Command Reference

This page summarizes the main MATCHA commands used to define the model input, run the matching, and inspect the output.

Loading commands

`LoadTools[]`

Loads FeynArts and FormCalc using the routes configured in Config.m.

Mathematica

LoadTools[]

Model input commands

`SetSMFields[assoc]`

Defines the mapping of the Standard Model fields to the field labels used in the FeynArts model file. The input can be an Association or a list of rules.

Allowed key	Meaning
`"Higgs"`	Standard Model Higgs field.
`"GaugeCharged"`	Charged electroweak gauge boson.
`"GaugeNeutral"`	Neutral electroweak gauge boson.
`"GoldstoneCharged"`	Charged Goldstone boson.
`"GoldstoneNeutral"`	Neutral Goldstone boson.
`"Quark"`	Quark field used in the Yukawa matching.

Field specifications follow the FeynArts class labels, for example {"S", n}, {"V", m}, {"F", k}, or {"F", k, {gen}}. The form {"U", n} is not used for SetSMFields.

Example

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

`SetBSMFields[fieldList]`

Defines the heavy Beyond Standard Model fields that are integrated out. The input is a list of fields using FeynArts-style specifications.

Entry form	Meaning
`{"S", n}`	Scalar field with FeynArts index `n`.
`{"V", m}`	Vector field with FeynArts index `m`.
`{"F", k}`	Fermion field with FeynArts index `k`.
`{"U", r}`	Ghost or unphysical field with FeynArts index `r`.
`{"F", k, {gen}}`	Fermion field with an explicit generation index.

Example

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

In this example, {"S", 6} identifies a heavy BSM scalar.

`SetSMParams[assoc]`

Optional command used to align the notation of the Standard Model parameters with the notation used in the UV model file. This can help simplify the final expressions.

Key	Meaning
`"HiggsMass"`	Symbol used for the Higgs mass.
`"SMvacuum"`	Symbol used for the electroweak vacuum expectation value.
`"WMass"`	Symbol used for the W-boson mass.
`"QuarkMass"`	Symbol used for the quark mass entering the Yukawa matching.

For Yukawa matching, "QuarkMass" should be set to the mass of the selected quark. Otherwise, the generic Mq may appear in the result.

Example

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

Matching command

`MatchToHEFT[modelModName, modelGenName, higgsOrderMax, massList]`

Runs the matching of the UV model onto HEFT. The argument modelModName specifies the .mod file and modelGenName specifies the corresponding .gen file. If both files have the same name, the short form MatchToHEFT[modelModName, higgsOrderMax, massList] can be used.

Argument	Meaning
`modelModName`	Name of the FeynArts `.mod` model to be matched.
`modelGenName`	Name of the corresponding FeynArts `.gen` file.
`higgsOrderMax`	Maximum Higgs order included in the calculation.
`massList`	List of heavy masses associated with the fields defined through `SetBSMFields`.

Options

Option	Meaning
`EFTorder -> 2`	EFT order used in the matching. Currently this is the implemented value.
`SimplifyResult -> True`	Simplifies the matching output.
`ExportDiagrams -> False`	Controls whether the corresponding Feynman diagrams are exported.
`OutputDirectory -> Automatic`	Controls the directory where diagram and coefficient files are written.
`AlternativeBasis -> True`	If `True`, MATCHA also exports the coefficient solutions before the final field redefinition, including the `p`-coefficients.
`OnlyRelevantDiagrams -> False`	If `True`, only relevant diagrams are generated and exported; `AllDiagrams` and `IgnoredDiagrams` are skipped.

Example

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

Output and diagram inspection

After executing MatchToHEFT, the following commands are available.

`Results["coupling"]`

Returns the final matching expression for the HEFT coupling specified by "coupling" in the canonical HEFT basis.

Example

Results["a2"]

`MATCHADiagrams["coupling"]`

Returns the diagram information associated with the HEFT coupling specified by "coupling". The entries below can be used to access the corresponding diagram categories.

Category	Meaning
`"RelevantDiagrams"`	Diagrams entering the matching, including contact diagrams and diagrams containing the heavy fields to be integrated out.
`"IgnoredDiagrams"`	Diagrams containing only light propagating fields.
`"AllDiagrams"`	Complete set of generated diagrams.

Example

Paint[MATCHADiagrams["a1"]["RelevantDiagrams"]]