•Generation of topologies and insertion of fields

Construction of topologies:

mesonstop = CreateTopologies[1, 2 -> 2, Adjacencies -> {3, 4, 5, 6}, ExcludeTopologies -> {SelfEnergies, WFCorrections}, CountertermOrder -> 0] ;

Field insertion:

mesonsinsert = InsertFields[mesonstop, {Pion[0, {i1}], Pion[0, {i2}]} -> {Pion[0, {i3}], Pion[0, {i4}]}, Model -> "Automatic", GenericModel -> "Automatic", InsertionLevel -> Classes] ;

Select graphs with less than 3 QED vertices

minsert = Select[mesonsinsert, ((Count[# // VerticesExtract, _ ? ((! FreeQ[#, Vector1]) &)] < 3) &)] ;

Graphical representation of the process:

mesonsinsert // Length

54

Length[#[[2]]] & /@ List @@ mesonsinsert

{2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}

Count[%, 2]

13

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

Converted by Mathematica  (July 10, 2003)