![lala = ArgumentsSupply[Lagrangian[QED[2]], x, RenormalizationState[0]]](../HTMLFiles/index_156.gif){kind=small}
The counterterm lagrangian:
![-δm^(0 ) Z _ 2^(0 ) Overscript[ψ^(0 ), _] . ψ^(0 ) - 1/4 (Z _ 3^(0 ) - 1) (∂ _ μ A^(0 ) _ ν^ó - ∂ _ ν A^(0 ) _ μ^ó ) . (∂ _ μ A^(0 ) _ ν^ó - ∂ _ ν A^(0 ) _ μ^ó ) + (Z _ 2^(0 ) - 1) (Overscript[ψ^(0 ), _] . γ^μ . (e^(0 ) A^(0 ) _ μ . ψ^(0 ) + i ∂ _ μ ψ^(0 ) _ ó ^ó ) - Overscript[ψ^(0 ), _] . ψ^(0 ) m _ ψ^(ó 0 ))](../HTMLFiles/index_157.gif){kind=small}
![fields = {QuantumField[Particle[Photon, RenormalizationState[0]], LorentzIndex[μ1]][p1], QuantumField[DiracBar[Particle[Electron, RenormalizationState[0]]]][p3], QuantumField[Particle[Electron, RenormalizationState[0]]][p4]}](../HTMLFiles/index_158.gif){kind=small}
![{A^(0 ) _ μ _ 1, Overscript[ψ^(0 ), _], ψ^(0 )}](../HTMLFiles/index_159.gif){kind=small}
The counterterm amplitude:
![amp4 = -I FeynRule[lala, fields] // Simplify](../HTMLFiles/index_160.gif){kind=small}
The photon selfenergy correction:
![llag = -I FeynRule[ArgumentsSupply[Lagrangian[QED[1]], x, RenormalizationState[0]], fields]](../HTMLFiles/index_162.gif){kind=small}
![amp2 = (1/Pair[Momentum[-p3 - p4], Momentum[-p3 - p4]] llag piren /. p1 -> -p3 - p4 // ScalarProductExpand) /. {Pair[Momentum[p3, ___], Momentum[p3, ___]] -> ParticleMass[Electron, RenormalizationState[0]]^2, Pair[Momentum[p4, ___], Momentum[p4, ___]] -> ParticleMass[Electron, RenormalizationState[0]]^2} /. Pair[Momentum[p3, ___], Momentum[p4, ___]] -> q^2/2 - ParticleMass[Electron, RenormalizationState[0]]^2 // Simplify](../HTMLFiles/index_164.gif)
![-((e^(0 ))^3 γ^μ _ 1 ((1 - 3 log((m _ ψ^(ó 0 ))^2)) q^2 - 6 log((m _ ψ^(ó 0 ))^2) (m _ ψ^(ó 0 ))^2 + 3 (Underoverscript[∫, 0, arg3] log((x - 1) x q^2 + (m _ ψ^(ó 0 ))^2) d x) (q^2 + 2 (m _ ψ^(ó 0 ))^2)))/(36 π^2 q^4)](../HTMLFiles/index_165.gif)
The above non-renormalization condition implies the following value of 
:
![ssolv = Solve[(Cancel[(amp2 + amp4)/DiracGamma[LorentzIndex[μ1]]] + f0 + g0/StandardMatrixElement[Spinor[-Momentum[p3], ParticleMass[Electron, RenormalizationState[0]], 1] . Spinor[Momentum[p4], ParticleMass[Electron, RenormalizationState[0]], 1]] /. CouplingConstant[QED[2], 2, RenormalizationState[0]] -> z2) == 1, z2] // Flatten // Simplify](../HTMLFiles/index_167.gif)
![{z2 -> 1/e^(0 ) (((Underoverscript[∫, 0, arg3] log((x - 1) x q^2 + (m _ ψ^(ó 0 ))^2) d x) (m _ ψ^(ó 0 ))^2 (e^(0 ))^3)/(6 π^2 q^4) - (log((m _ ψ^(ó 0 ))^2) (m _ ψ^(ó 0 ))^2 (e^(0 ))^3)/(6 π^2 q^4) + ((Underoverscript[∫, 0, arg3] log((x - 1) x q^2 + (m _ ψ^(ó 0 ))^2) d x) (e^(0 ))^3)/(12 π^2 q^2) - (log((m _ ψ^(ó 0 ))^2) (e^(0 ))^3)/(12 π^2 q^2) + 1/(64 π^2 (m _ ψ^(ó 0 ))^2) ((((÷J (D - 4) + 2) (log(π) D - 4 log(π) + 2) ((D - 4) log(μ) - 1) ((D - 4) log((m _ ψ^(ó 0 ))^2) + 2) ((m _ A^(ó 0 ))^2 - 6 (m _ ψ^(ó 0 ))^2))/(2 (D - 4)) + 2 (-4 (m _ ψ^(ó 0 ))^2 - 1/(4 (D - 4)) ((÷J (D - 4) + 2) ((D - 4) Underoverscript[∫, 0, arg3] log(x^2 (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x + 2) (log(π) D - 4 log(π) + 2) ((D - 4) log(μ) - 1) ((m _ A^(ó 0 ))^2 - 8 (m _ ψ^(ó 0 ))^2)) + (8 (m _ ψ^(ó 0 ))^4 - 8 (m _ A^(ó 0 ))^2 (m _ ψ^(ó 0 ))^2 + (m _ A^(ó 0 ))^4) C _ 0((m _ ψ^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2, 0, (m _ ψ^(ó 0 ))^2, (m _ A^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2))) (e^(0 ))^3) + 1/(128 π^2 (m _ ψ^(ó 0 ))^2) ((12 C _ 0((m _ ψ^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2, 0, (m _ ψ^(ó 0 ))^2, (m _ A^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2) (m _ A^(ó 0 ))^4 - (-(2 (÷J (D - 4) + 2) ((D - 4) Underoverscript[∫, 0, arg3] log(x (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x + 2) (log(π) D - 4 log(π) + 2) ((D - 4) log(μ) - 1))/(D - 4) + (5 (÷J (D - 4) + 2) ((D - 4) Underoverscript[∫, 0, arg3] log(x^2 (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x + 2) (log(π) D - 4 log(π) + 2) ((D - 4) log(μ) - 1))/(D - 4) + 4 (8 (m _ ψ^(ó 0 ))^2 C _ 0((m _ ψ^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2, 0, (m _ ψ^(ó 0 ))^2, (m _ A^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2) - (3 (÷J (D - 4) + 2) (log(π) D - 4 log(π) + 2) ((D - 4) log(μ) - 1) ((D - 4) log((m _ ψ^(ó 0 ))^2) + 2))/(4 (D - 4)))) (m _ A^(ó 0 ))^2 - 2 (((÷J (D - 4) + 2) ((D - 4) Underoverscript[∫, 0, arg3] log(x (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x + 2) (log(π) D - 4 log(π) + 2) ((D - 4) log(μ) - 1))/(D - 4) - (2 (÷J (D - 4) + 2) ((D - 4) Underoverscript[∫, 0, arg3] log(x^2 (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x + 2) (log(π) D - 4 log(π) + 2) ((D - 4) log(μ) - 1))/(D - 4) + ((÷J (D - 4) + 2) (log(π) D - 4 log(π) + 2) ((D - 4) log((m _ ψ^(ó 0 ))^2) + 2) ((D - 4) log(μ) - 1))/(D - 4) + 4) (m _ ψ^(ó 0 ))^2) (e^(0 ))^3) + (e^(0 ))^3/(36 π^2 q^2) + e^(0 ) + 1)}](../HTMLFiles/index_168.gif)
With this substitution, the full amplitude is ultraviolet finite, but remains infrared divergent:
![1/(16 π^2 (q^2 - 4 (m _ ψ^(ó 0 ))^2)^2) ((e^(0 ))^3 ((q^2 - 4 (m _ ψ^(ó 0 ))^2) {| ϕ ( -p _ 3 , m _ ψ^(ó 0 ) ) . γ^μ _ 1 . ϕ ( p _ 4 , m _ ψ^(ó 0 ) ) |} (((÷J δ + 2) (δ Underoverscript[∫, 0, arg3] log((x - 1) x q^2 + (m _ ψ^(ó 0 ))^2) d x + 2) (log(π) δ + 2) (δ log(μ) - 1) (3 q^2 - 12 (m _ ψ^(ó 0 ))^2 + 2 (m _ A^(ó 0 ))^2))/(4 δ) + 2 (q^2 - 4 (m _ ψ^(ó 0 ))^2 - ((÷J δ + 2) (δ Underoverscript[∫, 0, arg3] log(x^2 (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x + 2) (log(π) δ + 2) (δ log(μ) - 1) (2 q^2 - 8 (m _ ψ^(ó 0 ))^2 + (m _ A^(ó 0 ))^2))/(4 δ) + (8 (m _ ψ^(ó 0 ))^4 - 2 (3 q^2 + 4 (m _ A^(ó 0 ))^2) (m _ ψ^(ó 0 ))^2 + (q^2 + (m _ A^(ó 0 ))^2)^2) C _ 0((m _ ψ^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2, q^2, (m _ ψ^(ó 0 ))^2, (m _ A^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2))) - 1/m _ ψ^(ó 0 ) (2 (p _ 3^μ _ 1 - p _ 4^μ _ 1) {| ϕ ( -p _ 3 , m _ ψ^(ó 0 ) ) . ϕ ( p _ 4 , m _ ψ^(ó 0 ) ) |} (6 (m _ ψ^(ó 0 ))^2 C _ 0((m _ ψ^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2, q^2, (m _ ψ^(ó 0 ))^2, (m _ A^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2) (m _ A^(ó 0 ))^4 - 1/4 (8 (-(3 (÷J δ + 2) (δ Underoverscript[∫, 0, arg3] log((x - 1) x q^2 + (m _ ψ^(ó 0 ))^2) d x + 2) (log(π) δ + 2) (δ log(μ) - 1))/(4 δ) - 2 (q^2 - 4 (m _ ψ^(ó 0 ))^2) C _ 0((m _ ψ^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2, q^2, (m _ ψ^(ó 0 ))^2, (m _ A^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2)) (m _ ψ^(ó 0 ))^2 - ((÷J δ + 2) (δ Underoverscript[∫, 0, arg3] log(x^2 (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x + 2) (log(π) δ + 2) (δ log(μ) - 1) (q^2 - 10 (m _ ψ^(ó 0 ))^2))/δ + ((÷J δ + 2) (δ Underoverscript[∫, 0, arg3] log(x (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x + 2) (log(π) δ + 2) (δ log(μ) - 1) (q^2 - 4 (m _ ψ^(ó 0 ))^2))/δ) (m _ A^(ó 0 ))^2 + 1/4 (((÷J δ + 2) (δ Underoverscript[∫, 0, arg3] log((x - 1) x q^2 + (m _ ψ^(ó 0 ))^2) d x + 2) (log(π) δ + 2) (δ log(μ) - 1))/δ + ((÷J δ + 2) (δ Underoverscript[∫, 0, arg3] log(x (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x + 2) (log(π) δ + 2) (δ log(μ) - 1))/δ - (2 (÷J δ + 2) (δ Underoverscript[∫, 0, arg3] log(x^2 (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x + 2) (log(π) δ + 2) (δ log(μ) - 1))/δ + 4) (m _ ψ^(ó 0 ))^2 (q^2 - 4 (m _ ψ^(ó 0 ))^2)))))](../HTMLFiles/index_170.gif)
![ampct = (amp2 + amp4) /. DiracGamma[LorentzIndex[μ1]] -> StandardMatrixElement[Spinor[-Momentum[p3], ParticleMass[Electron, RenormalizationState[0]], 1] . DiracGamma[LorentzIndex[μ1]] . Spinor[Momentum[p4], ParticleMass[Electron, RenormalizationState[0]], 1]] /. CouplingConstant[QED[2], 2, RenormalizationState[0]] -> z2 /. ssolv /. D -> 4 + δ](../HTMLFiles/index_171.gif)
![e^(0 ) {| ϕ ( -p _ 3 , m _ ψ^(ó 0 ) ) . γ^μ _ 1 . ϕ ( p _ 4 , m _ ψ^(ó 0 ) ) |} (1/e^(0 ) (((Underoverscript[∫, 0, arg3] log((x - 1) x q^2 + (m _ ψ^(ó 0 ))^2) d x) (m _ ψ^(ó 0 ))^2 (e^(0 ))^3)/(6 π^2 q^4) - (log((m _ ψ^(ó 0 ))^2) (m _ ψ^(ó 0 ))^2 (e^(0 ))^3)/(6 π^2 q^4) + ((Underoverscript[∫, 0, arg3] log((x - 1) x q^2 + (m _ ψ^(ó 0 ))^2) d x) (e^(0 ))^3)/(12 π^2 q^2) - (log((m _ ψ^(ó 0 ))^2) (e^(0 ))^3)/(12 π^2 q^2) + 1/(64 π^2 (m _ ψ^(ó 0 ))^2) ((((÷J δ + 2) (log(π) (δ + 4) - 4 log(π) + 2) (δ log(μ) - 1) (δ log((m _ ψ^(ó 0 ))^2) + 2) ((m _ A^(ó 0 ))^2 - 6 (m _ ψ^(ó 0 ))^2))/(2 δ) + 2 (-4 (m _ ψ^(ó 0 ))^2 - 1/(4 δ) ((÷J δ + 2) (δ Underoverscript[∫, 0, arg3] log(x^2 (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x + 2) (log(π) (δ + 4) - 4 log(π) + 2) (δ log(μ) - 1) ((m _ A^(ó 0 ))^2 - 8 (m _ ψ^(ó 0 ))^2)) + (8 (m _ ψ^(ó 0 ))^4 - 8 (m _ A^(ó 0 ))^2 (m _ ψ^(ó 0 ))^2 + (m _ A^(ó 0 ))^4) C _ 0((m _ ψ^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2, 0, (m _ ψ^(ó 0 ))^2, (m _ A^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2))) (e^(0 ))^3) + 1/(128 π^2 (m _ ψ^(ó 0 ))^2) ((12 C _ 0((m _ ψ^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2, 0, (m _ ψ^(ó 0 ))^2, (m _ A^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2) (m _ A^(ó 0 ))^4 - (-(2 (÷J δ + 2) (δ Underoverscript[∫, 0, arg3] log(x (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x + 2) (log(π) (δ + 4) - 4 log(π) + 2) (δ log(μ) - 1))/δ + (5 (÷J δ + 2) (δ Underoverscript[∫, 0, arg3] log(x^2 (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x + 2) (log(π) (δ + 4) - 4 log(π) + 2) (δ log(μ) - 1))/δ + 4 (8 (m _ ψ^(ó 0 ))^2 C _ 0((m _ ψ^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2, 0, (m _ ψ^(ó 0 ))^2, (m _ A^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2) - (3 (÷J δ + 2) (log(π) (δ + 4) - 4 log(π) + 2) (δ log(μ) - 1) (δ log((m _ ψ^(ó 0 ))^2) + 2))/(4 δ))) (m _ A^(ó 0 ))^2 - 2 (((÷J δ + 2) (δ Underoverscript[∫, 0, arg3] log(x (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x + 2) (log(π) (δ + 4) - 4 log(π) + 2) (δ log(μ) - 1))/δ - (2 (÷J δ + 2) (δ Underoverscript[∫, 0, arg3] log(x^2 (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x + 2) (log(π) (δ + 4) - 4 log(π) + 2) (δ log(μ) - 1))/δ + ((÷J δ + 2) (log(π) (δ + 4) - 4 log(π) + 2) (δ log((m _ ψ^(ó 0 ))^2) + 2) (δ log(μ) - 1))/δ + 4) (m _ ψ^(ó 0 ))^2) (e^(0 ))^3) + (e^(0 ))^3/(36 π^2 q^2) + e^(0 ) + 1) - 1) - 1/(36 π^2 q^4) ((e^(0 ))^3 ((1 - 3 log((m _ ψ^(ó 0 ))^2)) q^2 - 6 log((m _ ψ^(ó 0 ))^2) (m _ ψ^(ó 0 ))^2 + 3 (Underoverscript[∫, 0, arg3] log((x - 1) x q^2 + (m _ ψ^(ó 0 ))^2) d x) (q^2 + 2 (m _ ψ^(ó 0 ))^2)) {| ϕ ( -p _ 3 , m _ ψ^(ó 0 ) ) . γ^μ _ 1 . ϕ ( p _ 4 , m _ ψ^(ó 0 ) ) |})](../HTMLFiles/index_172.gif)
Mathematica cannot take the limit of ampinf+ampct. Instead we notice that the coefficients of 
cancel, and find the limit by omitting this term and setting δ = 0:
![Coefficient[ampct δ^2, δ] // Simplify](../HTMLFiles/index_174.gif){kind=small}
![Coefficient[ampinf δ^2, δ] // Simplify](../HTMLFiles/index_176.gif){kind=small}
![vertexamp1 = Coefficient[(ampct + ampinf) δ^2, δ^2] // Collect[#, {_StandardMatrixElement}] & // Simplify](../HTMLFiles/index_178.gif){kind=small}
![1/(16 π^2 (m _ ψ^(ó 0 ))^2 (q^2 - 4 (m _ ψ^(ó 0 ))^2)^2) ((2 p _ 3^μ _ 1 m _ ψ^(ó 0 ) {| ϕ ( -p _ 3 , m _ ψ^(ó 0 ) ) . ϕ ( p _ 4 , m _ ψ^(ó 0 ) ) |} (-4 (-4 C _ 0((m _ ψ^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2, q^2, (m _ ψ^(ó 0 ))^2, (m _ A^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2) (m _ A^(ó 0 ))^2 + Underoverscript[∫, 0, arg3] log((x - 1) x q^2 + (m _ ψ^(ó 0 ))^2) d x + Underoverscript[∫, 0, arg3] log(x (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x - 2 Underoverscript[∫, 0, arg3] log(x^2 (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x - 1) (m _ ψ^(ó 0 ))^4 + (-6 C _ 0((m _ ψ^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2, q^2, (m _ ψ^(ó 0 ))^2, (m _ A^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2) (m _ A^(ó 0 ))^4 - 10 (Underoverscript[∫, 0, arg3] log(x^2 (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x) (m _ A^(ó 0 ))^2 - 4 q^2 C _ 0((m _ ψ^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2, q^2, (m _ ψ^(ó 0 ))^2, (m _ A^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2) (m _ A^(ó 0 ))^2 - q^2 - 2 q^2 Underoverscript[∫, 0, arg3] log(x^2 (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x + (Underoverscript[∫, 0, arg3] log(x (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x) (q^2 + 4 (m _ A^(ó 0 ))^2) + (Underoverscript[∫, 0, arg3] log((x - 1) x q^2 + (m _ ψ^(ó 0 ))^2) d x) (q^2 + 6 (m _ A^(ó 0 ))^2)) (m _ ψ^(ó 0 ))^2 + q^2 (Underoverscript[∫, 0, arg3] log(x^2 (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x - Underoverscript[∫, 0, arg3] log(x (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x) (m _ A^(ó 0 ))^2) + (q^2 - 4 (m _ ψ^(ó 0 ))^2) {| ϕ ( -p _ 3 , m _ ψ^(ó 0 ) ) . γ^μ _ 1 . ϕ ( p _ 4 , m _ ψ^(ó 0 ) ) |} (-16 (C _ 0((m _ ψ^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2, 0, (m _ ψ^(ó 0 ))^2, (m _ A^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2) - C _ 0((m _ ψ^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2, q^2, (m _ ψ^(ó 0 ))^2, (m _ A^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2)) (m _ ψ^(ó 0 ))^6 + 4 (C _ 0((m _ ψ^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2, 0, (m _ ψ^(ó 0 ))^2, (m _ A^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2) q^2 - 3 C _ 0((m _ ψ^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2, q^2, (m _ ψ^(ó 0 ))^2, (m _ A^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2) q^2 + 3 Underoverscript[∫, 0, arg3] log((x - 1) x q^2 + (m _ ψ^(ó 0 ))^2) d x - Underoverscript[∫, 0, arg3] log(x (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x + 2 Underoverscript[∫, 0, arg3] log(x^2 (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x - 4 log((m _ ψ^(ó 0 ))^2) + 8 (m _ A^(ó 0 ))^2 C _ 0((m _ ψ^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2, 0, (m _ ψ^(ó 0 ))^2, (m _ A^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2) - 4 (m _ A^(ó 0 ))^2 C _ 0((m _ ψ^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2, q^2, (m _ ψ^(ó 0 ))^2, (m _ A^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2) + 1) (m _ ψ^(ó 0 ))^4 + (2 C _ 0((m _ ψ^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2, q^2, (m _ ψ^(ó 0 ))^2, (m _ A^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2) q^4 - 2 (Underoverscript[∫, 0, arg3] log(x^2 (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x) q^2 + 4 log((m _ ψ^(ó 0 ))^2) q^2 - 8 (m _ A^(ó 0 ))^2 C _ 0((m _ ψ^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2, 0, (m _ ψ^(ó 0 ))^2, (m _ A^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2) q^2 + 4 (m _ A^(ó 0 ))^2 C _ 0((m _ ψ^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2, q^2, (m _ ψ^(ó 0 ))^2, (m _ A^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2) q^2 - q^2 - 10 (Underoverscript[∫, 0, arg3] log(x^2 (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x) (m _ A^(ó 0 ))^2 + 8 log((m _ ψ^(ó 0 ))^2) (m _ A^(ó 0 ))^2 - (Underoverscript[∫, 0, arg3] log((x - 1) x q^2 + (m _ ψ^(ó 0 ))^2) d x) (3 q^2 + 2 (m _ A^(ó 0 ))^2) + (Underoverscript[∫, 0, arg3] log(x (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x) (q^2 + 4 (m _ A^(ó 0 ))^2) - 8 (m _ A^(ó 0 ))^4 C _ 0((m _ ψ^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2, 0, (m _ ψ^(ó 0 ))^2, (m _ A^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2) + 2 (m _ A^(ó 0 ))^4 C _ 0((m _ ψ^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2, q^2, (m _ ψ^(ó 0 ))^2, (m _ A^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2)) (m _ ψ^(ó 0 ))^2 + q^2 (m _ A^(ó 0 ))^2 (2 C _ 0((m _ ψ^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2, 0, (m _ ψ^(ó 0 ))^2, (m _ A^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2) (m _ A^(ó 0 ))^2 - Underoverscript[∫, 0, arg3] log(x (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x + 3 Underoverscript[∫, 0, arg3] log(x^2 (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x - 2 log((m _ ψ^(ó 0 ))^2))) + 2 p _ 4^μ _ 1 m _ ψ^(ó 0 ) {| ϕ ( -p _ 3 , m _ ψ^(ó 0 ) ) . ϕ ( p _ 4 , m _ ψ^(ó 0 ) ) |} (4 (-4 C _ 0((m _ ψ^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2, q^2, (m _ ψ^(ó 0 ))^2, (m _ A^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2) (m _ A^(ó 0 ))^2 + Underoverscript[∫, 0, arg3] log((x - 1) x q^2 + (m _ ψ^(ó 0 ))^2) d x + Underoverscript[∫, 0, arg3] log(x (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x - 2 Underoverscript[∫, 0, arg3] log(x^2 (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x - 1) (m _ ψ^(ó 0 ))^4 + (6 C _ 0((m _ ψ^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2, q^2, (m _ ψ^(ó 0 ))^2, (m _ A^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2) (m _ A^(ó 0 ))^4 + 10 (Underoverscript[∫, 0, arg3] log(x^2 (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x) (m _ A^(ó 0 ))^2 + 4 q^2 C _ 0((m _ ψ^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2, q^2, (m _ ψ^(ó 0 ))^2, (m _ A^(ó 0 ))^2, (m _ ψ^(ó 0 ))^2) (m _ A^(ó 0 ))^2 + q^2 + 2 q^2 Underoverscript[∫, 0, arg3] log(x^2 (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x - (Underoverscript[∫, 0, arg3] log(x (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x) (q^2 + 4 (m _ A^(ó 0 ))^2) - (Underoverscript[∫, 0, arg3] log((x - 1) x q^2 + (m _ ψ^(ó 0 ))^2) d x) (q^2 + 6 (m _ A^(ó 0 ))^2)) (m _ ψ^(ó 0 ))^2 + q^2 (Underoverscript[∫, 0, arg3] log(x (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x - Underoverscript[∫, 0, arg3] log(x^2 (m _ ψ^(ó 0 ))^2 - (x - 1) (m _ A^(ó 0 ))^2) d x) (m _ A^(ó 0 ))^2)) (e^(0 ))^3 + 16 π^2 (m _ ψ^(ó 0 ))^2 (q^2 - 4 (m _ ψ^(ó 0 ))^2)^2 {| ϕ ( -p _ 3 , m _ ψ^(ó 0 ) ) . γ^μ _ 1 . ϕ ( p _ 4 , m _ ψ^(ó 0 ) ) |})](../HTMLFiles/index_179.gif)
Converted by Mathematica (July 10, 2003)