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•Loop contribution of fourth order in the chiral expansion

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${-(i (e^( ))^2 g^(μ _ 1 μ _ 2) ľ _ μ _ 1(p _ 1) ľ _ μ _ 2^*(p _ 3) ((δ _ (1 1) - δ _ (1 3)^2)/(q _ 1^2 - (m _ π^(1 ))^2) + (δ _ (2 2) - δ _ (2 3)^2)/(q _ 1^2 - (m _ π^(2 ))^2) - ((δ _ (3 3) - 1) δ _ (3 3))/(q _ 1^2 - (m _ π^(3 ))^2)))/(16 π^4), 1/(32 π^4) (i (e^( ))^2 (1/(q _ 1^2 - (m _ π^(1 ))^2) . ((p _ 3 + q _ 1)^2 - (m _ π^(2 ))^2) + 1/(q _ 1^2 - (m _ π^(2 ))^2) . ((p _ 3 + q _ 1)^2 - (m _ π^(1 ))^2)) (q _ 1^μ _ 1 + ((p _ 3 + q _ 1)^μ _ 1)) ľ _ μ _ 1(p _ 1) (q _ 1^μ _ 2 + ((p _ 3 + q _ 1)^μ _ 2)) ľ _ μ _ 2^*(p _ 3))}$

${-(i (e^( ))^2 (1/(q _ 1^2 - (m _ π^(1 ))^2) + 1/(q _ 1^2 - (m _ π^(2 ))^2)) ľ ( p _ 1 ) · ľ^* ( p _ 3 ))/(16 π^4), (i (e^( ))^2 (1/(q _ 1^2 - (m _ π^(1 ))^2) . ((p _ 3 + q _ 1)^2 - (m _ π^(2 ))^2) + 1/(q _ 1^2 - (m _ π^(2 ))^2) . ((p _ 3 + q _ 1)^2 - (m _ π^(1 ))^2)) (p _ 3 · ľ ( p _ 1 ) + 2 q _ 1 · ľ ( p _ 1 )) q _ 1 · ľ^* ( p _ 3 ))/(16 π^4)}$

${((A _ 0 ( (m _ π^(1 ))^2 ) + A _ 0 ( (m _ π^(2 ))^2 )) (e^( ))^2 ľ ( p _ 1 ) · ľ^* ( p _ 3 ))/(16 π^2), -1/(144 π^2 p _ 3^2) ((e^( ))^2 ľ ( p _ 1 ) · ľ^* ( p _ 3 ) (3 B _ 0 (0, (m _ π^(1 ))^2, (m _ π^(2 ))^2) (m _ π^(1 ))^4 - 3 B _ 0 (p _ 3^2, (m _ π^(1 ))^2, (m _ π^(2 ))^2) (m _ π^(1 ))^4 - 6 B _ 0 (0, (m _ π^(1 ))^2, (m _ π^(2 ))^2) (m _ π^(2 ))^2 (m _ π^(1 ))^2 + 6 B _ 0 (p _ 3^2, (m _ π^(1 ))^2, (m _ π^(2 ))^2) (m _ π^(2 ))^2 (m _ π^(1 ))^2 + 6 B _ 0 (p _ 3^2, (m _ π^(1 ))^2, (m _ π^(2 ))^2) p _ 3^2 (m _ π^(1 ))^2 + 6 p _ 3^2 (m _ π^(1 ))^2 + 3 B _ 0 (0, (m _ π^(1 ))^2, (m _ π^(2 ))^2) (m _ π^(2 ))^4 - 3 B _ 0 (p _ 3^2, (m _ π^(1 ))^2, (m _ π^(2 ))^2) (m _ π^(2 ))^4 - 3 B _ 0 (p _ 3^2, (m _ π^(1 ))^2, (m _ π^(2 ))^2) p _ 3^4 - 2 p _ 3^4 + 6 B _ 0 (p _ 3^2, (m _ π^(1 ))^2, (m _ π^(2 ))^2) p _ 3^2 (m _ π^(2 ))^2 + 6 p _ 3^2 (m _ π^(2 ))^2 + 3 A _ 0 ( (m _ π^(1 ))^2 ) p _ 3^2 + 3 A _ 0 ( (m _ π^(2 ))^2 ) p _ 3^2))}$

Converted by Mathematica (July 10, 2003)