•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, {d1}], Pion[0, {d2}]} -> {Pion[0, {d3}], Pion[0, {d4}]}, Model -> "Automatic", GenericModel -> "Automatic", InsertionLevel -> Classes] ;

Select graphs with less than 3 QED vertices

minsert = (If[Head[VerticesExtract[#][[1]]] === List, poss = Position[VerticesExtract[#], _ ? ((Count[#, _ ? ((! FreeQ[#, Vector1]) &)] < 3) &), {1}, Heads -> False] ; If[Flatten[poss] === {}, seq[], #[[1]] -> Part[#[[2]], Flatten[poss]]], If[Count[VerticesExtract[#], _ ? ((! FreeQ[#, Vector1]) &)] < 3, #, seq[]]] & /@ Take[mesonsinsert, {1, -1}]) /. seq -> Sequence ;

mesonsinsert // Length

54

minsert // Length

27

Graphical representation of the process:

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

Converted by Mathematica  (July 10, 2003)