(* ::Package:: *) localbasis[GGGG[4]] = {{M[GGGG[4], {pmmp, SUSYM}], H[1, 4]*H[2, 3]*(H[1, 4]*H[2, 3] + 2*X[1, 2, 4, 3])}, {M[GGGG[4], {pmmp, SUSYM}, tus], H[1, 3]*H[2, 4]* (H[1, 3]*H[2, 4] + 2*X[1, 2, 3, 4])}, {M[GGGG[4], {pmmp, SUSYM}, ust], H[1, 2]*H[3, 4]*(H[1, 2]*H[3, 4] + 2*X[1, 3, 2, 4])}, {M[GGGG[4], {ppppE, FULLSYM}], -1/8*(H[1, 2]*H[3, 4]*X[1, 2, 4, 3])/ (dot[p[1], p[2]]^2*dot[p[2], p[3]]^2)}, {M[GGGG[4], {pppmE, FULLSYM}], 8*HS*(HS + (2*(-2*dot[p[1], p[3]]*X[1, 2, 3, 4] - 2*dot[p[1], p[4]]* X[1, 2, 4, 3] - 2*dot[p[1], p[2]]*X[1, 3, 2, 4]))/3)}, {M[GGGG[4], {ppppO, FULLSYM}], -1/32*(H[1, 3]*H[2, 4]*(2*H[2, 4]*\[Epsilon][e[1], e[3], p[1], p[3]] + 2*H[1, 3]*\[Epsilon][e[2], e[4], p[2], p[4]]))/dot[p[1], p[3]]^4}, {M[GGGG[4], {pppmO, FULLSYM}], -8*(HS + (2*(-2*dot[p[1], p[3]]*X[1, 2, 3, 4] - 2*dot[p[1], p[4]]* X[1, 2, 4, 3] - 2*dot[p[1], p[2]]*X[1, 3, 2, 4]))/3)* (V[4]*(-(dot[p[2], p[3]]*\[Epsilon][e[1], e[2], e[3], p[1]]) - dot[e[3], p[2]]*\[Epsilon][e[1], e[2], p[1], p[3]] + dot[e[2], p[3]]*\[Epsilon][e[1], e[3], p[1], p[2]] - dot[e[2], e[3]]*\[Epsilon][e[1], p[1], p[2], p[3]]) + V[1]*(-(dot[p[3], p[4]]*\[Epsilon][e[2], e[3], e[4], p[2]]) - dot[e[4], p[3]]*\[Epsilon][e[2], e[3], p[2], p[4]] + dot[e[3], p[4]]*\[Epsilon][e[2], e[4], p[2], p[3]] - dot[e[3], e[4]]*\[Epsilon][e[2], p[2], p[3], p[4]]) + V[2]*(-(dot[p[1], p[4]]*\[Epsilon][e[1], e[3], e[4], p[3]]) - dot[e[4], p[1]]*\[Epsilon][e[1], e[3], p[3], p[4]] + dot[e[1], p[4]]*\[Epsilon][e[3], e[4], p[1], p[3]] - dot[e[1], e[4]]*\[Epsilon][e[3], p[1], p[3], p[4]]) + V[3]*(-(dot[p[1], p[2]]*\[Epsilon][e[1], e[2], e[4], p[4]]) - dot[e[2], p[1]]*\[Epsilon][e[1], e[4], p[2], p[4]] + dot[e[1], p[2]]*\[Epsilon][e[2], e[4], p[1], p[4]] - dot[e[1], e[2]]*\[Epsilon][e[4], p[1], p[2], p[4]]))}} vertices[GG[4]] = {(dot[ep[1], ep[2]]^2*Tableau[{evenn^J}])/Sqrt[2], (Sqrt[((-3 + J)*(-2 + J)*(-1 + J)*J)/((1 + J)*(2 + J)*(3 + J)*(4 + J))]* (-(dot[ep[1], ep[2]]^2*Tableau[{evenn^J}]) + 4*Tableau[{ep[1]}, {ep[1]}, {ep[2]}, {ep[2]}, {evenn^(-4 + J)}]))/ Sqrt[2], (dot[ep[1], ep[2]]*Tableau[{evenn^J}]*\[Epsilon][ep[1], ep[2], n])/Sqrt[2], Sqrt[2]*Sqrt[((-3 + J)*(-2 + J)*(-1 + J)*J)/ ((1 + J)*(2 + J)*(3 + J)*(4 + J))]*(Tableau[{ep[1], n}, {ep[1]}, {ep[2]}, {ep[2]}, {n}, {evenn^(-5 + J)}] + Tableau[{ep[2], n}, {ep[2]}, {ep[1]}, {ep[1]}, {n}, {evenn^(-5 + J)}])} amplow[GGG[4]] = Sqrt[G8\[Pi]]* ((2*dot[e[1], p[2]]*dot[e[2], e[3]] - 2*dot[e[1], e[3]]* dot[e[2], p[1]] + dot[e[1], e[2]]*(dot[e[3], p[1]] - dot[e[3], p[2]]))^2/2 + 4*G2*dot[e[1], p[2]]^2*dot[e[2], p[1]]^2* dot[e[3], p[1]]*dot[e[3], p[2]] + 2*GO*dot[e[1], p[2]]*dot[e[2], p[1]]* (-(dot[e[2], p[1]]*dot[e[3], p[2]]*\[Epsilon][p[1], p[2], e[1], e[3]]) + dot[e[1], p[2]]*dot[e[3], p[1]]*\[Epsilon][p[1], p[2], e[2], e[3]])) amplow[GGGG[4]] = {G8\[Pi]*(1/(s*(-s - t)*t) + ((G2^2 + GO^2)*s*(-s - t))/ (4*t)) + g[4, 0, {GGGG[4], pmmp}] + (s^2 + t^2 + u^2)* g[6, 0, {GGGG[4], pmmp}] + s*t*u*g[7, 0, {GGGG[4], pmmp}] + (s^2 + t^2 + u^2)^2*g[8, 0, {GGGG[4], pmmp}] + 2*s*t*u*(s^2 + t^2 + u^2)*g[9, 0, {GGGG[4], pmmp}] + (s^2 + t^2 + u^2)^3*g[10, 0, {GGGG[4], pmmp}] + t*g[5, T, 0, {GGGG[4], pmmp}] + t^2*g[6, T^2, 0, {GGGG[4], pmmp}] + t*(s^2 + t^2 + u^2)*g[7, T, 0, {GGGG[4], pmmp}] + s*t^2*u*g[8, T, 0, {GGGG[4], pmmp}], G8\[Pi]*(1/(s*(-s - t)*t) + ((G2^2 + GO^2)*s*t)/(4*(-s - t))) + g[4, 0, {GGGG[4], pmmp}] + (s^2 + t^2 + u^2)*g[6, 0, {GGGG[4], pmmp}] + s*t*u*g[7, 0, {GGGG[4], pmmp}] + (s^2 + t^2 + u^2)^2* g[8, 0, {GGGG[4], pmmp}] + 2*s*t*u*(s^2 + t^2 + u^2)* g[9, 0, {GGGG[4], pmmp}] + (s^2 + t^2 + u^2)^3* g[10, 0, {GGGG[4], pmmp}] + u*g[5, T, 0, {GGGG[4], pmmp}] + u^2*g[6, T^2, 0, {GGGG[4], pmmp}] + u*(s^2 + t^2 + u^2)* g[7, T, 0, {GGGG[4], pmmp}] + s*t*u^2*g[8, T, 0, {GGGG[4], pmmp}], G8\[Pi]*(1/(s*(-s - t)*t) + ((G2^2 + GO^2)*(-s - t)*t)/(4*s)) + g[4, 0, {GGGG[4], pmmp}] + (s^2 + t^2 + u^2)*g[6, 0, {GGGG[4], pmmp}] + s*t*u*g[7, 0, {GGGG[4], pmmp}] + (s^2 + t^2 + u^2)^2* g[8, 0, {GGGG[4], pmmp}] + 2*s*t*u*(s^2 + t^2 + u^2)* g[9, 0, {GGGG[4], pmmp}] + (s^2 + t^2 + u^2)^3* g[10, 0, {GGGG[4], pmmp}] + s*g[5, T, 0, {GGGG[4], pmmp}] + s^2*g[6, T^2, 0, {GGGG[4], pmmp}] + s*(s^2 + t^2 + u^2)* g[7, T, 0, {GGGG[4], pmmp}] + s^2*t*u*g[8, T, 0, {GGGG[4], pmmp}], -5*G2*G8\[Pi]*s*(-s - t)*t + (s^2 + t^2 + u^2)^2* g[4, 0, {GGGG[4], ppppE}] + 2*s*t*u*(s^2 + t^2 + u^2)* g[5, 0, {GGGG[4], ppppE}] + (s^2 + t^2 + u^2)^3* g[6, 0, {GGGG[4], ppppE}] + s^2*t^2*u^2*g[6, 1, {GGGG[4], ppppE}] + 3*s*t*u*(s^2 + t^2 + u^2)^2*g[7, 0, {GGGG[4], ppppE}] + 3*s^2*t^2*u^2*(s^2 + t^2 + u^2)*g[8, 1, {GGGG[4], ppppE}] + s^3*t^3*u^3*g[9, 1, {GGGG[4], ppppE}], -((G2*G8\[Pi])/(s*(-s - t)*t)) + g[6, 0, {GGGG[4], pppmE}] + (s^2 + t^2 + u^2)* g[8, 0, {GGGG[4], pppmE}] + s*t*u*g[9, 0, {GGGG[4], pppmE}], -5*G8\[Pi]*GO*s*(-s - t)*t + (s^2 + t^2 + u^2)^2* g[4, 0, {GGGG[4], ppppO}] + 2*s*t*u*(s^2 + t^2 + u^2)* g[5, 0, {GGGG[4], ppppO}] + (s^2 + t^2 + u^2)^3* g[6, 0, {GGGG[4], ppppO}] + s^2*t^2*u^2*g[6, 1, {GGGG[4], ppppO}] + 3*s*t*u*(s^2 + t^2 + u^2)^2*g[7, 0, {GGGG[4], ppppO}] + 3*s^2*t^2*u^2*(s^2 + t^2 + u^2)*g[8, 1, {GGGG[4], ppppO}] + s^3*t^3*u^3*g[9, 1, {GGGG[4], ppppO}], -((G8\[Pi]*GO)/(s*(-s - t)*t)) + g[6, 0, {GGGG[4], pppmO}] + (s^2 + t^2 + u^2)* g[8, 0, {GGGG[4], pppmO}] + s*t*u*g[9, 0, {GGGG[4], pppmO}]} ruleDtilde = {Dtilde[J_, m_, mp_, x_] :> Module[{max = Max[Abs[m], Abs[mp]]}, (1/Abs[m - mp]!)*Sqrt[Pochhammer[J - max + 1, Abs[m - mp]]* Pochhammer[J - max + Abs[m + mp] + 1, Abs[m - mp]]]* Hypergeometric2F1[max - J, max + J + 1, 1 + Abs[m - mp], (1 - x)/2]]} partialwavesNice[{GG[4], GG[4]}] = {exchange[{0}, {GGGG[4], s, 1 + (2*t)/s}, {{1, 1}, {1, 1}}, {{{0, 0, 1/(2*m2^4), 1/2, 0, 0, 0}, {0, 0, 0, 0, 0, 1/2, 0}}, {{0, 0, 0, 0, 0, 1/2, 0}, {0, 0, 1/(2*m2^4), -1/2, 0, 0, 0}}}], exchange[{2}, {GGGG[4], s, 1 + (2*t)/s}, {{1, 1}, {1, 1}}, {{{0, 0, (-1/4 + (3*x^2)/4)/m2^4, -1/4 + (3*x^2)/4, 0, 0, 0}, {0, 0, 0, 0, 0, -1/4 + (3*x^2)/4, 0}}, {{0, 0, 0, 0, 0, -1/4 + (3*x^2)/4, 0}, {0, 0, (-1/4 + (3*x^2)/4)/m2^4, 1/4 - (3*x^2)/4, 0, 0, 0}}}], exchange[{4 + 2*m}, {GGGG[4], s, 1 + (2*t)/s}, 1, {{{0, 0, Dtilde[J, 0, 0, x]/(2*m2^4), Dtilde[J, 0, 0, x]/2, 0, 0, 0}, {0, 0, 0, 0, Dtilde[J, 4, 0, x]/ (2*m2^6), 0, 0}, {0, 0, 0, 0, 0, Dtilde[J, 0, 0, x]/2, 0}}, {{0, 0, 0, 0, Dtilde[J, 4, 0, x]/(2*m2^6), 0, 0}, {Dtilde[J, 4, -4, x]/(2*m2^4), Dtilde[J, 4, 4, x]/(2*m2^4), 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, Dtilde[J, 4, 0, x]/(2*m2^6)}}, {{0, 0, 0, 0, 0, Dtilde[J, 0, 0, x]/2, 0}, {0, 0, 0, 0, 0, 0, Dtilde[J, 4, 0, x]/(2*m2^6)}, {0, 0, Dtilde[J, 0, 0, x]/(2*m2^4), -1/2*Dtilde[J, 0, 0, x], 0, 0, 0}}}], exchange[{5 + 2*m}, {GGGG[4], s, 1 + (2*t)/s}, 1, {{{-1/2*Dtilde[J, 4, -4, x]/m2^4, Dtilde[J, 4, 4, x]/(2*m2^4), 0, 0, 0, 0, 0}}}]} partialwaves[{GG[4], GG[4]}] = {exchange[{0}, {GGGG[4], s, 1 + (2*t)/s}, {{1, 1}, {1, 1}}, {{{0, 0, 1/(2*m2^4), 1/2, 0, 0, 0}, {0, 0, 0, 0, 0, 1/2, 0}}, {{0, 0, 0, 0, 0, 1/2, 0}, {0, 0, 1/(2*m2^4), -1/2, 0, 0, 0}}}], exchange[{2}, {GGGG[4], s, 1 + (2*t)/s}, {{1, 1}, {1, 1}}, {{{0, 0, (-1/4 + (3*x^2)/4)/m2^4, -1/4 + (3*x^2)/4, 0, 0, 0}, {0, 0, 0, 0, 0, -1/4 + (3*x^2)/4, 0}}, {{0, 0, 0, 0, 0, -1/4 + (3*x^2)/4, 0}, {0, 0, (-1/4 + (3*x^2)/4)/m2^4, 1/4 - (3*x^2)/4, 0, 0, 0}}}], exchange[{4 + 2*m}, {GGGG[4], s, 1 + (2*t)/s}, {{1/(2*m2^4), 8/(Sqrt[-3 + J]*Sqrt[-2 + J]*Sqrt[-1 + J]*Sqrt[J]* Sqrt[1 + J]*Sqrt[2 + J]*Sqrt[3 + J]*Sqrt[4 + J]*m2^6), 1/2}, {8/(Sqrt[-3 + J]*Sqrt[-2 + J]*Sqrt[-1 + J]*Sqrt[J]*Sqrt[1 + J]* Sqrt[2 + J]*Sqrt[3 + J]*Sqrt[4 + J]*m2^6), 8/((-3 + J)*(-2 + J)*(-1 + J)*J*(1 + J)*(2 + J)*(3 + J)*(4 + J)* m2^4), 8/(Sqrt[-3 + J]*Sqrt[-2 + J]*Sqrt[-1 + J]*Sqrt[J]* Sqrt[1 + J]*Sqrt[2 + J]*Sqrt[3 + J]*Sqrt[4 + J]*m2^6)}, {1/2, 8/(Sqrt[-3 + J]*Sqrt[-2 + J]*Sqrt[-1 + J]*Sqrt[J]*Sqrt[1 + J]* Sqrt[2 + J]*Sqrt[3 + J]*Sqrt[4 + J]*m2^6), 1/(2*m2^4)}}, {{{0, 0, pj[J, x, 4, 0], m2^4*pj[J, x, 4, 0], 0, 0, 0}, {0, 0, 0, 0, pj[J, x, 4, 4], 0, 0}, {0, 0, 0, 0, 0, pj[J, x, 4, 0], 0}}, {{0, 0, 0, 0, pj[J, x, 4, 4], 0, 0}, {(-96 - 14*J - 13*J^2 + 2*J^3 + J^4)*pj[J, x, 4, 4] + (-8*(-6 + J)*(7 + J) - 8*(3 + J + J^2)*x)*pj[J, x, 4, 5] + (8*(-27 + J + J^2) + 4*(18 + J + J^2)*x)*pj[J, x, 4, 6] + (8 - 48*x)*pj[J, x, 4, 7] + (8 + 8*x)*pj[J, x, 4, 8], (-96 - 14*J - 13*J^2 + 2*J^3 + J^4)*pj[J, x, 4, 4] + (8*(-6 + J)*(7 + J) - 8*(3 + J + J^2)*x)*pj[J, x, 4, 5] + (8*(-27 + J + J^2) - 4*(18 + J + J^2)*x)*pj[J, x, 4, 6] + (-8 - 48*x)*pj[J, x, 4, 7] + (8 - 8*x)*pj[J, x, 4, 8], 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, pj[J, x, 4, 4]}}, {{0, 0, 0, 0, 0, pj[J, x, 4, 0], 0}, {0, 0, 0, 0, 0, 0, pj[J, x, 4, 4]}, {0, 0, pj[J, x, 4, 0], -(m2^4*pj[J, x, 4, 0]), 0, 0, 0}}}], exchange[{5 + 2*m}, {GGGG[4], s, 1 + (2*t)/s}, {{8/((-3 + J)*(-2 + J)*(-1 + J)*J*(1 + J)*(2 + J)*(3 + J)*(4 + J)* m2^4)}}, {{{(96 + 14*J + 13*J^2 - 2*J^3 - J^4)*pj[J, x, 4, 4] + (8*(-6 + J)*(7 + J) + 8*(3 + J + J^2)*x)*pj[J, x, 4, 5] + (-8*(-27 + J + J^2) - 4*(18 + J + J^2)*x)*pj[J, x, 4, 6] + (-8 + 48*x)*pj[J, x, 4, 7] + (-8 - 8*x)*pj[J, x, 4, 8], (-96 - 14*J - 13*J^2 + 2*J^3 + J^4)*pj[J, x, 4, 4] + (8*(-6 + J)*(7 + J) - 8*(3 + J + J^2)*x)*pj[J, x, 4, 5] + (8*(-27 + J + J^2) - 4*(18 + J + J^2)*x)*pj[J, x, 4, 6] + (-8 - 48*x)*pj[J, x, 4, 7] + (8 - 8*x)*pj[J, x, 4, 8], 0, 0, 0, 0, 0}}}]} sumrules[bkimp[GGGG[4], 2]] = {(2*m2 - p2)*M[GGGG[4], {pmmp, SUSYM}, tus][s, -t][p2] + (2*m2 - p2)*M[GGGG[4], {pmmp, SUSYM}, ust][s, -t][p2], -(Derivative[1][M[GGGG[4], {pmmp, SUSYM}, tus][s, -t]][0]/ (m2*(m2 - p2))) + Derivative[1][M[GGGG[4], {pmmp, SUSYM}, ust][s, -t]][0]/(m2*(m2 + p2)) + ((2*m2 - p2)*M[GGGG[4], {pmmp, SUSYM}][s, -t][p2])/(m2^2*(m2 - p2)^2) - ((2*m2 - p2)*M[GGGG[4], {pmmp, SUSYM}, tus][s, -t][0])/ (m2^2*(m2 - p2)^2), (2*m2 - p2)*M[GGGG[4], {pppmE, FULLSYM}][s, -t][ p2], (-2*p2^3*Derivative[1][M[GGGG[4], {ppppE, FULLSYM}][s, -t]][0])/ (m2^3*(m2 - p2)*(m2 + p2)) - ((4*m2 - 3*p2)*p2^2* M[GGGG[4], {ppppE, FULLSYM}][s, -t][0])/(m2^4*(m2 - p2)^2) + ((2*m2 - p2)*M[GGGG[4], {ppppE, FULLSYM}][s, -t][p2])/ (m2^2*(m2 - p2)^2), (2*m2 - p2)*M[GGGG[4], {pppmO, FULLSYM}][s, -t][ p2], (-2*p2^3*Derivative[1][M[GGGG[4], {ppppO, FULLSYM}][s, -t]][0])/ (m2^3*(m2 - p2)*(m2 + p2)) - ((4*m2 - 3*p2)*p2^2* M[GGGG[4], {ppppO, FULLSYM}][s, -t][0])/(m2^4*(m2 - p2)^2) + ((2*m2 - p2)*M[GGGG[4], {ppppO, FULLSYM}][s, -t][p2])/ (m2^2*(m2 - p2)^2)} sumrules[bkimp[GGGG[4], 3]] = {-M[GGGG[4], {pmmp, SUSYM}, tus][s, -t][p2] + M[GGGG[4], {pmmp, SUSYM}, ust][s, -t][p2]} sumrules[bkimp[GGGG[4], 4]] = {-((p2^2*(m2^2 + 2*p2^2)*Derivative[1][M[GGGG[4], {pmmp, SUSYM}, tus][s, -t]][0])/m2^4) + ((m2 - p2)*p2^2*(m2 + p2)* Derivative[1][M[GGGG[4], {pmmp, SUSYM}, ust][s, -t]][0])/m2^4 - (p2^4*Derivative[2][M[GGGG[4], {pmmp, SUSYM}, tus][s, -t]][0])/ (2*m2^3) - (p2^4*Derivative[2][M[GGGG[4], {pmmp, SUSYM}, ust][s, -t]][ 0])/(2*m2^3) - (2*p2^6*M[GGGG[4], {pmmp, SUSYM}][s, -t][0])/ (m2^5*(m2 - p2)*(m2 + p2)) + (p2*(m2^4 - 2*m2^3*p2 - 2*m2^2*p2^2 - 2*m2*p2^3 - 2*p2^4)*M[GGGG[4], {pmmp, SUSYM}, tus][s, -t][0])/ (m2^5*(m2 + p2)) + ((2*m2 - p2)*M[GGGG[4], {pmmp, SUSYM}, tus][s, -t][ p2])/(m2*(m2 - p2)) - (p2*M[GGGG[4], {pmmp, SUSYM}, ust][s, -t][0])/ (m2*(m2 - p2)) + ((2*m2 - p2)*M[GGGG[4], {pmmp, SUSYM}, ust][s, -t][ p2])/(m2*(m2 - p2)), -(((2*m2 - p2)*Derivative[1][M[GGGG[4], {pmmp, SUSYM}, tus][s, -t]][0])/ (m2^3*(m2 - p2)^2)) - Derivative[1][M[GGGG[4], {pmmp, SUSYM}, ust][s, -t]][0]/(m2^3*(m2 + p2)) - Derivative[2][M[GGGG[4], {pmmp, SUSYM}, tus][s, -t]][0]/ (2*m2^2*(m2 - p2)) - Derivative[2][M[GGGG[4], {pmmp, SUSYM}, ust][s, -t]][0]/(2*m2^2*(m2 + p2)) + ((2*m2 - p2)*M[GGGG[4], {pmmp, SUSYM}][s, -t][p2])/(m2^3*(m2 - p2)^3) - ((2*m2 - p2)*M[GGGG[4], {pmmp, SUSYM}, tus][s, -t][0])/ (m2^3*(m2 - p2)^3), (-2*p2^2*M[GGGG[4], {pppmE, FULLSYM}][s, -t][0])/ (m2*(m2 - p2)*(m2 + p2)) + ((2*m2 - p2)*M[GGGG[4], {pppmE, FULLSYM}][s, -t][p2])/(m2*(m2 - p2)), -((p2^3*(4*m2^2 + 3*m2*p2 - 5*p2^2)* Derivative[1][M[GGGG[4], {ppppE, FULLSYM}][s, -t]][0])/ (m2^6*(m2 - p2)^2*(m2 + p2))) - (p2^4*Derivative[2][M[GGGG[4], {ppppE, FULLSYM}][s, -t]][0])/ (m2^5*(m2 - p2)*(m2 + p2)) - (p2^2*(6*m2^3 - 4*m2^2*p2 - 4*m2*p2^2 + 3*p2^3)*M[GGGG[4], {ppppE, FULLSYM}][s, -t][0])/(m2^7*(m2 - p2)^3) + ((2*m2 - p2)*M[GGGG[4], {ppppE, FULLSYM}][s, -t][p2])/ (m2^3*(m2 - p2)^3), (-2*p2^2*M[GGGG[4], {pppmO, FULLSYM}][s, -t][0])/ (m2*(m2 - p2)*(m2 + p2)) + ((2*m2 - p2)*M[GGGG[4], {pppmO, FULLSYM}][s, -t][p2])/(m2*(m2 - p2)), -((p2^3*(4*m2^2 + 3*m2*p2 - 5*p2^2)* Derivative[1][M[GGGG[4], {ppppO, FULLSYM}][s, -t]][0])/ (m2^6*(m2 - p2)^2*(m2 + p2))) - (p2^4*Derivative[2][M[GGGG[4], {ppppO, FULLSYM}][s, -t]][0])/ (m2^5*(m2 - p2)*(m2 + p2)) - (p2^2*(6*m2^3 - 4*m2^2*p2 - 4*m2*p2^2 + 3*p2^3)*M[GGGG[4], {ppppO, FULLSYM}][s, -t][0])/(m2^7*(m2 - p2)^3) + ((2*m2 - p2)*M[GGGG[4], {ppppO, FULLSYM}][s, -t][p2])/ (m2^3*(m2 - p2)^3)} sumrules[bkimp[GGGG[4], 5]] = {(2*p2^3*Derivative[1][M[GGGG[4], {pmmp, SUSYM}, tus][s, -t]][0])/m2^4 + (p2^3*Derivative[1][M[GGGG[4], {pmmp, SUSYM}, ust][s, -t]][0])/m2^4 + (p2^3*Derivative[2][M[GGGG[4], {pmmp, SUSYM}, tus][s, -t]][0])/ (2*m2^3) + (p2^3*Derivative[2][M[GGGG[4], {pmmp, SUSYM}, ust][s, -t]][ 0])/(2*m2^3) + (2*p2^5*M[GGGG[4], {pmmp, SUSYM}][s, -t][0])/ (m2^5*(m2 - p2)*(m2 + p2)) - (p2*(m2^3 - 2*m2*p2^2 - 2*p2^3)* M[GGGG[4], {pmmp, SUSYM}, tus][s, -t][0])/(m2^5*(m2 + p2)) - M[GGGG[4], {pmmp, SUSYM}, tus][s, -t][p2]/(m2*(m2 - p2)) - (p2*M[GGGG[4], {pmmp, SUSYM}, ust][s, -t][0])/(m2^2*(m2 - p2)) + M[GGGG[4], {pmmp, SUSYM}, ust][s, -t][p2]/(m2*(m2 - p2))} sumrules[bkimp[GGGG[4], 6]] = {(-2*p2^7*Derivative[1][M[GGGG[4], {pmmp, SUSYM}][s, -t]][0])/ (m2^7*(m2 - p2)*(m2 + p2)) + (p2^2*(m2^4 - 3*m2^3*p2 - 9*m2^2*p2^2 - 11*m2*p2^3 - 5*p2^4)*Derivative[1][M[GGGG[4], {pmmp, SUSYM}, tus][s, -t]][0])/(m2^7*(m2 + p2)) - (p2^2*(m2^4 - m2^3*p2 - 5*m2^2*p2^2 + 8*m2*p2^3 - 2*p2^4)* Derivative[1][M[GGGG[4], {pmmp, SUSYM}, ust][s, -t]][0])/ (m2^7*(m2 - p2)) - (p2^3*(m2^2 + 6*m2*p2 + 3*p2^2)* Derivative[2][M[GGGG[4], {pmmp, SUSYM}, tus][s, -t]][0])/(2*m2^6) + (p2^3*(m2^2 + 6*m2*p2 - 2*p2^2)* Derivative[2][M[GGGG[4], {pmmp, SUSYM}, ust][s, -t]][0])/(2*m2^6) - (p2^4*(3*m2 + p2)*Derivative[3][M[GGGG[4], {pmmp, SUSYM}, tus][s, -t]][ 0])/(6*m2^5) + ((3*m2 - p2)*p2^4* Derivative[3][M[GGGG[4], {pmmp, SUSYM}, ust][s, -t]][0])/(6*m2^5) - ((8*m2 - 7*p2)*p2^6*M[GGGG[4], {pmmp, SUSYM}][s, -t][0])/ (m2^8*(m2 - p2)^2) + (p2*(m2^4 - 5*m2^2*p2^2 - 6*m2*p2^3 - 7*p2^4)* M[GGGG[4], {pmmp, SUSYM}, tus][s, -t][0])/m2^8 + ((2*m2 - p2)*M[GGGG[4], {pmmp, SUSYM}, tus][s, -t][p2])/ (m2^2*(m2 - p2)^2) - (p2*(m2^2 + 2*m2*p2 - 2*p2^2)* M[GGGG[4], {pmmp, SUSYM}, ust][s, -t][0])/(m2^4*(m2 - p2)^2) + ((2*m2 - p2)*M[GGGG[4], {pmmp, SUSYM}, ust][s, -t][p2])/ (m2^2*(m2 - p2)^2), -(((2*m2 - p2)*Derivative[1][M[GGGG[4], {pmmp, SUSYM}, tus][s, -t]][0])/ (m2^4*(m2 - p2)^3)) + (2*Derivative[1][M[GGGG[4], {pmmp, SUSYM}, ust][s, -t]][0])/ (m2^5*(m2 + p2)) - ((2*m2 - p2)*Derivative[2][M[GGGG[4], {pmmp, SUSYM}, tus][s, -t]][0])/ (2*m2^4*(m2 - p2)^2) + Derivative[2][M[GGGG[4], {pmmp, SUSYM}, ust][s, -t]][0]/(m2^4*(m2 + p2)) - Derivative[3][M[GGGG[4], {pmmp, SUSYM}, tus][s, -t]][0]/ (6*m2^3*(m2 - p2)) + Derivative[3][M[GGGG[4], {pmmp, SUSYM}, ust][s, -t]][0]/(6*m2^3*(m2 + p2)) + ((2*m2 - p2)*M[GGGG[4], {pmmp, SUSYM}][s, -t][p2])/(m2^4*(m2 - p2)^4) - ((2*m2 - p2)*M[GGGG[4], {pmmp, SUSYM}, tus][s, -t][0])/ (m2^4*(m2 - p2)^4), (-2*p2^3*Derivative[1][M[GGGG[4], {pppmE, FULLSYM}][s, -t]][0])/ (m2^3*(m2 - p2)*(m2 + p2)) - ((4*m2 - 3*p2)*p2^2* M[GGGG[4], {pppmE, FULLSYM}][s, -t][0])/(m2^4*(m2 - p2)^2) + ((2*m2 - p2)*M[GGGG[4], {pppmE, FULLSYM}][s, -t][p2])/ (m2^2*(m2 - p2)^2), -((p2^3*(6*m2^4 + 6*m2^3*p2 - 7*m2^2*p2^2 - 13*m2*p2^3 + 10*p2^4)* Derivative[1][M[GGGG[4], {ppppE, FULLSYM}][s, -t]][0])/ (m2^9*(m2 - p2)^3*(m2 + p2))) - (p2^4*(4*m2^2 + 5*m2*p2 - 7*p2^2)* Derivative[2][M[GGGG[4], {ppppE, FULLSYM}][s, -t]][0])/ (2*m2^8*(m2 - p2)^2*(m2 + p2)) - (p2^5*Derivative[3][M[GGGG[4], {ppppE, FULLSYM}][s, -t]][0])/ (3*m2^7*(m2 - p2)*(m2 + p2)) - (p2^2*(8*m2^5 - 5*m2^4*p2 - 10*m2^3*p2^2 + 7*m2^2*p2^3 + 4*m2*p2^4 - 3*p2^5)*M[GGGG[4], {ppppE, FULLSYM}][s, -t][0])/ (m2^10*(m2 - p2)^4) + ((2*m2 - p2)*M[GGGG[4], {ppppE, FULLSYM}][s, -t][ p2])/(m2^4*(m2 - p2)^4), (-2*p2^3*Derivative[1][M[GGGG[4], {pppmO, FULLSYM}][s, -t]][0])/ (m2^3*(m2 - p2)*(m2 + p2)) - ((4*m2 - 3*p2)*p2^2* M[GGGG[4], {pppmO, FULLSYM}][s, -t][0])/(m2^4*(m2 - p2)^2) + ((2*m2 - p2)*M[GGGG[4], {pppmO, FULLSYM}][s, -t][p2])/ (m2^2*(m2 - p2)^2), -((p2^3*(6*m2^4 + 6*m2^3*p2 - 7*m2^2*p2^2 - 13*m2*p2^3 + 10*p2^4)* Derivative[1][M[GGGG[4], {ppppO, FULLSYM}][s, -t]][0])/ (m2^9*(m2 - p2)^3*(m2 + p2))) - (p2^4*(4*m2^2 + 5*m2*p2 - 7*p2^2)* Derivative[2][M[GGGG[4], {ppppO, FULLSYM}][s, -t]][0])/ (2*m2^8*(m2 - p2)^2*(m2 + p2)) - (p2^5*Derivative[3][M[GGGG[4], {ppppO, FULLSYM}][s, -t]][0])/ (3*m2^7*(m2 - p2)*(m2 + p2)) - (p2^2*(8*m2^5 - 5*m2^4*p2 - 10*m2^3*p2^2 + 7*m2^2*p2^3 + 4*m2*p2^4 - 3*p2^5)*M[GGGG[4], {ppppO, FULLSYM}][s, -t][0])/ (m2^10*(m2 - p2)^4) + ((2*m2 - p2)*M[GGGG[4], {ppppO, FULLSYM}][s, -t][ p2])/(m2^4*(m2 - p2)^4)} sumrules[bkimp[GGGG[4], 7]] = {(2*p2^6*Derivative[1][M[GGGG[4], {pmmp, SUSYM}][s, -t]][0])/ (m2^7*(m2 - p2)*(m2 + p2)) - (p2^2*(m2^3 - 5*m2*p2^2 - 5*p2^3)* Derivative[1][M[GGGG[4], {pmmp, SUSYM}, tus][s, -t]][0])/ (m2^7*(m2 + p2)) - (p2^2*(m2^3 - 2*m2*p2^2 + 2*p2^3)* Derivative[1][M[GGGG[4], {pmmp, SUSYM}, ust][s, -t]][0])/ (m2^7*(m2 - p2)) + (3*p2^4*Derivative[2][M[GGGG[4], {pmmp, SUSYM}, tus][s, -t]][0])/ (2*m2^6) + (p2^4*Derivative[2][M[GGGG[4], {pmmp, SUSYM}, ust][s, -t]][ 0])/m2^6 + (p2^4*Derivative[3][M[GGGG[4], {pmmp, SUSYM}, tus][s, -t]][0])/(6*m2^5) + (p2^4*Derivative[3][M[GGGG[4], {pmmp, SUSYM}, ust][s, -t]][0])/ (6*m2^5) + (p2^5*(4*m2^2 + 5*m2*p2 - 7*p2^2)* M[GGGG[4], {pmmp, SUSYM}][s, -t][0])/(m2^8*(m2 - p2)^2*(m2 + p2)) - (p2*(m2^4 + 2*m2^3*p2 - m2^2*p2^2 - 7*m2*p2^3 - 7*p2^4)* M[GGGG[4], {pmmp, SUSYM}, tus][s, -t][0])/(m2^8*(m2 + p2)) - M[GGGG[4], {pmmp, SUSYM}, tus][s, -t][p2]/(m2^2*(m2 - p2)^2) - (p2*(m2^3 + 2*m2^2*p2 - 3*m2*p2^2 + p2^3)* M[GGGG[4], {pmmp, SUSYM}, ust][s, -t][0])/(m2^6*(m2 - p2)^2) + M[GGGG[4], {pmmp, SUSYM}, ust][s, -t][p2]/(m2^2*(m2 - p2)^2)} Attributes[Derivative] = {NHoldAll} sumruleslow[bkimp[GGGG[4], 2]] = {(2*G8\[Pi])/p2 + (G2^2*G8\[Pi]*p2^3)/4 + (G8\[Pi]*GO^2*p2^3)/4, (G2^2*G8\[Pi])/(4*p2) + (G8\[Pi]*GO^2)/(4*p2), -((G2*G8\[Pi])/p2), -5*G2*G8\[Pi]*p2, -((G8\[Pi]*GO)/p2), -5*G8\[Pi]*GO*p2} sumruleslow[bkimp[GGGG[4], 3]] = {-1/4*(G2^2*G8\[Pi]*p2^2) - (G8\[Pi]*GO^2*p2^2)/4} sumruleslow[bkimp[GGGG[4], 4]] = {(G2^2*G8\[Pi]*p2)/2 + (G8\[Pi]*GO^2*p2)/2 + 2*g[4, 0, {GGGG[4], pmmp}], 0, g[6, 0, {GGGG[4], pppmE}], 4*g[4, 0, {GGGG[4], ppppE}] + 4*p2*g[5, 0, {GGGG[4], ppppE}] + p2^2*g[6, 1, {GGGG[4], ppppE}], g[6, 0, {GGGG[4], pppmO}], 4*g[4, 0, {GGGG[4], ppppO}] + 4*p2*g[5, 0, {GGGG[4], ppppO}] + p2^2*g[6, 1, {GGGG[4], ppppO}]} sumruleslow[bkimp[GGGG[4], 5]] = {-2*p2*g[6, 0, {GGGG[4], pmmp}] + g[5, T, 0, {GGGG[4], pmmp}]} sumruleslow[bkimp[GGGG[4], 6]] = {4*g[6, 0, {GGGG[4], pmmp}] + 2*p2*g[7, 0, {GGGG[4], pmmp}] + 8*p2^2*g[8, 0, {GGGG[4], pmmp}] + 2*g[6, T^2, 0, {GGGG[4], pmmp}], 0, 2*g[8, 0, {GGGG[4], pppmE}] + p2*g[9, 0, {GGGG[4], pppmE}], 8*g[6, 0, {GGGG[4], ppppE}] + 12*p2*g[7, 0, {GGGG[4], ppppE}] + 6*p2^2*g[8, 1, {GGGG[4], ppppE}] + p2^3*g[9, 1, {GGGG[4], ppppE}], 2*g[8, 0, {GGGG[4], pppmO}] + p2*g[9, 0, {GGGG[4], pppmO}], 8*g[6, 0, {GGGG[4], ppppO}] + 12*p2*g[7, 0, {GGGG[4], ppppO}] + 6*p2^2*g[8, 1, {GGGG[4], ppppO}] + p2^3*g[9, 1, {GGGG[4], ppppO}]} sumruleslow[bkimp[GGGG[4], 7]] = {-4*p2*g[8, 0, {GGGG[4], pmmp}] - 4*p2^2*g[9, 0, {GGGG[4], pmmp}] - 8*p2^3*g[10, 0, {GGGG[4], pmmp}] + 2*g[7, T, 0, {GGGG[4], pmmp}] + p2*g[8, T, 0, {GGGG[4], pmmp}]} sumrulesKK[bkimp[GGGG[4], 2], {GG[4], GG[4]}] = {exchange[{0}, {{{(2*m2 - p2)/2, 0}, {0, (2*m2 - p2)/2}}, {{0, 0}, {0, 0}}, {{0, 0}, {0, 0}}, {{(2*m2 + 3*p2)/2, 0}, {0, (-2*m2 - 3*p2)/2}}, {{0, 0}, {0, 0}}, {{0, (2*m2 + 3*p2)/2}, {(2*m2 + 3*p2)/2, 0}}}], exchange[{2}, {{{(2*m2^3 - 13*m2^2*p2 + 18*m2*p2^2 - 6*p2^3)/2, 0}, {0, (2*m2^3 - 13*m2^2*p2 + 18*m2*p2^2 - 6*p2^3)/2}}, {{-3/(m2 + p2), 0}, {0, -3/(m2 + p2)}}, {{0, 0}, {0, 0}}, {{-1/2*(m2^2*(-2*m2 + 9*p2 + (6*p2^2)/(m2 + p2))), 0}, {0, -1/2*(m2^2*(2*m2 - 9*p2 - (6*p2^2)/(m2 + p2)))}}, {{0, 0}, {0, 0}}, {{0, -1/2*(m2^2*(-2*m2 + 9*p2 + (6*p2^2)/(m2 + p2)))}, {-1/2*(m2^2*(-2*m2 + 9*p2 + (6*p2^2)/(m2 + p2))), 0}}}]} sumrulesKK[bkimp[GGGG[4], 3], {GG[4], GG[4]}] = {exchange[{0}, {{{1/2, 0}, {0, 1/2}}}], exchange[{2}, {{{(m2^2 - 6*m2*p2 + 6*p2^2)/2, 0}, {0, (m2^2 - 6*m2*p2 + 6*p2^2)/2}}}]} sumrulesKK[bkimp[GGGG[4], 4], {GG[4], GG[4]}] = {exchange[{0}, {{{0, 0}, {0, 0}}, {{0, 0}, {0, 0}}, {{0, 0}, {0, 0}}, {{0, 0}, {0, 0}}, {{0, 0}, {0, 0}}, {{0, 0}, {0, 0}}}], exchange[{2}, {{{-6*p2, 0}, {0, -6*p2}}, {{0, 0}, {0, 0}}, {{0, 0}, {0, 0}}, {{0, 0}, {0, 0}}, {{0, 0}, {0, 0}}, {{0, 0}, {0, 0}}}]} sumrulesKK[bkimp[GGGG[4], 5], {GG[4], GG[4]}] = {exchange[{0}, {{{0, 0}, {0, 0}}}], exchange[{2}, {{{0, 0}, {0, 0}}}]} sumrulesKK[bkimp[GGGG[4], 6], {GG[4], GG[4]}] = {exchange[{0}, {{{0, 0}, {0, 0}}, {{0, 0}, {0, 0}}, {{0, 0}, {0, 0}}, {{0, 0}, {0, 0}}, {{0, 0}, {0, 0}}, {{0, 0}, {0, 0}}}], exchange[{2}, {{{0, 0}, {0, 0}}, {{0, 0}, {0, 0}}, {{0, 0}, {0, 0}}, {{0, 0}, {0, 0}}, {{0, 0}, {0, 0}}, {{0, 0}, {0, 0}}}]} sumrulesKK[bkimp[GGGG[4], 7], {GG[4], GG[4]}] = {exchange[{0}, {{{0, 0}, {0, 0}}}], exchange[{2}, {{{0, 0}, {0, 0}}}]} ampKK[{GG[4], GG[4]}] = {exchange[{0}, {{{-1/2*1/(mh2^4*(-mh2 + t)), 0}, {0, -1/2*1/(mh2^4*(-mh2 + t))}}, {{-1/2*1/(mh2^4*(-mh2 - s - t)), 0}, {0, -1/2*1/(mh2^4*(-mh2 - s - t))}}, {{-1/2*1/(mh2^4*(-mh2 + s)), 0}, {0, -1/2*1/(mh2^4*(-mh2 + s))}}, {{-1/2*(s^4/(-mh2 + s) + (-s - t)^4/(-mh2 - s - t) + t^4/(-mh2 + t))/ mh2^4, 0}, {0, (s^4/(-mh2 + s) + (-s - t)^4/(-mh2 - s - t) + t^4/(-mh2 + t))/(2*mh2^4)}}, {{0, 0}, {0, 0}}, {{0, -1/2*(s^4/(-mh2 + s) + (-s - t)^4/(-mh2 - s - t) + t^4/(-mh2 + t))/ mh2^4}, {-1/2*(s^4/(-mh2 + s) + (-s - t)^4/(-mh2 - s - t) + t^4/(-mh2 + t))/mh2^4, 0}}, {{0, 0}, {0, 0}}}], exchange[{2}, {{{-1/2*(1 - (6*s*(-s - t))/mh2^2)/(mh2^4*(-mh2 + t)), 0}, {0, -1/2*(1 - (6*s*(-s - t))/mh2^2)/(mh2^4*(-mh2 + t))}}, {{-1/2*(1 - (6*s*t)/mh2^2)/(mh2^4*(-mh2 - s - t)), 0}, {0, -1/2*(1 - (6*s*t)/mh2^2)/(mh2^4*(-mh2 - s - t))}}, {{-1/2*(1 - (6*(-s - t)*t)/mh2^2)/(mh2^4*(-mh2 + s)), 0}, {0, -1/2*(1 - (6*(-s - t)*t)/mh2^2)/(mh2^4*(-mh2 + s))}}, {{-1/2*(((-s - t)^2*((-s - t)^2 - 6*s*t))/(-mh2 - s - t) + (s^2*(s^2 - 6*(-s - t)*t))/(-mh2 + s) + (t^2*(-6*s*(-s - t) + t^2))/(-mh2 + t))/mh2^4, 0}, {0, (((-s - t)^2*((-s - t)^2 - 6*s*t))/(-mh2 - s - t) + (s^2*(s^2 - 6*(-s - t)*t))/(-mh2 + s) + (t^2*(-6*s*(-s - t) + t^2))/ (-mh2 + t))/(2*mh2^4)}}, {{0, 0}, {0, 0}}, {{0, -1/2*(((-s - t)^2*((-s - t)^2 - 6*s*t))/(-mh2 - s - t) + (s^2*(s^2 - 6*(-s - t)*t))/(-mh2 + s) + (t^2*(-6*s*(-s - t) + t^2))/(-mh2 + t))/mh2^4}, {-1/2*(((-s - t)^2*((-s - t)^2 - 6*s*t))/(-mh2 - s - t) + (s^2*(s^2 - 6*(-s - t)*t))/(-mh2 + s) + (t^2*(-6*s*(-s - t) + t^2))/(-mh2 + t))/mh2^4, 0}}, {{0, 0}, {0, 0}}}]}