Usage

A Mathematica notebook with this workflow is available in the GitHub repository.

1) Open Mathematica and move to the MATCHA installation directory

Open a Mathematica notebook and set the working directory to the folder where MATCHA was cloned:

SetDirectory["/path/to/MATCHA-release"]

2) Load MATCHA

Load MATCHA and then load the external tools before defining the model fields and parameters:

<< MATCHA`
LoadTools[]

Once the tools have been loaded, the next step is to define the Standard Model fields, the heavy BSM fields, and the Standard Model parameters according to the conventions used in the user’s FeynArts model files.

To illustrate this setup, we consider below the Real Singlet Extension (RSE) example used in the manuscript.

Example: Real Singlet Extension (RSE)

In the corresponding .mod file, the Standard Model Higgs is represented by S[15], the charged W boson by V[2], the charged Goldstone boson by S[5], the neutral Goldstone boson by S[3], and the quark field used in the Yukawa matching, which in this example is the top quark, by F[1]. In MATCHA, these are passed as field specifications such as {"S", 15}, {"V", 2}, and {"F", 1}.

The model used in the manuscript is Singlet_for_MATCHA. The .mod model file and the corresponding .gen file should be available through the configured ModelPath.

3) Define the Standard Model fields

Use SetSMFields to specify the FeynArts labels associated with the Standard Model fields entering the matching calculation:

SetSMFields[<|
  "Higgs" -> {"S", 15},
  "GaugeCharged" -> {"V", 2},
  "GoldstoneCharged" -> {"S", 5},
  "GoldstoneNeutral" -> {"S", 3},
  "Quark" -> {"F", 1}
|>]

4) Define the heavy BSM fields

Use SetBSMFields to specify the heavy fields that are integrated out. For the Real Singlet Extension, the heavy scalar singlet is represented by S[6]:

SetBSMFields[{{"S", 6}}]

5) Define the Standard Model parameters

Use SetSMParams to identify the symbols used in the model file for the Higgs mass, electroweak vacuum expectation value, W-boson mass, and quark mass used in the Yukawa matching:

SetSMParams[<|
  "HiggsMass" -> m,
  "SMvacuum" -> v,
  "WMass" -> Mw,
  "QuarkMass" -> Mt
|>]

6) Run the matching

Finally, call MatchToHEFT with the model name, the desired Higgs order, and the heavy mass parameters. In this example, diagrams are exported and only the diagrams entering the matching are kept:

MatchToHEFT["Singlet_for_MATCHA", 3, {M},
  ExportDiagrams -> True,
  OnlyRelevantDiagrams -> True
]