•Wave function renormalized second order tree amplitude

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

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}] ;

[Graphics:../HTMLFiles/index_15.gif]

ampl2mult = (CreateFCAmp[mesontreeinsert, WFRenormalize -> True] /. D -> Sequence[] // DoSumOver // PropagatorDenominatorExplicit // SUNReduce) /. deltaReduce // Simplify

{(2 (12 π^2 (f _ π^(ó  ))^2 + (-384 π^2 L _ 4^( ) - 192 π^2 L _ 5^( ) + 32 π^2 λ + log((m _ π^(ó  ))^2/μ^2)) (m _ π^(ó  ))^2) (!, _ 0^( ))^3 δ _ (0 i _ 1)^(2) δ _ (i _ 2 i _ 3)^(2))/(3 π^2 (p _ 3^2 - (m _ π^(ó  ))^2) ((m _ π^(ó  ))^2 - p _ 4^2))}

Converted by Mathematica  (July 10, 2003)