Matchete`

FeynmanRules

computes all Feynman rules for the given Lagrangian lag and returns them as an association where the keys are given by the field labels in each vertex.

FeynmanRules[lag,fields]

computes the Feynman rules for the given ensemble of fields from the given Lagrangian lag. The fields should be stated only by their label (Bar[label] or Conj[label] for conjugated fields).

Details and Options

The following options can be given:

Legs

All

Is an option used to limit the amount of derived Feynman rules based on the amount of external legs. Allowed values are positive integers (inclusive) or a list containing one positive integer (exclusive).

"ExternalMomentum"

"incoming"

This option allows to control the direction of the external momenta. The allowed values are "incoming" and "outgoing". Note that ExportUFO uses the opposite default "ExternalMomentum"  "outgoing" to comply with MadGraph conventions although this is in contradiction to the definitions of the UFO format.

"FermionFlow"

"Standard"

This option determines how fermionic Feynman rules are determined. By default the standard text book derivation is used. If set to "DEHK" the algorithm based on the fermion flow and developed by Denner, Eck, Hahn, and Kublbeck (Phys.Lett.B 291 (1992) 278-280) is used, where the Grassmannian minus signs are neglected and charge conjugation matrices are dropped, which is required when running MadGraph. Note that for this reason ExportUFO uses "FermionFlow"  "DEHK" as default instead.

Examples

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Basic Examples (1)

Take the Standard Model as an example. The Feynman rule for the three-gluon vertex in the unbroken electroweak phase can be determined using:

The complete set of Feynman rules can be derived using:

Options (3)

Legs (1)

The number of external legs to consider when deriving Feynman rules can be changed using the option Legs. For example, we can compute the SM Feynman rules up to three external legs using:

Alternatively we can also only compute the Feynman rules with exactly four external legs:

"FermionFlow" (1)

The option "FermionFlow" allows to determine the algorithm used to derive the Feynman rules. Two algorithms are available "Standard" and "DEHK".

As an example consider adding a Yukawa interaction for the SM neutrinos:

Note the sign change in the Feynman rule containing the due to the different treatment of the Grassmann numbers and the missing of the charge conjugation matrix.