ mu- > z|a > vlm+ vlm-
check: 2 check performed in 0 second
INFO: Note That all width have been set to zero for those checks

Lorentz invariance results:
Process Min element Max element Relative diff. Result
mu+ mu- > vlm+ vl1.9452879273e-02 1.9452879273e-02 6.5989993267e-15 Passed
Summary: 1/1 passed, 0/1 failed
Process permutation results:
Process Min element Max element Relative diff. Result
mu+ mu- > vlm+ vlm- 1.9729300627e-02 1.9729300627e-02 1.7585250575e-15 Passed
Summary: 1/1 passed, 0/1 failed

I guess this means it is not a problem to use this syntax?

Best regards,

Feyza

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