•The fourth order tree amplitude

mesonstop = CreateCTTopologies[1, 1 -> 2, Adjacencies -> {3, 4}, ExcludeTopologies -> {SelfEnergyCTs, WFCorrectionCTs, TadpoleCTs}] ;

mesontreeinsert = InsertFields[mesonstop, {Scalar[2][0, {i1}]} -> {PhiMeson[0, {i2}], PhiMeson[0, {i3}]}, Model -> "Automatic", GenericModel -> "Automatic", InsertionLevel -> Classes] ;

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

[Graphics:../HTMLFiles/index_65.gif]

amp4 = (CreateFCAmp[mesontreeinsert, Sum -> True] /. D -> Sequence[] /. channel // PropagatorDenominatorExplicit // DoSumOver[#, Drop -> {}] & // SUNReduce[#, FullReduce -> True] &) /. subpar /. udrules // ScalarProductExpand // SUNReduce // Simplify

{-(16 (8 L _ 6^( ) (m _ π^(ó  ))^2 + 4 L _ 8^( ) (m _ π^(ó  ))^2 + 4 L _ 6^( ) (m _ K^(ó  ))^2 + 3 L _ 4^( ) p _ 3 · p _ 4 + L _ 5^( ) p _ 3 · p _ 4) !, _ 0^( ))/(f _ ϕ^(ó  ))^2}

Converted by Mathematica  (July 10, 2003)