(* ::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}}}]}