•Calculation of the amplitude

Calculation of the amplitude:

$ConstantIsoIndices = {i1, i3} ;

ampFC = CreateFCAmp[mesontreeinsert] ;

amplFC4 = ((# // DoSumOver // PropagatorDenominatorExplicit) /. subpar /. udrules /. i3 -> i1 // SUNReduce[#, FullReduce -> True] & // Simplify) & /@ ampFC

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

Converted by Mathematica  (July 10, 2003)