•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 -> 1, Adjacencies -> {3, 4}, ExcludeTopologies -> {TadpoleCTs (* , SelfEnergyCTs, WFCorrectionCTs *)}]]]] ;

Field insertion:

$VerticesSpecifications = {{VertexFields -> {PseudoScalar[0][0], PhiMeson[0]}, PhiModel -> ChPT3, PerturbationOrder -> {2, 4}, CouplingSign -> 1, XFileName -> Automatic}, {VertexFields -> {PseudoScalar[0][0], PhiMeson[0], Scalar[1][0]}, PhiModel -> ChPTW3, PerturbationOrder -> {2, 4}, CouplingSign -> 1, XFileName -> {"ChPTW3P00P10S10o2", "ChPTW3P00P10o4"}}, {VertexFields -> {PhiMeson[0], PhiMeson[0], Scalar[1][0]}, PhiModel -> ChPTW3, PerturbationOrder -> {2, 4}, CouplingSign -> 1, XFileName -> {"ChPTW3P10P10o2", "ChPTW3P10P10o4"}}, {VertexFields -> {PseudoScalar[0][0], PseudoScalar[0][0], Scalar[1][0]}, PhiModel -> ChPT3, PerturbationOrder -> {2, 4}, CouplingSign -> 1, XFileName -> {"ChPTW3P00P00o2", "ChPTW3P00P00o4"}}} ;

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

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

Graphical representation of the process:

FeynArts`Graphics`VertexGraphics[e_][n_] := Point[Vertex[e][n]]

rect[p_List, r_] := Rectangle[p - {r, r}, p + {r, r}] ;

FeynArts`Graphics`VertexGraphics[e_, 2][n_] := {FeynArts`Graphics`CrossMark[Vertex[e, 2][n]], Array[rect[Vertex[e, 2][n], 0.15 * FeynArts`Graphics`CrossDiameter * #] &, 3]}

FeynArts`Graphics`VertexGraphics[e_, 3][n_] := {Array[rect[Vertex[e, 3][n], 0.4 * FeynArts`Graphics`CrossDiameter * #] &, 3]}

(* Vertices with a scalar leg *) boxrules4 = {Propagator[ty_][Vertex[l_, 1][n_], v2 : Vertex[__][_], Field[2]] /; l > 1 -> Propagator[ty][Vertex[l, 2][n], v2, Field[2]], Propagator[ty_][v2 : Vertex[__][_], Vertex[l_, 1][n_], Field[2]] /; l > 1 -> Propagator[ty][v2, Vertex[l, 2][n], Field[2]]} ;

Paint[mesontreeinsert /. boxrules4, PaintLevel -> {Classes}, AutoEdit -> False, SheetHeader -> False, Numbering -> False, ColumnsXRows -> {2, 2}] ;

[Graphics:../HTMLFiles/index_104.gif]

[Graphics:../HTMLFiles/index_105.gif]

Converted by Mathematica  (July 10, 2003)