•The wave function renormalized second order tree amplitude

mesonstop = CreateTopologies[0, 1 -> 2, Adjacencies -> {3}] ;

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_24.gif]

$ConstantIsoIndices = {} ;

amplFC = CreateFCAmp[mesontreeinsert] /. D -> Sequence[] // PropagatorDenominatorExplicit // SUNReduce // SUNReduce // Simplify

{-2 !, _ 0^( ) δ _ (0 i _ 1)^(2) δ _ (i _ 2 i _ 3)^(2)}

zpipi = CheckF[zpipi, "ChPT2P20o2.Fac"]

((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)/(24 π^2 (f _ π^(ó  ))^2) + 1

ampl2mult = (2 ((3 - zpipi)/2) - 1) amplFC // Simplify

{-2 (1 - ((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)/(24 π^2 (f _ π^(ó  ))^2)) !, _ 0^( ) δ _ (0 i _ 1)^(2) δ _ (i _ 2 i _ 3)^(2)}

Converted by Mathematica  (July 10, 2003)