•Generation of topologies and insertion of fields

Construction of topologies:

mesonstop = Union[#, AddExternalLegs[#]] &[CreateCTTopologies[1, 1 -> 2, Adjacencies -> {3, 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 -> {AxialVector[0][0], PhiMeson[0], PhiMeson[0]}, PhiModel -> ChPTW3, PerturbationOrder -> {2}, CouplingSign -> 1, XFileName -> Automatic}, {VertexFields -> {PhiMeson[0], PhiMeson[0], PhiMeson[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], PhiMeson[0]}, PhiModel -> ChPT3, PerturbationOrder -> {2}, CouplingSign -> 1, XFileName -> Automatic}} ;

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

mesontreeinsert = InsertFields[mesonstop, {AxialVector[0][0, {i1}]} -> {PhiMeson[0, {i2}], PhiMeson[0, {i3}]}, Model -> "Automatic", GenericModel -> "Automatic", InsertionLevel -> Classes] ;

Graphical representation of the process:

Paint[mesontreeinsert /. {Propagator[Internal][Vertex[l_ ? OddQ][n_], v2 : Vertex[_][_], f_] -> Propagator[Internal][Vertex[l, 1][n], v2, f], Propagator[Internal][v2 : Vertex[_][_], Vertex[l_ ? OddQ][n_], f_] -> Propagator[Internal][v2, Vertex[l, 1][n], f]} /. {Propagator[ty_][Vertex[l_ ? OddQ][n_], v2 : Vertex[_][_], f_] /; l > 2 -> Propagator[ty][Vertex[l, 1][n], v2, f], Propagator[ty_][v2 : Vertex[_][_], Vertex[l_ ? OddQ][n_], f_] /; l > 2 -> Propagator[ty][v2, Vertex[l, 1][n], f]}, PaintLevel -> {Classes}, AutoEdit -> True, SheetHeader -> False, Numbering -> False, ColumnsXRows -> {2, 2}] ;

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

Converted by Mathematica  (July 10, 2003)