•The fourth order tree amplitude

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

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

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

[Graphics:../HTMLFiles/index_35.gif]

$ConstantIsoIndices = {} ;

ampl4 = CreateFCAmp[mesontreeinsert] /. D -> Sequence[] // PropagatorDenominatorExplicit // SUNReduce[#, FullReduce -> True] & // Simplify

{-(16 (4 (2 L _ 6^( ) + L _ 8^( )) (m _ π^(ó  ))^2 + 2 L _ 4^( ) p _ 3 · p _ 4 + L _ 5^( ) p _ 3 · p _ 4) !, _ 0^( ) δ _ (0 i _ 1)^(2) δ _ (i _ 2 i _ 3)^(2))/(f _ π^(ó  ))^2}

Converted by Mathematica  (July 10, 2003)