•Generation of topologies and insertion of fields

Construction of topologies:

mesonstop = TopologyList @@ Union[Flatten[{#, List @@ AddExternalLegs[#, ExternalPropagators -> 1], List @@ AddExternalLegs[#, ExternalPropagators -> 2]} &[CreateCTTopologies[1, 2 -> 2, Adjacencies -> {4}, ExcludeTopologies -> {SelfEnergyCTs, WFCorrectionCTs}] // DiscardCT]]] ;

(* Paint[mesonstop, AutoEdit -> False, SheetHeader -> False, Numbering -> True, ColumnsXRows -> {2, 2}] ; *)

Field insertion:

$VerticesSpecifications = {{VertexFields -> {PhiMeson[0]}, PhiModel -> ChPTW3, PerturbationOrder -> {2}, CouplingSign -> 1, XFileName -> Automatic}, {VertexFields -> {AxialVector[0][0], PhiMeson[0]}, PhiModel -> ChPT3, PerturbationOrder -> {2}, CouplingSign -> 1, XFileName -> Automatic}, {VertexFields -> {PhiMeson[0], Scalar[1][0]}, PhiModel -> ChPTW3, PerturbationOrder -> {2}, CouplingSign -> 1, XFileName -> Automatic}, {VertexFields -> {AxialVector[0][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 -> {AxialVector[0][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]}, PhiModel -> ChPT3, PerturbationOrder -> {2}, CouplingSign -> 1, XFileName -> Automatic}} ;

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

mesontreeinsert = InsertFields[mesonstop, {AxialVector[0][0, {i1}], Scalar[1][0]} -> {PhiMeson[0, {i3}], PhiMeson[0, {i4}]}, Model -> "Automatic", GenericModel -> "Automatic", InsertionLevel -> Classes] ;

mesontreeinsert // Length

4

Selecting only the graphs we need:

mesonins = Select[mesontreeinsert, (Count[#[[1]] /. List @@ #[[2, 1, 1]], Vertex[_ ? OddQ, ___][___], Infinity] < 6) &] ;

mesonins // Length

4

(* Vertices with a scalar leg *) boxrules3 = {Propagator[ty_][Vertex[l_][n_], v2 : Vertex[__][_], Field[2]] /; l > 1 -> Propagator[ty][Vertex[l, 1][n], v2, Field[2]], Propagator[ty_][v2 : Vertex[__][_], Vertex[l_][n_], Field[2]] /; l > 1 -> Propagator[ty][v2, Vertex[l, 1][n], Field[2]]} ;

Graphical representation of the process:

Paint[mesonins /. boxrules3, PaintLevel -> {Classes}, AutoEdit -> False, SheetHeader -> False, Numbering -> False, ColumnsXRows -> {2, 2}] ;

[Graphics:../HTMLFiles/index_46.gif]

Converted by Mathematica  (July 10, 2003)