•The wave function renormalized second order tree amplitude

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

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_37.gif]

amplFC = CreateFCAmp[mesontreeinsert, Sum -> True, WFRenormalize -> True] /. D -> Sequence[] /. channel // PropagatorDenominatorExplicit // SUNReduce[#, FullReduce -> True] & // Simplify

{-1/(24 π^2 (f _ ϕ^(ó  ))^2) ((48 π^2 (f _ ϕ^(ó  ))^2 - 384 π^2 L _ 5^( ) (m _ π^(ó  ))^2 + 64 π^2 λ (m _ π^(ó  ))^2 + 2 log((m _ π^(ó  ))^2/μ^2) (m _ π^(ó  ))^2 + 32 π^2 λ (m _ K^(ó  ))^2 + log((m _ K^(ó  ))^2/μ^2) (m _ K^(ó  ))^2 - 384 π^2 L _ 4^( ) ((m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2)) !, _ 0^( ))}

ampl2mult = (DoSumOver[#] /. subpar /. udrules // SUNReduce[#, FullReduce -> True] & // Simplify) & /@ amplFC // Simplify

{-1/(24 π^2 (f _ ϕ^(ó  ))^2) ((48 π^2 (f _ ϕ^(ó  ))^2 - 384 π^2 L _ 5^( ) (m _ π^(ó  ))^2 + 64 π^2 λ (m _ π^(ó  ))^2 + 2 log((m _ π^(ó  ))^2/μ^2) (m _ π^(ó  ))^2 + 32 π^2 λ (m _ K^(ó  ))^2 + log((m _ K^(ó  ))^2/μ^2) (m _ K^(ó  ))^2 - 384 π^2 L _ 4^( ) ((m _ π^(ó  ))^2 + 2 (m _ K^(ó  ))^2)) !, _ 0^( ))}

Converted by Mathematica  (July 10, 2003)