* "The two-loop helicity amplitudes for qqb' -> V1V2 -> 4 leptons" * T. Gehrmann, A. von Manteuffel, L. Tancredi * * This file contains the definition of the integrands of the master * integrals M[] described in section 5.1 and 5.2 with respect to the * integral families given in the file "integralfamilies.yaml". * * Except for the "addon" integrals, the master integrals M[] coincide exactly * with the definitions of arXiv:1402.7078 and arXiv:1404.5590v2 * under the corresponding names. Note that we differ in the overall * normalisation from these references. In particular, we always use a * uniform integral measure for all of the M[] integrals irrespective of * the integral family they are associated to. * * We use the following definition of the Mandelstam variables: * s = (p1+p2)^2, t=(p1-p3)^2, u=(p2-p3)^2, p3^2=ma2, p4^2=mb2, * and root denotes the Kaellen function in eq. (2.5): * root = Sqrt( s^2 + ma2^2 + mb2^2 - 2 (s ma2 + ma2 mb2 + mb2 s) ). * id M(addon, 1) = + INT(PL1, 4, 387, 6, 0, [], 2, 2, 0, 0, 0, 0, 0, 1, 1) *(((-4 + d)^2*mb2^2)/4) ; id M(addon, 2) = + INT(PL1, 4, 480, 6, 0, [], 0, 0, 0, 0, 0, 2, 2, 1, 1) *(((-4 + d)^2*ma2^2)/4) ; id M(addon, 3) = + INT(PL1, 5, 419, 6, 0, [], 1, 2, 0, 0, 0, 1, 0, 1, 1) *(-((-4 + d)^3*mb2*root)/8) ; id M(addon, 4) = + INT(PL1, 5, 481, 6, 0, [], 1, 0, 0, 0, 0, 1, 2, 1, 1) *(-((-4 + d)^3*ma2*root)/8) ; id M(addon, 5) = + INT(PL1, 6, 427, 7, 0, [], 1, 2, 0, 1, 0, 1, 0, 1, 1) *(-((-4 + d)^3*mb2*s*(ma2 + mb2 - s - t))/8) ; id M(addon, 6) = + INT(PL1, 6, 489, 7, 0, [], 1, 0, 0, 1, 0, 1, 2, 1, 1) *(-((-4 + d)^3*ma2*s*(ma2 + mb2 - s - t))/8) ; id M(addon, 7) = + INT(PL2, 6, 249, 7, 0, [], 1, 0, 0, 1, 2, 1, 1, 1, 0) *(-((-4 + d)^3*ma2*(ma2*mb2 - ma2*t - mb2*t + s*t + t^2))/8) ; id M(addon, 8) = + INT(PL2, 6, 427, 7, 0, [], 1, 2, 0, 1, 0, 1, 0, 1, 1) *(-((-4 + d)^3*mb2*(ma2*mb2 - ma2*t - mb2*t + s*t + t^2))/8) ; id M(P12, 1) = + INT(PL1x12, 3, 148, 5, 0, [], 0, 0, 2, 0, 2, 0, 0, 1, 0) *(-((-4 + d)^2*t)/4) ; id M(P12, 2) = + INT(PL1, 3, 134, 5, 0, [], 0, 2, 2, 0, 0, 0, 0, 1, 0) *(-((-4 + d)^2*mb2)/4) ; id M(P12, 3) = + INT(PL1, 3, 196, 5, 0, [], 0, 0, 2, 0, 0, 0, 2, 1, 0) *(-((-4 + d)^2*ma2)/4) ; id M(P12, 4) = + INT(PL1, 3, 38, 5, 0, [], 0, 2, 2, 0, 0, 1, 0, 0, 0) *(-((-4 + d)^2*s)/4) ; id M(P12, 5) = + INT(PL1, 4, 198, 5, 0, [], 0, 1, 2, 0, 0, 0, 1, 1, 0) *(((-4 + d)^3*root)/8) ; id M(P12, 6) = + INT(PL1, 4, 198, 5, 0, [], 0, 1, 2, 0, 0, 0, 1, 1, 0) *(-((-4 + d)^3*(ma2 - mb2 - s))/16) + INT(PL1, 4, 198, 6, 1, [], 0, 1, 2, 0, 0, 0, 2, 1, -1) *(-((-4 + d)^2*s)/4) ; id M(P12, 7) = + INT(PL1x12, 4, 149, 5, 0, [], 1, 0, 1, 0, 2, 0, 0, 1, 0) *(((-4 + d)^3*(mb2 - t))/8) ; id M(P12, 8) = + INT(PL1, 4, 197, 5, 0, [], 1, 0, 1, 0, 0, 0, 2, 1, 0) *(((-4 + d)^3*root)/8) ; id M(P12, 9) = + INT(PL1, 4, 197, 5, 0, [], 1, 0, 1, 0, 0, 0, 2, 1, 0) *((3*(-4 + d)^3*(ma2 - mb2 + s))/16) + INT(PL1, 5, 229, 6, 0, [], 1, 0, 2, 0, 0, 1, 1, 1, 0) *(-((-6 + d)*(-4 + d)^2*ma2*s)/8) ; id M(P12, 10) = + INT(PL1, 4, 195, 6, 0, [], 2, 2, 0, 0, 0, 0, 1, 1, 0) *(((-4 + d)^2*mb2*s)/4) ; id M(P12, 11) = + INT(PL1x12, 4, 180, 5, 0, [], 0, 0, 2, 0, 1, 1, 0, 1, 0) *(((-4 + d)^3*(ma2 - t))/8) ; id M(P12, 12) = + INT(PL1, 4, 166, 5, 0, [], 0, 2, 1, 0, 0, 1, 0, 1, 0) *(((-4 + d)^3*root)/8) ; id M(P12, 13) = + INT(PL1, 4, 166, 5, 0, [], 0, 2, 1, 0, 0, 1, 0, 1, 0) *((-3*(-4 + d)^3*(ma2 - mb2 - s))/16) + INT(PL1, 5, 167, 6, 0, [], 1, 2, 1, 0, 0, 1, 0, 1, 0) *(-((-6 + d)*(-4 + d)^2*mb2*s)/8) ; id M(P12, 14) = + INT(PL1, 4, 226, 6, 0, [], 0, 2, 0, 0, 0, 2, 1, 1, 0) *(((-4 + d)^2*ma2*s)/4) ; id M(P12, 15) = + INT(PL1, 4, 53, 5, 0, [], 1, 0, 1, 0, 2, 1, 0, 0, 0) *(((-4 + d)^3*s)/8) ; id M(P12, 16) = + INT(PL1, 4, 99, 6, 0, [], 2, 2, 0, 0, 0, 1, 1, 0, 0) *(((-4 + d)^2*s^2)/4) ; id M(P12, 17) = + INT(PL1x12, 5, 214, 6, 0, [], 0, 1, 2, 0, 1, 0, 1, 1, 0) *(-((-4 + d)^3*s*t)/8) ; id M(P12, 18) = + INT(PL1x12, 5, 213, 5, 0, [], 1, 0, 1, 0, 1, 0, 1, 1, 0) *(-((-4 + d)^4*(ma2 - s - t))/16) ; id M(P12, 19) = + INT(PL1x12, 5, 213, 6, 0, [], 1, 0, 2, 0, 1, 0, 1, 1, 0) *(-((-4 + d)^3*s*t)/8) ; id M(P12, 20) = + INT(PL1, 5, 199, 5, 0, [], 1, 1, 1, 0, 0, 0, 1, 1, 0) *(-((-4 + d)^4*root)/16) ; id M(P12, 21) = + INT(PL1x12, 5, 182, 5, 0, [], 0, 1, 1, 0, 1, 1, 0, 1, 0) *(((-4 + d)^4*(mb2 - s - t))/16) ; id M(P12, 22) = + INT(PL1x12, 5, 182, 6, 0, [], 0, 1, 2, 0, 1, 1, 0, 1, 0) *(-((-4 + d)^3*s*t)/8) ; id M(P12, 23) = + INT(PL1, 5, 230, 5, 0, [], 0, 1, 1, 0, 0, 1, 1, 1, 0) *(-((-4 + d)^4*root)/16) ; id M(P12, 24) = + INT(PL1x12, 5, 181, 6, 0, [], 1, 0, 2, 0, 1, 1, 0, 1, 0) *(-((-4 + d)^3*s*t)/8) ; id M(P12, 25) = + INT(PL1x12, 5, 181, 6, 1, [], 1, 0, 2, -1, 1, 1, 0, 1, 0) *(((-4 + d)^3*root)/8) ; id M(P12, 26) = + INT(PL1, 5, 227, 6, 0, [], 1, 2, 0, 0, 0, 1, 1, 1, 0) *(-((-4 + d)^3*root*s)/8) ; id M(P12, 27) = + INT(PL1x12, 6, 215, 6, 0, [], 1, 1, 1, 0, 1, 0, 1, 1, 0) *(-((-4 + d)^4*s*(mb2 - t))/16) ; id M(P12, 28) = + INT(PL1x12, 6, 246, 6, 0, [], 0, 1, 1, 0, 1, 1, 1, 1, 0) *(-((-4 + d)^4*s*(ma2 - t))/16) ; id M(P12, 29) = + INT(PL1x12, 7, 247, 7, 0, [], 1, 1, 1, 0, 1, 1, 1, 1, 0) *(-((-4 + d)^4*s^2*t)/16) ; id M(P12, 30) = + INT(PL1x12, 5, 181, 6, 0, [], 1, 0, 2, 0, 1, 1, 0, 1, 0) *(-((-4 + d)^3*(ma2 + mb2)*s)/8) + INT(PL1x12, 5, 182, 6, 0, [], 0, 1, 2, 0, 1, 1, 0, 1, 0) *(((-4 + d)^3*mb2*s)/16) + INT(PL1x12, 5, 213, 6, 0, [], 1, 0, 2, 0, 1, 0, 1, 1, 0) *(((-4 + d)^3*ma2*s)/16) + INT(PL1x12, 7, 247, 7, 1, [], 1, 1, 1, 0, 1, 1, 1, 1, -1) *(((-4 + d)^4*s^2)/16) ; id M(P12, 31) = + INT(PL1x12, 7, 247, 7, 1, [], 1, 1, 1, -1, 1, 1, 1, 1, 0) *(((-4 + d)^4*root*s)/16) ; id M(P13, 7) = + INT(PL1x12, 4, 204, 5, 0, [], 0, 0, 1, 1, 0, 0, 2, 1, 0) *(((-4 + d)^3*(ma2 - t))/8) ; id M(P13, 12) = + INT(PL1, 4, 418, 6, 0, [], 0, 1, 0, 0, 0, 1, 0, 2, 2) *(((-4 + d)^2*ma2*mb2)/4) ; id M(P13, 13) = + INT(PL1x12, 4, 432, 6, 0, [], 0, 0, 0, 0, 1, 1, 0, 2, 2) *(((-4 + d)^2*ma2*t)/4) ; id M(P13, 14) = + INT(PL1x12, 4, 142, 5, 0, [], 0, 2, 1, 1, 0, 0, 0, 1, 0) *(((-4 + d)^3*(mb2 - t))/8) ; id M(P13, 15) = + INT(PL1x12, 4, 394, 6, 0, [], 0, 2, 0, 2, 0, 0, 0, 1, 1) *(((-4 + d)^2*mb2*t)/4) ; id M(P13, 16) = + INT(PL1x12, 4, 408, 6, 0, [], 0, 0, 0, 2, 2, 0, 0, 1, 1) *(((-4 + d)^2*t^2)/4) ; id M(P13, 17) = + INT(PL1x12, 5, 205, 6, 0, [], 1, 0, 2, 1, 0, 0, 1, 1, 0) *(-((-4 + d)^3*s*t)/8) ; id M(P13, 22) = + INT(PL1, 5, 422, 5, 0, [], 0, 1, 1, 0, 0, 1, 0, 1, 1) *(-((-4 + d)^4*root)/16) ; id M(P13, 23) = + INT(PL1x12, 5, 436, 5, 0, [], 0, 0, 1, 0, 1, 1, 0, 1, 1) *(-((-4 + d)^4*(ma2 - t))/16) ; id M(P13, 24) = + INT(PL1x12, 5, 174, 6, 0, [], 0, 2, 1, 1, 0, 1, 0, 1, 0) *(-((-4 + d)^3*s*t)/8) ; id M(P13, 25) = + INT(PL1x12, 5, 398, 5, 0, [], 0, 1, 1, 1, 0, 0, 0, 1, 1) *(-((-4 + d)^4*(mb2 - t))/16) ; id M(P13, 26) = + INT(PL1x12, 6, 438, 6, 0, [], 0, 1, 1, 0, 1, 1, 0, 1, 1) *(((-4 + d)^4*(ma2*mb2 - ma2*t + s*t))/16) ; id M(P13, 27) = + INT(PL1x12, 6, 430, 6, 0, [], 0, 1, 1, 1, 0, 1, 0, 1, 1) *(((-4 + d)^4*(ma2*mb2 - mb2*t + s*t))/16) ; id M(P13, 28) = + INT(PL1x12, 7, 446, 7, 0, [], 0, 1, 1, 1, 1, 1, 0, 1, 1) *(-((-4 + d)^4*s*t^2)/16) ; id M(P13, 29) = + INT(PL1x12, 6, 430, 6, 0, [], 0, 1, 1, 1, 0, 1, 0, 1, 1) *(((-4 + d)^4*(ma2 - mb2 + s)*t)/16) + INT(PL1x12, 7, 446, 7, 1, [], 0, 1, 1, 1, 1, 1, -1, 1, 1) *(((-4 + d)^4*(mb2 - t)*t)/16) ; id M(P23, 15) = + INT(PL2x12, 5, 174, 6, 0, [], 0, 1, 2, 1, 0, 1, 0, 1, 0) *(((-4 + d)^3*(ma2*mb2 - ma2*t - mb2*t + s*t + t^2))/4) ; id M(P23, 16) = + INT(PL2, 5, 213, 5, 0, [], 1, 0, 1, 0, 1, 0, 1, 1, 0) *(-((-4 + d)^4*root)/4) ; id M(P23, 17) = + INT(PL2, 5, 213, 6, 0, [], 1, 0, 2, 0, 1, 0, 1, 1, 0) *(((-4 + d)^3*(ma2*mb2 - ma2*t - mb2*t + s*t + t^2))/4) ; id M(P23, 18) = + INT(PL2, 5, 213, 6, 0, [], 2, 0, 1, 0, 1, 0, 1, 1, 0) *(((-4 + d)^3*mb2*(ma2 - t))/4) ; id M(P23, 19) = + INT(PL2, 5, 213, 6, 0, [], 1, 0, 1, 0, 1, 0, 2, 1, 0) *(((-4 + d)^3*ma2*(mb2 - t))/4) ; id M(P23, 20) = + INT(PL2, 5, 213, 6, 0, [], 1, 0, 1, 0, 2, 0, 1, 1, 0) *(-((-4 + d)^3*ma2*(ma2 - s - t))/4) ; id M(P23, 22) = + INT(PL2, 5, 182, 6, 0, [], 0, 1, 2, 0, 1, 1, 0, 1, 0) *(((-4 + d)^3*(ma2*mb2 - ma2*t - mb2*t + s*t + t^2))/4) ; id M(P23, 23) = + INT(PL2, 5, 181, 6, 0, [], 1, 0, 1, 0, 2, 1, 0, 1, 0) *(((-4 + d)^3*(ma2*mb2 - ma2*t - mb2*t + s*t + t^2))/4) ; id M(P23, 25) = + INT(PL2, 6, 215, 6, 0, [], 1, 1, 1, 0, 1, 0, 1, 1, 0) *(-((-4 + d)^4*(ma2 - s - t)*t)/4) ; id M(P23, 26) = + INT(PL2x12, 6, 221, 6, 0, [], 1, 0, 1, 1, 1, 0, 1, 1, 0) *(-((-4 + d)^4*(mb2 - s - t)*t)/4) ; id M(P23, 27) = + INT(PL2, 7, 247, 7, 0, [], 1, 1, 1, 0, 1, 1, 1, 1, 0) *(-((-4 + d)^4*t*(ma2*mb2 - ma2*t - mb2*t + s*t + t^2))/4) ; id M(P23, 28) = + INT(PL2, 5, 181, 6, 0, [], 1, 0, 1, 0, 2, 1, 0, 1, 0) *(((-4 + d)^3*mb2*(ma2 - t))/2) + INT(PL2, 5, 182, 6, 0, [], 0, 1, 2, 0, 1, 1, 0, 1, 0) *(-((-4 + d)^3*mb2*(ma2 - t))/4) + INT(PL2, 7, 247, 7, 1, [], 1, 1, 1, 0, 1, 1, 1, 1, -1) *(-((-4 + d)^4*(ma2 - t)*t)/4) ; id M(N12, 28) = + INT(NPL, 6, 318, 6, 0, [], 0, 1, 1, 1, 1, 1, 0, 0, 1) *(((-4 + d)^4*s^2)/16) ; id M(N12, 29) = + INT(NPL, 6, 378, 6, 0, [], 0, 1, 0, 1, 1, 1, 1, 0, 1) *(((-4 + d)^4*mb2*s)/16) ; id M(N12, 30) = + INT(NPL, 6, 378, 6, 0, [], 0, 1, 0, 1, 1, 1, 1, 0, 1) *(-((-4 + d)^4*s*(mb2 - t))/16) + INT(NPL, 6, 378, 6, 1, [], -1, 1, 0, 1, 1, 1, 1, 0, 1) *(((-4 + d)^4*(mb2 - t))/16) + INT(PL1, 3, 134, 5, 0, [], 0, 2, 2, 0, 0, 0, 0, 1, 0) *(((-4 + d)^2*mb2*(mb2 - t))/(16*(-ma2 + s + t))) + INT(PL1, 3, 148, 5, 0, [], 0, 0, 2, 0, 2, 0, 0, 1, 0) *(-((-4 + d)^2*(ma2 + mb2 - s - t)*(ma2 - 2*mb2 - s + t))/(32*(ma2 - s - t))) + INT(PL1, 3, 196, 5, 0, [], 0, 0, 2, 0, 0, 0, 2, 1, 0) *(((-4 + d)^2*ma2)/16) + INT(PL1, 4, 149, 5, 0, [], 1, 0, 1, 0, 2, 0, 0, 1, 0) *(-((-4 + d)^3*(ma2 + 2*mb2 - s - 3*t))/16) + INT(PL1, 5, 213, 5, 0, [], 1, 0, 1, 0, 1, 0, 1, 1, 0) *(-((-4 + d)^4*(mb2 - t))/32) + INT(PL1, 5, 213, 6, 0, [], 1, 0, 2, 0, 1, 0, 1, 1, 0) *(-((-4 + d)^3*s*(-ma2 - mb2 + s + t))/32) + INT(PL1x12, 3, 148, 5, 0, [], 0, 0, 2, 0, 2, 0, 0, 1, 0) *(-((-4 + d)^2*t)/32) + INT(PL1x12, 4, 149, 5, 0, [], 1, 0, 1, 0, 2, 0, 0, 1, 0) *(((-4 + d)^3*(mb2 - t))/16) + INT(PL1x12, 5, 213, 5, 0, [], 1, 0, 1, 0, 1, 0, 1, 1, 0) *(((-4 + d)^4*(ma2 - s - t))/32) + INT(PL1x12, 5, 213, 6, 0, [], 1, 0, 2, 0, 1, 0, 1, 1, 0) *(-((-4 + d)^3*s*t)/32) + INT(PL2, 5, 182, 6, 0, [], 0, 1, 2, 0, 1, 1, 0, 1, 0) *(-((-4 + d)^3*(ma2*mb2 - ma2*t - mb2*t + s*t + t^2))/48) ; id M(N12, 31) = + INT(NPL, 6, 126, 6, 0, [], 0, 1, 1, 1, 1, 1, 1, 0, 0) *(((-4 + d)^4*ma2*s)/16) ; id M(N12, 32) = + INT(NPL, 6, 126, 6, 1, [], -1, 1, 1, 1, 1, 1, 1, 0, 0) *(((-4 + d)^4*(mb2 - s - t))/16) + INT(PL1, 3, 134, 5, 0, [], 0, 2, 2, 0, 0, 0, 0, 1, 0) *(((-4 + d)^2*mb2)/16) + INT(PL1, 4, 180, 5, 0, [], 0, 0, 2, 0, 1, 1, 0, 1, 0) *(-((-4 + d)^3*(mb2 - s - t))/8) + INT(PL1, 5, 182, 5, 0, [], 0, 1, 1, 0, 1, 1, 0, 1, 0) *(-((-4 + d)^4*(mb2 - s - t))/16) + INT(PL1x12, 3, 148, 5, 0, [], 0, 0, 2, 0, 2, 0, 0, 1, 0) *(-((-4 + d)^2*t)/16) + INT(PL1x12, 5, 182, 5, 0, [], 0, 1, 1, 0, 1, 1, 0, 1, 0) *(((-4 + d)^4*(mb2 - s - t))/16) + INT(PL2, 5, 182, 6, 0, [], 0, 1, 2, 0, 1, 1, 0, 1, 0) *(-((-4 + d)^3*(ma2*mb2 - ma2*t - mb2*t + s*t + t^2))/48) ; id M(N12, 33) = + INT(NPL, 6, 126, 6, 0, [], 0, 1, 1, 1, 1, 1, 1, 0, 0) *(-((-4 + d)^4*s*t*(-mb2 + s + t))/(16*(-ma2 + mb2 + s))) + INT(NPL, 6, 318, 6, 0, [], 0, 1, 1, 1, 1, 1, 0, 0, 1) *(((-4 + d)^4*s^2*t)/(16*(-ma2 + mb2 + s))) + INT(NPL, 6, 378, 6, 0, [], 0, 1, 0, 1, 1, 1, 1, 0, 1) *(((-4 + d)^4*s*(ma2 - s - t)*t)/(16*(ma2 - mb2 - s))) + INT(NPL, 7, 382, 7, 0, [], 0, 1, 1, 1, 1, 1, 1, 0, 1) *(-((-4 + d)^4*s^2*(ma2 + mb2 - s - t)*t)/(16*(ma2 - mb2 - s))) + INT(NPL, 7, 382, 7, 1, [], 0, 1, 1, 1, 1, 1, 1, -1, 1) *(-((-4 + d)^4*s^2*t)/(8*(-ma2 + mb2 + s))) + INT(PL1, 5, 181, 6, 0, [], 1, 0, 2, 0, 1, 1, 0, 1, 0) *(-((-4 + d)^3*(ma2 - mb2)*s*t)/(4*(ma2 - mb2 - s))) + INT(PL1, 5, 182, 6, 0, [], 0, 1, 2, 0, 1, 1, 0, 1, 0) *(((-4 + d)^3*s*(ma2 - s - t)*t)/(8*(ma2 - mb2 - s))) + INT(PL1, 5, 213, 6, 0, [], 1, 0, 2, 0, 1, 0, 1, 1, 0) *(-((-4 + d)^3*s*t*(-mb2 + s + t))/(8*(-ma2 + mb2 + s))) + INT(PL1x12, 5, 181, 6, 0, [], 1, 0, 2, 0, 1, 1, 0, 1, 0) *(((-4 + d)^3*s*t)/4) + INT(PL1x12, 5, 182, 6, 0, [], 0, 1, 2, 0, 1, 1, 0, 1, 0) *(-((-4 + d)^3*s*(mb2 - t)*t)/(8*(-ma2 + mb2 + s))) + INT(PL1x12, 5, 213, 6, 0, [], 1, 0, 2, 0, 1, 0, 1, 1, 0) *(-((-4 + d)^3*s*(ma2 - s - t)*t)/(8*(ma2 - mb2 - s))) ; id M(N12, 34) = + INT(NPL, 6, 126, 6, 0, [], 0, 1, 1, 1, 1, 1, 1, 0, 0) *(-((-4 + d)^4*s*(ma2 - 2*s - t)*(ma2 + mb2 - s - t))/(16*(ma2 - mb2 - s))) + INT(NPL, 6, 318, 6, 0, [], 0, 1, 1, 1, 1, 1, 0, 0, 1) *(-((-4 + d)^4*s^2*(ma2 + mb2 - s - t))/(16*(ma2 - mb2 - s))) + INT(NPL, 6, 378, 6, 0, [], 0, 1, 0, 1, 1, 1, 1, 0, 1) *(((-4 + d)^4*s*(mb2 - t)*(ma2 + mb2 - s - t))/(16*(ma2 - mb2 - s))) + INT(NPL, 7, 382, 7, 0, [], 0, 1, 1, 1, 1, 1, 1, 0, 1) *(-((-4 + d)^4*s^2*(2*mb2 - t)*(ma2 + mb2 - s - t))/(16*(ma2 - mb2 - s))) + INT(NPL, 7, 382, 7, 1, [], 0, 1, 1, 1, 1, 1, 1, -1, 1) *(((-4 + d)^4*s^2*(ma2 + mb2 - s - t))/(8*(ma2 - mb2 - s))) + INT(PL1, 5, 181, 6, 0, [], 1, 0, 2, 0, 1, 1, 0, 1, 0) *(-((-4 + d)^3*(ma2 - mb2)*s*(ma2 + mb2 - s - t))/(4*(ma2 - mb2 - s))) + INT(PL1, 5, 182, 6, 0, [], 0, 1, 2, 0, 1, 1, 0, 1, 0) *(((-4 + d)^3*s*(ma2 - s - t)*(ma2 + mb2 - s - t))/(8*(ma2 - mb2 - s))) + INT(PL1, 5, 213, 6, 0, [], 1, 0, 2, 0, 1, 0, 1, 1, 0) *(-((-4 + d)^3*s*(mb2 - s - t)*(ma2 + mb2 - s - t))/(8*(ma2 - mb2 - s))) + INT(PL1x12, 5, 181, 6, 0, [], 1, 0, 2, 0, 1, 1, 0, 1, 0) *(-((-4 + d)^3*s*(-ma2 - mb2 + s + t))/4) + INT(PL1x12, 5, 182, 6, 0, [], 0, 1, 2, 0, 1, 1, 0, 1, 0) *(((-4 + d)^3*s*(mb2 - t)*(ma2 + mb2 - s - t))/(8*(ma2 - mb2 - s))) + INT(PL1x12, 5, 213, 6, 0, [], 1, 0, 2, 0, 1, 0, 1, 1, 0) *(-((-4 + d)^3*s*(ma2 - s - t)*(ma2 + mb2 - s - t))/(8*(ma2 - mb2 - s))) ; id M(N12, 35) = + INT(NPL, 6, 126, 6, 0, [], 0, 1, 1, 1, 1, 1, 1, 0, 0) *(-((-4 + d)^4*root*s*(ma2 - 2*s - t))/(16*(ma2 - mb2 - s))) + INT(NPL, 6, 126, 6, 1, [], -1, 1, 1, 1, 1, 1, 1, 0, 0) *(-((-4 + d)^4*root)/16) + INT(NPL, 6, 318, 6, 0, [], 0, 1, 1, 1, 1, 1, 0, 0, 1) *(((-4 + d)^4*root*s^2)/(16*(-ma2 + mb2 + s))) + INT(NPL, 6, 378, 6, 0, [], 0, 1, 0, 1, 1, 1, 1, 0, 1) *(-((-4 + d)^4*root*s*(mb2 - t))/(16*(-ma2 + mb2 + s))) + INT(NPL, 6, 378, 6, 1, [], -1, 1, 0, 1, 1, 1, 1, 0, 1) *(((-4 + d)^4*root)/16) + INT(NPL, 7, 382, 7, 0, [], 0, 1, 1, 1, 1, 1, 1, 0, 1) *(((-4 + d)^4*root*s^2*(2*mb2 - t))/(16*(-ma2 + mb2 + s))) + INT(NPL, 7, 382, 7, 1, [], 0, 1, 1, 1, 1, 1, 1, -1, 1) *(-((-4 + d)^4*root*s^2)/(8*(-ma2 + mb2 + s))) + INT(NPL, 7, 382, 7, 2, [], -2, 1, 1, 1, 1, 1, 1, 0, 1) *(-((-4 + d)^4*root)/16) + INT(PL1, 3, 38, 5, 0, [], 0, 2, 2, 0, 0, 1, 0, 0, 0) *((-3*(-4 + d)^3*root*s*(-mb2^2 - ma2*s + mb2*s + s^2 + 2*mb2*t - t^2))/(64*(-3 + d)*(mb2 - t)*(-ma2 + s + t)*(-mb2 + s + t))) + INT(PL1, 3, 134, 5, 0, [], 0, 2, 2, 0, 0, 0, 0, 1, 0) *(((-4 + d)^3*mb2*root*(-ma2 + mb2 + s))/(64*(-3 + d)*(mb2 - t)*(ma2 - s - t))) + INT(PL1, 3, 148, 5, 0, [], 0, 0, 2, 0, 2, 0, 0, 1, 0) *(-((-4 + d)^3*root*(ma2 + mb2 - 2*s - 2*t)*(ma2 + mb2 - s - t))/(64*(-3 + d)*(ma2 - s - t)*(mb2 - s - t))) + INT(PL1, 3, 196, 5, 0, [], 0, 0, 2, 0, 0, 0, 2, 1, 0) *(((-4 + d)^3*ma2*root)/(64*(-3 + d)*(mb2 - s - t))) + INT(PL1, 4, 149, 5, 0, [], 1, 0, 1, 0, 2, 0, 0, 1, 0) *(((-4 + d)^4*root*(3*ma2 - 2*mb2 - s - t))/(32*(-3 + d)*(mb2 - s - t))) + INT(PL1, 4, 166, 5, 0, [], 0, 2, 1, 0, 0, 1, 0, 1, 0) *(((-4 + d)^3*root*(-12*ma2^2 + 3*d*ma2^2 + 2*d*ma2*mb2 - 12*mb2^2 + 3*d*mb2^2 + 24*ma2*s - 6*d*ma2*s - 2*d*mb2*s - 12*s^2 + 3*d*s^2 + 24*ma2*t - 8*d*ma2*t + 24*mb2*t - 8*d*mb2*t - 24*s*t + 8*d*s*t - 24*t^2 + 8*d*t^2))/(32*(-3 + d)*(mb2 - t)*(-ma2 + s + t))) + INT(PL1, 4, 180, 5, 0, [], 0, 0, 2, 0, 1, 1, 0, 1, 0) *(-((-4 + d)^4*root*(2*ma2 - 3*mb2 + s + t))/(32*(-3 + d)*(ma2 - s - t))) + INT(PL1, 4, 197, 5, 0, [], 1, 0, 1, 0, 0, 0, 2, 1, 0) *(-((-4 + d)^3*root*(-12*ma2 + 3*d*ma2 - 8*mb2 + 3*d*mb2 + 8*s - 3*d*s + 20*t - 6*d*t))/(32*(-3 + d)*(mb2 - s - t))) + INT(PL1, 5, 167, 6, 0, [], 1, 2, 1, 0, 0, 1, 0, 1, 0) *(-((-6 + d)*(-4 + d)^3*mb2*root*s*(-ma2 + mb2 + s))/(16*(-3 + d)*(mb2 - t)*(-ma2 + s + t))) + INT(PL1, 5, 181, 6, 0, [], 1, 0, 2, 0, 1, 1, 0, 1, 0) *(((-4 + d)^3*root*s*(-4*ma2 + d*ma2 + 4*mb2 - d*mb2 + 7*s - 2*d*s))/(4*(-3 + d)*(ma2 - mb2 - s))) + INT(PL1, 5, 181, 6, 1, [], 1, 0, 2, -1, 1, 1, 0, 1, 0) *(((-4 + d)^3*root)/4) + INT(PL1, 5, 182, 5, 0, [], 0, 1, 1, 0, 1, 1, 0, 1, 0) *(-((-4 + d)^5*root*(ma2 - 4*s - t))/(64*(-3 + d)*(ma2 - s - t))) + INT(PL1, 5, 182, 6, 0, [], 0, 1, 2, 0, 1, 1, 0, 1, 0) *(((-4 + d)^3*root*s*(d*ma2^2 - 28*ma2*mb2 + 8*d*ma2*mb2 + 4*mb2^2 - d*mb2^2 - 2*d*ma2*s + 28*mb2*s - 8*d*mb2*s + d*s^2 + 24*ma2*t - 9*d*ma2*t + 24*mb2*t - 7*d*mb2*t - 24*s*t + 9*d*s*t - 24*t^2 + 8*d*t^2))/(64*(-3 + d)*(ma2 - mb2 - s)*(ma2 - s - t))) + INT(PL1, 5, 213, 5, 0, [], 1, 0, 1, 0, 1, 0, 1, 1, 0) *(-((-4 + d)^5*root*(mb2 - 4*s - t))/(64*(-3 + d)*(mb2 - s - t))) + INT(PL1, 5, 213, 6, 0, [], 1, 0, 2, 0, 1, 0, 1, 1, 0) *(((-4 + d)^3*root*s*(-4*ma2^2 + d*ma2^2 + 28*ma2*mb2 - 8*d*ma2*mb2 - d*mb2^2 - 20*ma2*s + 6*d*ma2*s - 48*mb2*s + 16*d*mb2*s + 48*s^2 - 15*d*s^2 - 24*ma2*t + 7*d*ma2*t - 24*mb2*t + 9*d*mb2*t + 72*s*t - 23*d*s*t + 24*t^2 - 8*d*t^2))/(64*(-3 + d)*(ma2 - mb2 - s)*(mb2 - s - t))) + INT(PL1, 5, 229, 6, 0, [], 1, 0, 2, 0, 0, 1, 1, 1, 0) *(-((-6 + d)*(-4 + d)^3*ma2*root*s)/(16*(-3 + d)*(-mb2 + s + t))) + INT(PL1x12, 3, 148, 5, 0, [], 0, 0, 2, 0, 2, 0, 0, 1, 0) *(((-4 + d)^3*root*t)/(64*(-3 + d)*(mb2 - t))) + INT(PL1x12, 4, 149, 5, 0, [], 1, 0, 1, 0, 2, 0, 0, 1, 0) *(-((-4 + d)^4*root)/(16*(-3 + d))) + INT(PL1x12, 4, 180, 5, 0, [], 0, 0, 2, 0, 1, 1, 0, 1, 0) *((-3*(-4 + d)^4*root*(ma2 - t))/(32*(-3 + d)*(-mb2 + t))) + INT(PL1x12, 5, 181, 6, 0, [], 1, 0, 2, 0, 1, 1, 0, 1, 0) *(((-4 + d)^3*(-7 + 2*d)*root*s)/(8*(-3 + d))) + INT(PL1x12, 5, 181, 6, 1, [], 1, 0, 2, -1, 1, 1, 0, 1, 0) *(((-4 + d)^3*(-10 + 3*d)*root)/(16*(-3 + d))) + INT(PL1x12, 5, 182, 5, 0, [], 0, 1, 1, 0, 1, 1, 0, 1, 0) *(-((-4 + d)^5*root*(mb2 + 3*s - t))/(64*(-3 + d)*(mb2 - t))) + INT(PL1x12, 5, 182, 6, 0, [], 0, 1, 2, 0, 1, 1, 0, 1, 0) *(-((-4 + d)^3*root*s*(-4*ma2*mb2 + 28*mb2^2 - 8*d*mb2^2 + 4*mb2*s + d*ma2*t - 48*mb2*t + 15*d*mb2*t - d*s*t + 24*t^2 - 8*d*t^2))/(64*(-3 + d)*(ma2 - mb2 - s)*(mb2 - t))) + INT(PL1x12, 5, 213, 6, 0, [], 1, 0, 2, 0, 1, 0, 1, 1, 0) *(-((-4 + d)^3*root*s*(ma2 - s - t))/(8*(ma2 - mb2 - s))) ; id M(N13, 35) = + INT(NPL, 6, 207, 6, 0, [], 1, 1, 1, 1, 0, 0, 1, 1, 0) *(-((-4 + d)^4*(ma2^2 - ma2*mb2 - ma2*s - ma2*t + mb2*t))/16) ; id M(N13, 36) = + INT(NPL, 6, 207, 6, 1, [], 1, 1, 1, 1, -1, 0, 1, 1, 0) *(-((-4 + d)^4*root)/16) + INT(PL1, 5, 182, 5, 0, [], 0, 1, 1, 0, 1, 1, 0, 1, 0) *(((-4 + d)^4*root)/16) ; id M(N13, 37) = + INT(NPL, 6, 207, 6, 0, [], 1, 1, 1, 1, 0, 0, 1, 1, 0) *(-((-4 + d)^4*(ma2 - mb2 - s)*(ma2 - t))/16) + INT(NPL, 6, 207, 6, 1, [], 1, 1, 1, 1, 0, 0, 1, 1, -1) *(-((-4 + d)^4*(ma2 - t))/16) + INT(PL1, 3, 134, 5, 0, [], 0, 2, 2, 0, 0, 0, 0, 1, 0) *(((-4 + d)^2*mb2*(ma2 - t))/(16*(ma2 - s - t))) + INT(PL1, 3, 148, 5, 0, [], 0, 0, 2, 0, 2, 0, 0, 1, 0) *(-((-4 + d)^2*(ma2 - t)*(ma2 + mb2 - s - t))/(16*(ma2 - s - t))) + INT(PL1, 4, 149, 5, 0, [], 1, 0, 1, 0, 2, 0, 0, 1, 0) *(((-4 + d)^3*(ma2 - t))/8) + INT(PL1x12, 5, 213, 5, 0, [], 1, 0, 1, 0, 1, 0, 1, 1, 0) *(((-4 + d)^4*(ma2 - s - t))/16) ; id M(N13, 38) = + INT(NPL, 6, 207, 6, 0, [], 1, 1, 1, 1, 0, 0, 1, 1, 0) *(((-4 + d)^4*(ma2 - mb2)*(ma2 - s - t))/16) + INT(NPL, 6, 207, 6, 1, [], 1, 1, 1, 1, 0, -1, 1, 1, 0) *(-((-4 + d)^4*(ma2 - s - t))/16) + INT(NPL, 6, 207, 6, 1, [], 1, 1, 1, 1, 0, 0, 1, 1, -1) *(((-4 + d)^4*(ma2 - s - t))/16) + INT(PL1, 3, 196, 5, 0, [], 0, 0, 2, 0, 0, 0, 2, 1, 0) *(-((-4 + d)^2*ma2*(ma2 - s - t))/(16*(ma2 - t))) + INT(PL1, 5, 182, 5, 0, [], 0, 1, 1, 0, 1, 1, 0, 1, 0) *(((-4 + d)^4*s)/16) + INT(PL1x12, 3, 148, 5, 0, [], 0, 0, 2, 0, 2, 0, 0, 1, 0) *(((-4 + d)^2*(ma2 - s - t)*t)/(16*(ma2 - t))) + INT(PL1x12, 4, 180, 5, 0, [], 0, 0, 2, 0, 1, 1, 0, 1, 0) *(((-4 + d)^3*(ma2 - s - t))/8) + INT(PL1x12, 5, 213, 5, 0, [], 1, 0, 1, 0, 1, 0, 1, 1, 0) *(-((-4 + d)^4*(ma2 - s - t))/16) + INT(PL2, 5, 213, 5, 0, [], 1, 0, 1, 0, 1, 0, 1, 1, 0) *(((-4 + d)^4*(ma2 - s - t))/16) ; id M(N13, 40) = + INT(NPLx12, 6, 252, 6, 0, [], 0, 0, 1, 1, 1, 1, 1, 1, 0) *(((-4 + d)^4*(ma2 - t)^2)/16) ; id M(N13, 42) = + INT(NPL, 6, 126, 6, 0, [], 0, 1, 1, 1, 1, 1, 1, 0, 0) *(-((-4 + d)^4*s*t*(-mb2 + s + t))/(16*(mb2 - t))) + INT(NPL, 6, 126, 6, 1, [], -1, 1, 1, 1, 1, 1, 1, 0, 0) *(-((-4 + d)^4*s*t*(-mb2 + s + t))/(4*(ma2 - t)*(-mb2 + t))) + INT(NPL, 6, 207, 6, 0, [], 1, 1, 1, 1, 0, 0, 1, 1, 0) *(-((-4 + d)^4*s*t*(-3*ma2 + 2*mb2 + 3*s + t))/(16*(mb2 - t))) + INT(NPL, 6, 207, 6, 1, [], 1, 1, 1, 1, 0, 0, 1, 1, -1) *(-((-4 + d)^4*s*t)/(4*(-mb2 + t))) + INT(NPLx12, 6, 252, 6, 0, [], 0, 0, 1, 1, 1, 1, 1, 1, 0) *(((-4 + d)^4*s*(ma2 - t)*t)/(16*(-mb2 + t))) + INT(NPLx12, 7, 254, 7, 0, [], 0, 1, 1, 1, 1, 1, 1, 1, 0) *(((-4 + d)^4*s*t*(ma2*mb2 - ma2*t - mb2*t + s*t + t^2))/(16*(mb2 - t))) + INT(NPLx12, 7, 254, 7, 1, [], -1, 1, 1, 1, 1, 1, 1, 1, 0) *(((-4 + d)^4*s*t^2)/(8*(-mb2 + t))) + INT(PL1, 3, 38, 5, 0, [], 0, 2, 2, 0, 0, 1, 0, 0, 0) *((-3*(-4 + d)^2*s^2*t)/(16*(ma2 - t)*(-mb2 + t))) + INT(PL1, 3, 134, 5, 0, [], 0, 2, 2, 0, 0, 0, 0, 1, 0) *(((-4 + d)^2*mb2*s*t)/(4*(mb2 - t)*(-ma2 + s + t))) + INT(PL1, 3, 148, 5, 0, [], 0, 0, 2, 0, 2, 0, 0, 1, 0) *(-((-4 + d)^2*s*(ma2 + s - t)*t*(-ma2 - mb2 + s + t))/(8*(ma2 - t)*(-mb2 + t)*(-ma2 + s + t))) + INT(PL1, 3, 196, 5, 0, [], 0, 0, 2, 0, 0, 0, 2, 1, 0) *((3*(-4 + d)^2*ma2*s*t)/(16*(ma2 - t)*(-mb2 + t))) + INT(PL1, 4, 149, 5, 0, [], 1, 0, 1, 0, 2, 0, 0, 1, 0) *(((-4 + d)^3*s*t)/(2*(-mb2 + t))) + INT(PL1, 4, 180, 5, 0, [], 0, 0, 2, 0, 1, 1, 0, 1, 0) *(((-4 + d)^3*s*t*(-mb2 + s + t))/(4*(ma2 - t)*(-mb2 + t))) + INT(PL1, 4, 197, 5, 0, [], 1, 0, 1, 0, 0, 0, 2, 1, 0) *((-3*(-4 + d)^3*s*(ma2 - mb2 + s)*t)/(8*(ma2 - t)*(mb2 - t))) + INT(PL1, 5, 182, 5, 0, [], 0, 1, 1, 0, 1, 1, 0, 1, 0) *(((-4 + d)^4*s*t*(ma2 - 2*mb2 + 2*s + t))/(8*(ma2 - t)*(-mb2 + t))) + INT(PL1, 5, 182, 6, 0, [], 0, 1, 2, 0, 1, 1, 0, 1, 0) *(((-4 + d)^3*s^2*t*(-ma2 - mb2 + s + t))/(8*(ma2 - t)*(-mb2 + t))) + INT(PL1, 5, 229, 6, 0, [], 1, 0, 2, 0, 0, 1, 1, 1, 0) *(-((-6 + d)*(-4 + d)^2*ma2*s^2*t)/(4*(ma2 - t)*(-mb2 + t))) + INT(PL1x12, 3, 148, 5, 0, [], 0, 0, 2, 0, 2, 0, 0, 1, 0) *((-5*(-4 + d)^2*s*t^2)/(16*(ma2 - t)*(-mb2 + t))) + INT(PL1x12, 4, 149, 5, 0, [], 1, 0, 1, 0, 2, 0, 0, 1, 0) *((-3*(-4 + d)^3*s*t)/(8*(ma2 - t))) + INT(PL1x12, 4, 180, 5, 0, [], 0, 0, 2, 0, 1, 1, 0, 1, 0) *((-3*(-4 + d)^3*s*t)/(4*(-mb2 + t))) + INT(PL1x12, 4, 204, 5, 0, [], 0, 0, 1, 1, 0, 0, 2, 1, 0) *(-((-4 + d)^3*s*t)/(2*(-mb2 + t))) + INT(PL1x12, 5, 182, 5, 0, [], 0, 1, 1, 0, 1, 1, 0, 1, 0) *(-((-4 + d)^4*s*t*(-mb2 + s + t))/(8*(mb2 - t)*(-ma2 + t))) + INT(PL1x12, 5, 182, 6, 0, [], 0, 1, 2, 0, 1, 1, 0, 1, 0) *(-((-4 + d)^3*s^2*t^2)/(8*(-ma2 + t)*(-mb2 + t))) + INT(PL1x12, 5, 213, 5, 0, [], 1, 0, 1, 0, 1, 0, 1, 1, 0) *((-3*(-4 + d)^4*s*t*(-ma2 + s + t))/(16*(ma2 - t)*(-mb2 + t))) + INT(PL1x12, 5, 213, 6, 0, [], 1, 0, 2, 0, 1, 0, 1, 1, 0) *(-((-4 + d)^3*s^2*t^2)/(16*(ma2 - t)*(-mb2 + t))) + INT(PL1x12, 5, 436, 5, 0, [], 0, 0, 1, 0, 1, 1, 0, 1, 1) *(((-4 + d)^4*s*t)/(4*(-mb2 + t))) + INT(PL1x12, 6, 438, 6, 0, [], 0, 1, 1, 0, 1, 1, 0, 1, 1) *(((-4 + d)^4*mb2*s*t)/(8*(mb2 - t))) + INT(PL2, 5, 181, 6, 0, [], 1, 0, 1, 0, 2, 1, 0, 1, 0) *(-((-4 + d)^3*s*t)/4) + INT(PL2, 5, 182, 6, 0, [], 0, 1, 2, 0, 1, 1, 0, 1, 0) *(((-4 + d)^3*s*t)/8) + INT(PL2, 5, 213, 6, 0, [], 2, 0, 1, 0, 1, 0, 1, 1, 0) *(-((-4 + d)^3*mb2*s*t)/(4*(mb2 - t))) ; id M(N13, 43) = + INT(NPL, 6, 126, 6, 0, [], 0, 1, 1, 1, 1, 1, 1, 0, 0) *(((-4 + d)^4*s*(ma2*mb2 - ma2*t - mb2*t + s*t + t^2))/(16*(mb2 - t))) + INT(NPL, 6, 126, 6, 1, [], -1, 1, 1, 1, 1, 1, 1, 0, 0) *(-((-4 + d)^4*(-mb2 + s + t)*(-(ma2*mb2) + ma2*t + mb2*t - s*t - t^2))/(4*(ma2 - t)*(-mb2 + t))) + INT(NPL, 6, 207, 6, 0, [], 1, 1, 1, 1, 0, 0, 1, 1, 0) *((-3*(-4 + d)^4*(ma2 - mb2 - s)*(ma2*mb2 - ma2*t - mb2*t + s*t + t^2))/(16*(mb2 - t))) + INT(NPL, 6, 207, 6, 1, [], 1, 1, 1, 1, 0, 0, 1, 1, -1) *(((-4 + d)^4*(-(ma2*mb2) + ma2*t + mb2*t - s*t - t^2))/(4*(mb2 - t))) + INT(NPLx12, 6, 252, 6, 0, [], 0, 0, 1, 1, 1, 1, 1, 1, 0) *(((-4 + d)^4*(ma2 - t)*(-(ma2*mb2) + ma2*t + mb2*t - s*t - t^2))/(16*(-mb2 + t))) + INT(NPLx12, 7, 254, 7, 0, [], 0, 1, 1, 1, 1, 1, 1, 1, 0) *(-((-4 + d)^4*s*t*(ma2*mb2 - ma2*t - mb2*t + s*t + t^2))/(16*(mb2 - t))) + INT(NPLx12, 7, 254, 7, 1, [], -1, 1, 1, 1, 1, 1, 1, 1, 0) *(-((-4 + d)^4*t*(-(ma2*mb2) + ma2*t + mb2*t - s*t - t^2))/(8*(mb2 - t))) + INT(PL1, 3, 38, 5, 0, [], 0, 2, 2, 0, 0, 1, 0, 0, 0) *((3*(-4 + d)^2*s*(ma2*mb2 - ma2*t - mb2*t + s*t + t^2))/(16*(ma2 - t)*(-mb2 + t))) + INT(PL1, 3, 134, 5, 0, [], 0, 2, 2, 0, 0, 0, 0, 1, 0) *(((-4 + d)^2*mb2*(-(ma2*mb2) + ma2*t + mb2*t - s*t - t^2))/(4*(mb2 - t)*(-ma2 + s + t))) + INT(PL1, 3, 148, 5, 0, [], 0, 0, 2, 0, 2, 0, 0, 1, 0) *(-((-4 + d)^2*(ma2 + mb2 - s - t)*(ma2 + s - t)*(-(ma2*mb2) + ma2*t + mb2*t - s*t - t^2))/(8*(ma2 - t)*(ma2 - s - t)*(-mb2 + t))) + INT(PL1, 3, 196, 5, 0, [], 0, 0, 2, 0, 0, 0, 2, 1, 0) *((3*(-4 + d)^2*ma2*(-(ma2*mb2) + ma2*t + mb2*t - s*t - t^2))/(16*(ma2 - t)*(-mb2 + t))) + INT(PL1, 4, 149, 5, 0, [], 1, 0, 1, 0, 2, 0, 0, 1, 0) *(-((-4 + d)^3*(-(ma2*mb2) + ma2*t + mb2*t - s*t - t^2))/(2*(mb2 - t))) + INT(PL1, 4, 180, 5, 0, [], 0, 0, 2, 0, 1, 1, 0, 1, 0) *(((-4 + d)^3*(-mb2 + s + t)*(-(ma2*mb2) + ma2*t + mb2*t - s*t - t^2))/(4*(ma2 - t)*(-mb2 + t))) + INT(PL1, 4, 197, 5, 0, [], 1, 0, 1, 0, 0, 0, 2, 1, 0) *((3*(-4 + d)^3*(ma2 - mb2 + s)*(ma2*mb2 - ma2*t - mb2*t + s*t + t^2))/(8*(ma2 - t)*(mb2 - t))) + INT(PL1, 5, 182, 5, 0, [], 0, 1, 1, 0, 1, 1, 0, 1, 0) *(((-4 + d)^4*(ma2 - 2*mb2 + 2*s + t)*(-(ma2*mb2) + ma2*t + mb2*t - s*t - t^2))/(8*(ma2 - t)*(-mb2 + t))) + INT(PL1, 5, 182, 6, 0, [], 0, 1, 2, 0, 1, 1, 0, 1, 0) *(-((-4 + d)^3*s*(-ma2 - mb2 + s + t)*(ma2*mb2 - ma2*t - mb2*t + s*t + t^2))/(8*(ma2 - t)*(-mb2 + t))) + INT(PL1, 5, 229, 6, 0, [], 1, 0, 2, 0, 0, 1, 1, 1, 0) *(-((-6 + d)*(-4 + d)^2*ma2*s*(-(ma2*mb2) + ma2*t + mb2*t - s*t - t^2))/(4*(ma2 - t)*(-mb2 + t))) + INT(PL1x12, 3, 148, 5, 0, [], 0, 0, 2, 0, 2, 0, 0, 1, 0) *((-5*(-4 + d)^2*t*(-(ma2*mb2) + ma2*t + mb2*t - s*t - t^2))/(16*(ma2 - t)*(-mb2 + t))) + INT(PL1x12, 4, 149, 5, 0, [], 1, 0, 1, 0, 2, 0, 0, 1, 0) *((-3*(-4 + d)^3*(-(ma2*mb2) + ma2*t + mb2*t - s*t - t^2))/(8*(ma2 - t))) + INT(PL1x12, 4, 180, 5, 0, [], 0, 0, 2, 0, 1, 1, 0, 1, 0) *((3*(-4 + d)^3*(-(ma2*mb2) + ma2*t + mb2*t - s*t - t^2))/(4*(mb2 - t))) + INT(PL1x12, 4, 204, 5, 0, [], 0, 0, 1, 1, 0, 0, 2, 1, 0) *(((-4 + d)^3*(-(ma2*mb2) + ma2*t + mb2*t - s*t - t^2))/(2*(mb2 - t))) + INT(PL1x12, 5, 182, 5, 0, [], 0, 1, 1, 0, 1, 1, 0, 1, 0) *(-((-4 + d)^4*(-mb2 + s + t)*(-(ma2*mb2) + ma2*t + mb2*t - s*t - t^2))/(8*(ma2 - t)*(-mb2 + t))) + INT(PL1x12, 5, 182, 6, 0, [], 0, 1, 2, 0, 1, 1, 0, 1, 0) *(-((-4 + d)^3*s*t*(ma2*mb2 - ma2*t - mb2*t + s*t + t^2))/(8*(ma2 - t)*(-mb2 + t))) + INT(PL1x12, 5, 213, 5, 0, [], 1, 0, 1, 0, 1, 0, 1, 1, 0) *((3*(-4 + d)^4*(ma2 - s - t)*(-(ma2*mb2) + ma2*t + mb2*t - s*t - t^2))/(16*(ma2 - t)*(-mb2 + t))) + INT(PL1x12, 5, 213, 6, 0, [], 1, 0, 2, 0, 1, 0, 1, 1, 0) *(((-4 + d)^3*s*t*(ma2*mb2 - ma2*t - mb2*t + s*t + t^2))/(16*(ma2 - t)*(-mb2 + t))) + INT(PL1x12, 5, 436, 5, 0, [], 0, 0, 1, 0, 1, 1, 0, 1, 1) *(-((-4 + d)^4*(-(ma2*mb2) + ma2*t + mb2*t - s*t - t^2))/(4*(mb2 - t))) + INT(PL1x12, 6, 438, 6, 0, [], 0, 1, 1, 0, 1, 1, 0, 1, 1) *(((-4 + d)^4*mb2*(-(ma2*mb2) + ma2*t + mb2*t - s*t - t^2))/(8*(mb2 - t))) + INT(PL2, 5, 181, 6, 0, [], 1, 0, 1, 0, 2, 1, 0, 1, 0) *(((-4 + d)^3*(ma2*mb2 - ma2*t - mb2*t + s*t + t^2))/4) + INT(PL2, 5, 182, 6, 0, [], 0, 1, 2, 0, 1, 1, 0, 1, 0) *(-((-4 + d)^3*(ma2*mb2 - ma2*t - mb2*t + s*t + t^2))/8) + INT(PL2, 5, 213, 6, 0, [], 2, 0, 1, 0, 1, 0, 1, 1, 0) *(-((-4 + d)^3*mb2*(-(ma2*mb2) + ma2*t + mb2*t - s*t - t^2))/(4*(mb2 - t))) ; id M(N34, 47) = + INT(NPL, 6, 231, 6, 0, [], 1, 1, 1, 0, 0, 1, 1, 1, 0) *(((-4 + d)^4*(ma2^2 - 2*ma2*mb2 + mb2^2 - 2*ma2*s - 2*mb2*s + s^2))/16) ; id M(N34, 50) = + INT(NPL, 6, 207, 6, 0, [], 1, 1, 1, 1, 0, 0, 1, 1, 0) *(((-4 + d)^4*s*(-ma2 - mb2 + s + t))/32) + INT(NPL, 7, 239, 7, 0, [], 1, 1, 1, 1, 0, 1, 1, 1, 0) *(((-4 + d)^4*s*(ma2*mb2 - mb2^2 + mb2*s - ma2*t + mb2*t + s*t))/32) + INT(NPL, 7, 239, 7, 1, [], 1, 1, 1, 1, 0, 1, 1, 1, -1) *(-((-4 + d)^4*s*(-ma2 - mb2 + s + 2*t))/32) + INT(NPLx12, 6, 207, 6, 0, [], 1, 1, 1, 1, 0, 0, 1, 1, 0) *(-((-4 + d)^4*s*t)/32) + INT(PL1, 6, 215, 6, 0, [], 1, 1, 1, 0, 1, 0, 1, 1, 0) *(((-4 + d)^4*s*(-ma2 - mb2 + s + 2*t))/32) + INT(PL1, 6, 246, 6, 0, [], 0, 1, 1, 0, 1, 1, 1, 1, 0) *(((-4 + d)^4*s*(-ma2 - mb2 + s + 2*t))/32) + INT(PL1x12, 6, 246, 6, 0, [], 0, 1, 1, 0, 1, 1, 1, 1, 0) *(-((-4 + d)^4*s*(-ma2 - mb2 + s + 2*t))/32) ; id M(N34, 51) = + INT(NPL, 6, 207, 6, 0, [], 1, 1, 1, 1, 0, 0, 1, 1, 0) *(-((-4 + d)^4*root*(ma2 - s - t))/16) + INT(NPL, 7, 239, 7, 0, [], 1, 1, 1, 1, 0, 1, 1, 1, 0) *(((-4 + d)^4*root*s*(mb2 - t))/16) + INT(NPL, 7, 239, 7, 1, [], 1, 1, 1, 1, 0, 1, 1, 1, -1) *(-((-4 + d)^4*root*s)/16) + INT(NPLx12, 6, 207, 6, 0, [], 1, 1, 1, 1, 0, 0, 1, 1, 0) *(-((-4 + d)^4*root*(mb2 - t))/16) + INT(PL1, 6, 215, 6, 0, [], 1, 1, 1, 0, 1, 0, 1, 1, 0) *(((-4 + d)^4*root*s)/16) + INT(PL1, 6, 246, 6, 0, [], 0, 1, 1, 0, 1, 1, 1, 1, 0) *(((-4 + d)^4*root*s)/16) + INT(PL1x12, 6, 246, 6, 0, [], 0, 1, 1, 0, 1, 1, 1, 1, 0) *(-((-4 + d)^4*root*s)/16) ;