Question: FCFAConvert output from 4-fermion (current-current) model is not directly in FeynCalc syntax

[UserName402394]

Summary:

I'm a complete beginner using FeynCalc, FeynArts, and FeynRules together. I'm working with a toy model defined in a model.fr file (attached below), creating a 4-fermion current-current vertex.

Setup:

• Mathematica: 13.3.1
• FeynRules: 2.3.49 (29 September 2021)
• FeynArts: 3.12 (27 Mar 2025)
• FeynCalc: 10.2.0 (stable)

Files attached:

• model.nb (Mathematica notebook showing session and steps)
• model.fr (model definition)

What I did:

• Used WriteFeynArtsOutput to export the model from FeynRules
• Used FeynArts to create the topology and diagrams
• Used FeynArts' output as input for FeynCalc, running FCFAConvert on the amplitude

Problem:

• The output of FCFAConvert is not in typical or standard FeynCalc syntax (it does not look like standard amplitude/output as seen in FeynCalc docs).
• There is a warning about IndexSum in the output, and I'm unsure how to interpret or process it for the calculation I want to do.
• No explicit error; just not clear how to proceed further in FeynCalc to calculate the spin-spin averaged squared matrix element from this output.

What I have tried/read:

• Briefly read manuals for all three packages
• Examined Dirac sign conventions, and all seem handled as in the literature/manuals
• Tried DropIndexSum -> False but still unsure how to proceed with the output

Goal:
I want to compute the spin-spin averaged absolute square matrix element for this model using FeynCalc. I am mostly looking for practical guidance on what to do with the FCFAConvert output or how to get it into a directly usable FeynCalc format for further calculations (averages, traces, squaring, etc.) for 4-fermion current-current vertices.

Questions:

1. Am I missing a step in importing/exporting between packages, or is extra processing needed for models with 4-fermion (current-current) vertices?
2. How do I best proceed from the FCFAConvert output to calculate the desired matrix element in FeynCalc?
3. Is there something subtle about the Dirac index handling or the structure of the amplitude that requires extra manipulation?

Thank you for your time and for this software!

model.zip

[vsht]

Did you patch the model for compatibility with FeynCalc?

https://feyncalc.github.io/FeynCalcBook/Extra/CustomModels.html

[UserName402394]

I actually managed to find the solution just a day before your response, but thank you! Everything seems to be working smoothly now using the following sequence:

$LoadFeynArts = True;
<< FeynCalc`
FAPatch[PatchModelsOnly -> True]
$FAVerbose = False;

I do have two quick follow-up questions regarding some warnings:

When running WriteFeynArtsOutput for a custom model involving 4-fermion interactions, I get a shadowing warning: "Globala$: Symbol a$ appears in multiple contexts {Global, FeynRules`}". This only happens on the first run and disappears on the second. Does this require special treatment, or is it safe to ignore?

When using FCFAConvert, I receive a warning that "The diagrams contain some explicit summations denoted with IndexSum that might become obscured during the conversion," suggesting I set DropIndexSum -> False. However, when I tried setting it to False, I encountered the following error:

"FCFADiracChainJoin: Cannot process input expressions with unresolved FeynArts index sums."

For these types of 4-fermion interactions, is the default behavior (dropping the sums) safe, or should I be concerned about losing terms during the conversion?

[vsht]

When running WriteFeynArtsOutput for a custom model involving 4-fermion interactions, I get a shadowing warning: "Globala$: Symbol a$ appears in multiple contexts {Global, FeynRules`}". This only happens on the first run and disappears on the second. Does this require special treatment, or is it safe to ignore?

I assume that one can ignore it, but given the overall development state of FeynRules (last updated 2021 according to UpdateNotes.txt, not compatible with Mathematica 14.3) it is a somewhat dangerous statement. It doesn't seem like there is anyone regularly taking of care of the code at the moment, so whichever bugs you might encounter, they are entirely yours to deal with.

For these types of 4-fermion interactions, is the default behavior (dropping the sums) safe, or should I be concerned about losing terms during the conversion?

Since FeynCalc does not resolve IndexSum sums automatically, any kind of nontrivial sums (e.g. from some group theoretical factors) are left to the user to deal with. For 4-fermion operators there is an IndexSum over Lorentz indices
that one has to omit to be able to rebuild the chains. You can also use

FCFAConvert[..., DropIndexSum -> False, FCFADiracChainJoin -> False]

to examine the output, as there might be nontrivial combinations of 4-fermion operators and other IndexSums where user interaction is needed.

In this case it seems fine to drop it.