•Generation of topologies and insertion of fields

This FeynArts filter discards topologies with more than one odd vertex:

$ExcludeTopologies[SeveralOddVertices] = ((Length[Union[Cases[#, Vertex[_ ? (OddQ[#] &), ___][_], Infinity]]] < 5) &) ;

Construction of topologies:

mesonstop = TopologyList @@ Union[Flatten[{#, List @@ AddExternalLegs[#, ExternalPropagators -> 1, SelfEnergies -> False], List @@ AddExternalLegs[#, ExternalPropagators -> 2, SelfEnergies -> False]} &[CreateTopologies[1, 2 -> 1, Adjacencies -> {3, 4, 5, 6}, ExcludeTopologies -> {SelfEnergyCTs, WFCorrections (* , SeveralOddVertices *)}]]]] ;

Length[mesonstop]

42

Paint[Take[mesonstop, {1, -1}], AutoEdit -> False, SheetHeader -> False, Numbering -> True, ColumnsXRows -> {2, 1}] ;

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Field insertion:

$VerticesSpecifications = {{VertexFields -> {PhiMeson[0], Scalar[1][0]}, PhiModel -> ChPTW3, PerturbationOrder -> {2}, CouplingSign -> 1, XFileName -> Automatic}, {VertexFields -> {PhiMeson[0], PhiMeson[0], Scalar[1][0]}, PhiModel -> ChPTW3, PerturbationOrder -> {2}, CouplingSign -> 1, XFileName -> Automatic}, (* ! *) {VertexFields -> {PhiMeson[0], PhiMeson[0], Scalar[2][0]}, PhiModel -> ChPT3, PerturbationOrder -> {2}, CouplingSign -> 1, XFileName -> Automatic}, (* ! *) {VertexFields -> {PhiMeson[0], Scalar[2][0], Scalar[1][0]}, PhiModel -> ChPTW3, PerturbationOrder -> {2}, CouplingSign -> 1, XFileName -> {"ChPTW3P10S20o2"}}, {VertexFields -> {PhiMeson[0], PhiMeson[0], PhiMeson[0], PhiMeson[0]}, PhiModel -> ChPT3, PerturbationOrder -> {2}, CouplingSign -> 1, XFileName -> Automatic}, {VertexFields -> {PhiMeson[0], PhiMeson[0], PhiMeson[0], Scalar[1][0]}, PhiModel -> ChPTW3, PerturbationOrder -> {2}, CouplingSign -> 1, XFileName -> Automatic}, (* ! *) {VertexFields -> {PhiMeson[0], PhiMeson[0], PhiMeson[0], PhiMeson[0], Scalar[2][0]}, PhiModel -> ChPT3, PerturbationOrder -> {2}, CouplingSign -> 1, XFileName -> Automatic}, (* ! *) {VertexFields -> {PhiMeson[0], PhiMeson[0], PhiMeson[0], Scalar[2][0], Scalar[1][0]}, PhiModel -> ChPTW3, PerturbationOrder -> {2}, CouplingSign -> 1, XFileName -> {"ChPTW3P10P10P10S20o2"}}} ;

InitializeModel["Automatic", GenericModel -> "Automatic", Reinitialize -> True] ;

mesontreeinsert = InsertFields[mesonstop, {PhiMeson[0, {7}], Scalar[1][0]} -> {Scalar[2][0, {i}]}, Model -> "Automatic", GenericModel -> "Automatic", InsertionLevel -> Classes] ;

mesontreeinsert // Length

4

Graphical representation of the process:

Paint[mesontreeinsert, PaintLevel -> {Classes}, AutoEdit -> False, SheetHeader -> False, Numbering -> False, ColumnsXRows -> {2, 1}] ;

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Converted by Mathematica  (July 10, 2003)