•The fourth order tree amplitude

mesonstop = CreateCTTopologies[1, 1 -> 2, Adjacencies -> {3, 4}, ExcludeTopologies -> {SelfEnergyCTs, WFCorrectionCTs, TadpoleCTs}] // DiscardCT // Union[#, AddExternalLegs[#, ExternalPropagators -> 1], AddExternalLegs[#, ExternalPropagators -> 2]] & // Flatten // AddCT ;

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

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

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ampl4 = (CreateFCAmp[mesontreeinsert] /. D -> Sequence[] // PropagatorDenominatorExplicit // DoSumOver // SUNReduce) /. deltaReduce // Simplify

{-(128 (!, _ 0^( ))^3 (2 L _ 7^( ) δ _ (0 i _ 3)^(2) δ _ (i _ 1 i _ 2)^(2) + 2 L _ 6^( ) δ _ (0 i _ 1)^(2) δ _ (i _ 2 i _ 3)^(2) + L _ 8^( ) (δ _ (0 i _ 3)^(2) δ _ (i _ 1 i _ 2)^(2) + δ _ (0 i _ 1)^(2) δ _ (i _ 2 i _ 3)^(2))))/(p _ 3^2 - (m _ π^(ó  ))^2), -(128 (!, _ 0^( ))^3 (2 L _ 7^( ) δ _ (0 i _ 2)^(2) δ _ (i _ 1 i _ 3)^(2) + 2 L _ 6^( ) δ _ (0 i _ 1)^(2) δ _ (i _ 2 i _ 3)^(2) + L _ 8^( ) (δ _ (0 i _ 2)^(2) δ _ (i _ 1 i _ 3)^(2) + δ _ (0 i _ 1)^(2) δ _ (i _ 2 i _ 3)^(2))))/(p _ 4^2 - (m _ π^(ó  ))^2), (128 (2 L _ 6^( ) + L _ 8^( )) (m _ π^(ó  ))^2 (!, _ 0^( ))^3 δ _ (0 i _ 1)^(2) δ _ (i _ 2 i _ 3)^(2))/((p _ 3^2 - (m _ π^(ó  ))^2) ((m _ π^(ó  ))^2 - p _ 4^2)), (128 (2 L _ 6^( ) + L _ 8^( )) (m _ π^(ó  ))^2 (!, _ 0^( ))^3 δ _ (0 i _ 1)^(2) δ _ (i _ 2 i _ 3)^(2))/((p _ 3^2 - (m _ π^(ó  ))^2) ((m _ π^(ó  ))^2 - p _ 4^2)), (64 (4 (2 L _ 6^( ) + L _ 8^( )) (m _ π^(ó  ))^2 + 2 L _ 4^( ) p _ 3 · p _ 4 + L _ 5^( ) p _ 3 · p _ 4) (!, _ 0^( ))^3 δ _ (0 i _ 1)^(2) δ _ (i _ 2 i _ 3)^(2))/((p _ 3^2 - (m _ π^(ó  ))^2) ((m _ π^(ó  ))^2 - p _ 4^2))}

Converted by Mathematica  (July 10, 2003)