•The fourth order tree amplitude

•Generation of topologies and insertion of fields

Construction of topologies:

mesonstop = CreateTopologies[0, 2 -> 2, Adjacencies -> {4}, ExcludeTopologies -> {SelfEnergies, WFCorrections}, CountertermOrder -> 1] ;

mesontreeinsert = InsertFields[mesonstop, {PhiMeson[0, {i1}], PhiMeson[0, {i2}]} -> {PhiMeson[0, {i3}], PhiMeson[0, {i4}]}, Model -> "Automatic", GenericModel -> "Automatic", InsertionLevel -> Classes] ;

•Calculation and reduction of the amplitude

ampp4 = (CreateFCAmp[mesontreeinsert][[1]] /. D -> Sequence[] /. channel // WriteOutUMatrices // SUNReduce) ;

ampl4 = ampp4 /. subpar /. udrules // MandelstamReduce // Simplify

1/(f _ π^(ó  ))^4 (8 (6 L _ 3^( ) (m _ π^(ó  ))^4 - 4 L _ 4^( ) (m _ π^(ó  ))^4 - 2 L _ 5^( ) (m _ π^(ó  ))^4 + 14 L _ 6^( ) (m _ π^(ó  ))^4 + 8 L _ 8^( ) (m _ π^(ó  ))^4 + 4 L _ 6^( ) (m _ K^(ó  ))^2 (m _ π^(ó  ))^2 - 4 s L _ 3^( ) (m _ π^(ó  ))^2 - 4 t L _ 3^( ) (m _ π^(ó  ))^2 + s^2 L _ 3^( ) + t^2 L _ 3^( ) + s t L _ 3^( ) + 2 L _ 1^( ) (6 (m _ π^(ó  ))^4 - 4 (s + t) (m _ π^(ó  ))^2 + s^2 + t^2 + s t) + 2 L _ 2^( ) (6 (m _ π^(ó  ))^4 - 4 (s + t) (m _ π^(ó  ))^2 + s^2 + t^2 + s t)))

Converted by Mathematica  (July 10, 2003)