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•The wave function renormalized second order tree amplitude

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${-1/((p _ 3^2 - (m _ ϕ^(I _ 1 ))^2) (p _ 4^2 - (m _ ϕ^(I _ 2 ))^2)) (8 (f _ ϕ^(ó ))^2 (!, _ 0^( ))^3 δ _ (3 I _ 1)^(3) δ _ (3 I _ 2)^(3) δ _ (I _ 1 I _ 2)^(3) SumOver(I _ 1, {0, 1, 2, 3, 4, 5, 6, 7, 8}) SumOver(I _ 2, {0, 1, 2, 3, 4, 5, 6, 7, 8}) (WFFactor1(Propagator (Internal) (Vertex (2) (6), Vertex (3) (4), PseudoScalar1(0, {I _ 1}))) + WFFactor1(Propagator (Internal) (Vertex (2) (7), Vertex (3) (4), PseudoScalar1(0, {I _ 2}))) + 1))}$

${1/(3 π^2 (p _ 3^2 - (m _ π^(ó ))^2) ((m _ π^(ó ))^2 - p _ 4^2)) ((24 π^2 (f _ ϕ^(ó ))^2 - 384 π^2 L _ 5^( ) (m _ π^(ó ))^2 + 64 π^2 λ (m _ π^(ó ))^2 + 2 log((m _ π^(ó ))^2/μ^2) (m _ π^(ó ))^2 + 32 π^2 λ (m _ K^(ó ))^2 + log((m _ K^(ó ))^2/μ^2) (m _ K^(ó ))^2 - 384 π^2 L _ 4^( ) ((m _ π^(ó ))^2 + 2 (m _ K^(ó ))^2)) (!, _ 0^( ))^3)}$

Converted by Mathematica (July 10, 2003)