* The two-loop helicity amplitudes for qqb -> VV' -> 4 leptons * T. Gehrmann, A. von Manteuffel, L. Tancredi *** * In this FORM-readable file we present the formulas (2.15). * These relations are needed to express the coefficients $A_j$ defined * in (2.11) in terms of the coefficients $tau_j$ defined in (2.14): * $ A_j = \sum_{i=1}^10 B_{ji} \tau_i $. *** * 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 'd' is the dimensional regularisation parameter. *** * In these files we use the notation * Num(n?) = n ; * Den(n?) = 1/n ; *** id A1 = + tau1 * ( - 1/2*Den( - 3 + d)*Den(mb2*ma2 - t*u)^3*Den(ma2 + mb2 - u - t)^ 2*Num(mb2 - t)^2*Num(ma2 - u)^2*d ) + tau2 * ( - 1/2*Den( - 3 + d)*Den(mb2*ma2 - t*u)^3*Den(ma2 + mb2 - u - t)^ 2*Num(ma2 - u)*Num( - 4*mb2*ma2^2 - 2*mb2^2*ma2 + 4*u*mb2*ma2 + 2* t*mb2*ma2 + 4*t*u*ma2 + 2*t*u*mb2 - 4*t*u^2 - 2*t^2*u + 2*d*mb2* ma2^2 + d*mb2^2*ma2 - 3*d*u*mb2*ma2 - d*u*mb2^2 + d*u^2*mb2 - d*t* mb2*ma2 - d*t*u*ma2 + d*t*u*mb2 + d*t*u^2) ) + tau3 * ( - 1/2*Den( - 3 + d)*Den(mb2*ma2 - t*u)^3*Den(ma2 + mb2 - u - t)^ 2*Num(mb2 - t)*Num( - 2*mb2*ma2^2 - 4*mb2^2*ma2 + 2*u*mb2*ma2 + 4* t*mb2*ma2 + 2*t*u*ma2 + 4*t*u*mb2 - 2*t*u^2 - 4*t^2*u + d*mb2* ma2^2 + 2*d*mb2^2*ma2 - d*u*mb2*ma2 - d*t*ma2^2 - 3*d*t*mb2*ma2 + d *t*u*ma2 - d*t*u*mb2 + d*t^2*ma2 + d*t^2*u) ) + tau4 * ( - 1/2*Den( - 3 + d)*Den(mb2*ma2 - t*u)^3*Den(ma2 + mb2 - u - t)^ 2*Num( - 4*mb2*mb2^3 - 12*mb2^2*ma2^2 - 4*ma2^3*ma2 + 4*u*mb2*ma2^2 + 4 *u*mb2^2*ma2 + 4*t*mb2*ma2^2 + 4*t*mb2^2*ma2 + 4*t*u*ma2^2 + 16*t*u* mb2*ma2 + 4*t*u*mb2^2 - 4*t*u^2*ma2 - 4*t*u^2*mb2 - 4*t^2*u*ma2 - 4*t^2*u*mb2 - 4*t^2*u^2 + 2*d*mb2*mb2^3 + 5*d*mb2^2*ma2^2 + 2*d* ma2^3*ma2 - 3*d*u*mb2*ma2^2 - 3*d*u*mb2^2*ma2 + d*u^2*mb2*ma2 - 3*d *t*mb2*ma2^2 - 3*d*t*mb2^2*ma2 - d*t*u*ma2^2 - 2*d*t*u*mb2*ma2 - d*t *u*mb2^2 + d*t*u^2*ma2 + d*t*u^2*mb2 + d*t^2*mb2*ma2 + d*t^2*u* ma2 + d*t^2*u*mb2 + d*t^2*u^2) ) + tau5 * ( - 1/2*Den( - 3 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^ 2*Num(mb2 - t)*Num(ma2 - u)*Num(ma2 + 2*mb2 - u - 2*t) ) + tau6 * ( - 1/2*Den( - 3 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^ 2*Num(ma2 - u)*Num(3*mb2*ma2 + 2*mb2^2 - 2*u*mb2 - t*ma2 - 3*t* mb2 + t^2) ) + tau7 * ( + 1/2*Den( - 3 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^ 2*Num(mb2 - t)*Num(ma2 - u)^2 ) + tau8 * ( + 1/2*Den( - 3 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^ 2*Num(mb2 - t)*Num(ma2^2 + 2*mb2*ma2 - u*ma2 - t*ma2 - t*u) ) + tau9 * ( + 1/4*Den( - 3 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)* Num(mb2 - t)*Num(ma2 - u) ) + tau10 * ( + 1/4*Den( - 3 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)* Num(mb2 - t)*Num(ma2 - u) ); id A2 = + tau1 * ( - 1/2*Den( - 3 + d)*Den(mb2*ma2 - t*u)^3*Den(ma2 + mb2 - u - t)^ 2*Num(ma2 - u)*Num( - 4*mb2*ma2^2 - 2*mb2^2*ma2 + 4*u*mb2*ma2 + 2* t*mb2*ma2 + 4*t*u*ma2 + 2*t*u*mb2 - 4*t*u^2 - 2*t^2*u + 2*d*mb2* ma2^2 + d*mb2^2*ma2 - 3*d*u*mb2*ma2 - d*u*mb2^2 + d*u^2*mb2 - d*t* mb2*ma2 - d*t*u*ma2 + d*t*u*mb2 + d*t*u^2) ) + tau2 * ( - 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)^3*Den(ma2 + mb2 - u - t)^2*Num(4*mb2^2*ma2^2 - 16*u*mb2*ma2^2 - 16*u*mb2^2*ma2 + 16*u^2*mb2*ma2 + 8*t*u*mb2*ma2 + 16*t*u^2*ma2 + 16*t*u^2*mb2 - 16*t*u^3 - 12*t^2*u^2 - 4*d*mb2^2*ma2^2 + 12*d*u*mb2*ma2^2 + 12*d*u* mb2^2*ma2 - 4*d*u^2*ma2^2 - 20*d*u^2*mb2*ma2 - 4*d*u^2*mb2^2 + 8*d* u^3*ma2 + 8*d*u^3*mb2 - 4*d*u^4 - 4*d*t*u*mb2*ma2 - 4*d*t*u^2* ma2 - 4*d*t*u^2*mb2 + 4*d*t*u^3 + 4*d*t^2*u^2 + d^2*mb2^2*ma2^2 - 2* d^2*u*mb2*ma2^2 - 2*d^2*u*mb2^2*ma2 + d^2*u^2*ma2^2 + 4*d^2*u^2*mb2* ma2 + d^2*u^2*mb2^2 - 2*d^2*u^3*ma2 - 2*d^2*u^3*mb2 + d^2*u^4) ) + tau3 * ( - 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)^3*Den(ma2 + mb2 - u - t)^2*Num(16*mb2*mb2^3 + 44*mb2^2*ma2^2 + 16*ma2^3*ma2 - 24*u *mb2*ma2^2 - 24*u*mb2^2*ma2 + 8*u^2*mb2*ma2 - 24*t*mb2*ma2^2 - 24*t *mb2^2*ma2 - 16*t*u*ma2^2 - 40*t*u*mb2*ma2 - 16*t*u*mb2^2 + 24*t*u^2* ma2 + 24*t*u^2*mb2 - 8*t*u^3 + 8*t^2*mb2*ma2 + 24*t^2*u*ma2 + 24 *t^2*u*mb2 - 4*t^2*u^2 - 8*t^3*u - 12*d*mb2*mb2^3 - 32*d*mb2^2*ma2^2 - 12*d*ma2^3*ma2 + 18*d*u*mb2*ma2^2 + 18*d*u*mb2^2*ma2 - 6*d*u^2* mb2*ma2 + 18*d*t*mb2*ma2^2 + 18*d*t*mb2^2*ma2 + 8*d*t*u*ma2^2 + 20*d *t*u*mb2*ma2 + 8*d*t*u*mb2^2 - 10*d*t*u^2*ma2 - 10*d*t*u^2*mb2 + 2 *d*t*u^3 - 6*d*t^2*mb2*ma2 - 10*d*t^2*u*ma2 - 10*d*t^2*u*mb2 - 4* d*t^2*u^2 + 2*d*t^3*u + 2*d^2*mb2*mb2^3 + 5*d^2*mb2^2*ma2^2 + 2*d^2* ma2^3*ma2 - 3*d^2*u*mb2*ma2^2 - 3*d^2*u*mb2^2*ma2 + d^2*u^2*mb2*ma2 - 3*d^2*t*mb2*ma2^2 - 3*d^2*t*mb2^2*ma2 - d^2*t*u*ma2^2 - 2*d^2*t*u* mb2*ma2 - d^2*t*u*mb2^2 + d^2*t*u^2*ma2 + d^2*t*u^2*mb2 + d^2*t^2* mb2*ma2 + d^2*t^2*u*ma2 + d^2*t^2*u*mb2 + d^2*t^2*u^2) ) + tau4 * ( - 1/2*Den( - 3 + d)*Den(mb2*ma2 - t*u)^3*Den(ma2 + mb2 - u - t)^ 2*Num(mb2 - u)*Num( - 2*mb2*ma2^2 - 4*mb2^2*ma2 + 4*u*mb2*ma2 + 2* t*mb2*ma2 + 2*t*u*ma2 + 4*t*u*mb2 - 4*t*u^2 - 2*t^2*u + d*mb2* ma2^2 + 2*d*mb2^2*ma2 - d*u*ma2^2 - 3*d*u*mb2*ma2 + d*u^2*ma2 - d*t* mb2*ma2 + d*t*u*ma2 - d*t*u*mb2 + d*t*u^2) ) + tau5 * ( - 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^2*Num( - 2*mb2*ma2^2 + 4*u*ma2^2 + 14*u*mb2*ma2 + 8*u* mb2^2 - 8*u^2*ma2 - 12*u^2*mb2 + 4*u^3 - 10*t*u*ma2 - 16*t*u*mb2 + 10*t*u^2 + 8*t^2*u + d*mb2*ma2^2 - d*u*ma2^2 - 4*d*u*mb2*ma2 - 2* d*u*mb2^2 + 2*d*u^2*ma2 + 3*d*u^2*mb2 - d*u^3 + 2*d*t*u*ma2 + 4*d*t *u*mb2 - 2*d*t*u^2 - 2*d*t^2*u) ) + tau6 * ( + 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^2*Num( - 2*mb2*ma2^2 - 4*u*ma2^2 - 12*u*mb2*ma2 - 8*u* mb2^2 + 12*u^2*ma2 + 16*u^2*mb2 - 8*u^3 + 2*t*mb2*ma2 + 10*t*u* ma2 + 12*t*u*mb2 - 12*t*u^2 - 6*t^2*u + d*mb2*ma2^2 + d*u*ma2^2 + 3* d*u*mb2*ma2 + 2*d*u*mb2^2 - 3*d*u^2*ma2 - 4*d*u^2*mb2 + 2*d*u^3 - d*t*mb2*ma2 - 3*d*t*u*ma2 - 3*d*t*u*mb2 + 3*d*t*u^2 + 2*d*t^2*u) ) + tau7 * ( - 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^2*Num(ma2 - u)*Num(2*mb2*ma2 - 4*u*ma2 - 4*u*mb2 + 4*u^2 + 2*t*u - d*mb2*ma2 + d*u*ma2 + d*u*mb2 - d*u^2) ) + tau8 * ( + 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^2*Num( - 6*mb2*ma2^2 - 8*mb2^2*ma2 + 4*u*ma2^2 + 12*u* mb2*ma2 - 4*u^2*ma2 + 6*t*mb2*ma2 - 2*t*u*ma2 + 4*t*u*mb2 - 4* t*u^2 - 2*t^2*u + d*mb2*ma2^2 + 2*d*mb2^2*ma2 - d*u*ma2^2 - 3*d*u*mb2 *ma2 + d*u^2*ma2 - d*t*mb2*ma2 + d*t*u*ma2 - d*t*u*mb2 + d*t* u^2) ) + tau9 * ( - 1/4*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)*Num( - 6*mb2*ma2 - 4*u*ma2 - 4*u*mb2 + 4*u^2 + 10*t *u + d*mb2*ma2 + d*u*ma2 + d*u*mb2 - d*u^2 - 2*d*t*u) ) + tau10 * ( - 1/4*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)*Num( - 2*mb2*ma2 - 4*u*ma2 - 4*u*mb2 + 4*u^2 + 6*t* u + d*mb2*ma2 + d*u*ma2 + d*u*mb2 - d*u^2 - 2*d*t*u) ); id A3 = + tau1 * ( - 1/2*Den( - 3 + d)*Den(mb2*ma2 - t*u)^3*Den(ma2 + mb2 - u - t)^ 2*Num(mb2 - t)*Num( - 2*mb2*ma2^2 - 4*mb2^2*ma2 + 2*u*mb2*ma2 + 4* t*mb2*ma2 + 2*t*u*ma2 + 4*t*u*mb2 - 2*t*u^2 - 4*t^2*u + d*mb2* ma2^2 + 2*d*mb2^2*ma2 - d*u*mb2*ma2 - d*t*ma2^2 - 3*d*t*mb2*ma2 + d *t*u*ma2 - d*t*u*mb2 + d*t^2*ma2 + d*t^2*u) ) + tau2 * ( - 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)^3*Den(ma2 + mb2 - u - t)^2*Num(16*mb2*mb2^3 + 44*mb2^2*ma2^2 + 16*ma2^3*ma2 - 24*u *mb2*ma2^2 - 24*u*mb2^2*ma2 + 8*u^2*mb2*ma2 - 24*t*mb2*ma2^2 - 24*t *mb2^2*ma2 - 16*t*u*ma2^2 - 40*t*u*mb2*ma2 - 16*t*u*mb2^2 + 24*t*u^2* ma2 + 24*t*u^2*mb2 - 8*t*u^3 + 8*t^2*mb2*ma2 + 24*t^2*u*ma2 + 24 *t^2*u*mb2 - 4*t^2*u^2 - 8*t^3*u - 12*d*mb2*mb2^3 - 32*d*mb2^2*ma2^2 - 12*d*ma2^3*ma2 + 18*d*u*mb2*ma2^2 + 18*d*u*mb2^2*ma2 - 6*d*u^2* mb2*ma2 + 18*d*t*mb2*ma2^2 + 18*d*t*mb2^2*ma2 + 8*d*t*u*ma2^2 + 20*d *t*u*mb2*ma2 + 8*d*t*u*mb2^2 - 10*d*t*u^2*ma2 - 10*d*t*u^2*mb2 + 2 *d*t*u^3 - 6*d*t^2*mb2*ma2 - 10*d*t^2*u*ma2 - 10*d*t^2*u*mb2 - 4* d*t^2*u^2 + 2*d*t^3*u + 2*d^2*mb2*mb2^3 + 5*d^2*mb2^2*ma2^2 + 2*d^2* ma2^3*ma2 - 3*d^2*u*mb2*ma2^2 - 3*d^2*u*mb2^2*ma2 + d^2*u^2*mb2*ma2 - 3*d^2*t*mb2*ma2^2 - 3*d^2*t*mb2^2*ma2 - d^2*t*u*ma2^2 - 2*d^2*t*u* mb2*ma2 - d^2*t*u*mb2^2 + d^2*t*u^2*ma2 + d^2*t*u^2*mb2 + d^2*t^2* mb2*ma2 + d^2*t^2*u*ma2 + d^2*t^2*u*mb2 + d^2*t^2*u^2) ) + tau3 * ( - 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)^3*Den(ma2 + mb2 - u - t)^2*Num(4*mb2^2*ma2^2 - 16*t*mb2*ma2^2 - 16*t*mb2^2*ma2 + 8 *t*u*mb2*ma2 + 16*t^2*mb2*ma2 + 16*t^2*u*ma2 + 16*t^2*u*mb2 - 12*t^2*u^2 - 16*t^3*u - 4*d*mb2^2*ma2^2 + 12*d*t*mb2*ma2^2 + 12*d*t* mb2^2*ma2 - 4*d*t*u*mb2*ma2 - 4*d*t^2*ma2^2 - 20*d*t^2*mb2*ma2 - 4 *d*t^2*mb2^2 - 4*d*t^2*u*ma2 - 4*d*t^2*u*mb2 + 4*d*t^2*u^2 + 8*d*t^3 *ma2 + 8*d*t^3*mb2 + 4*d*t^3*u - 4*d*t^4 + d^2*mb2^2*ma2^2 - 2*d^2*t* mb2*ma2^2 - 2*d^2*t*mb2^2*ma2 + d^2*t^2*ma2^2 + 4*d^2*t^2*mb2*ma2 + d^2*t^2*mb2^2 - 2*d^2*t^3*ma2 - 2*d^2*t^3*mb2 + d^2*t^4) ) + tau4 * ( - 1/2*Den( - 3 + d)*Den(mb2*ma2 - t*u)^3*Den(ma2 + mb2 - u - t)^ 2*Num(ma2 - t)*Num( - 4*mb2*ma2^2 - 2*mb2^2*ma2 + 2*u*mb2*ma2 + 4* t*mb2*ma2 + 4*t*u*ma2 + 2*t*u*mb2 - 2*t*u^2 - 4*t^2*u + 2*d*mb2* ma2^2 + d*mb2^2*ma2 - d*u*mb2*ma2 - 3*d*t*mb2*ma2 - d*t*mb2^2 - d*t *u*ma2 + d*t*u*mb2 + d*t^2*mb2 + d*t^2*u) ) + tau5 * ( + 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^2*Num( - 2*mb2*ma2^2 + 2*u*mb2*ma2 - 4*t*ma2^2 - 12*t* mb2*ma2 - 8*t*mb2^2 + 10*t*u*ma2 + 12*t*u*mb2 - 6*t*u^2 + 12*t^2* ma2 + 16*t^2*mb2 - 12*t^2*u - 8*t^3 + d*mb2*ma2^2 - d*u*mb2*ma2 + d*t*ma2^2 + 3*d*t*mb2*ma2 + 2*d*t*mb2^2 - 3*d*t*u*ma2 - 3*d*t*u* mb2 + 2*d*t*u^2 - 3*d*t^2*ma2 - 4*d*t^2*mb2 + 3*d*t^2*u + 2*d*t^3) ) + tau6 * ( - 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^2*Num( - 2*mb2*ma2^2 + 4*t*ma2^2 + 14*t*mb2*ma2 + 8*t* mb2^2 - 10*t*u*ma2 - 16*t*u*mb2 + 8*t*u^2 - 8*t^2*ma2 - 12*t^2*mb2 + 10*t^2*u + 4*t^3 + d*mb2*ma2^2 - d*t*ma2^2 - 4*d*t*mb2*ma2 - 2*d* t*mb2^2 + 2*d*t*u*ma2 + 4*d*t*u*mb2 - 2*d*t*u^2 + 2*d*t^2*ma2 + 3*d *t^2*mb2 - 2*d*t^2*u - d*t^3) ) + tau7 * ( + 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^2*Num( - 6*mb2*ma2^2 - 8*mb2^2*ma2 + 6*u*mb2*ma2 + 4* t*ma2^2 + 12*t*mb2*ma2 - 2*t*u*ma2 + 4*t*u*mb2 - 2*t*u^2 - 4*t^2* ma2 - 4*t^2*u + d*mb2*ma2^2 + 2*d*mb2^2*ma2 - d*u*mb2*ma2 - d*t* ma2^2 - 3*d*t*mb2*ma2 + d*t*u*ma2 - d*t*u*mb2 + d*t^2*ma2 + d*t^2 *u) ) + tau8 * ( - 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^2*Num(ma2 - t)*Num(2*mb2*ma2 - 4*t*ma2 - 4*t*mb2 + 2*t*u + 4*t^2 - d*mb2*ma2 + d*t*ma2 + d*t*mb2 - d*t^2) ) + tau9 * ( - 1/4*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)*Num( - 2*mb2*ma2 - 4*t*ma2 - 4*t*mb2 + 6*t*u + 4* t^2 + d*mb2*ma2 + d*t*ma2 + d*t*mb2 - 2*d*t*u - d*t^2) ) + tau10 * ( - 1/4*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)*Num( - 6*mb2*ma2 - 4*t*ma2 - 4*t*mb2 + 10*t*u + 4* t^2 + d*mb2*ma2 + d*t*ma2 + d*t*mb2 - 2*d*t*u - d*t^2) ); id A4 = + tau1 * ( - 1/2*Den( - 3 + d)*Den(mb2*ma2 - t*u)^3*Den(ma2 + mb2 - u - t)^ 2*Num( - 4*mb2*mb2^3 - 12*mb2^2*ma2^2 - 4*ma2^3*ma2 + 4*u*mb2*ma2^2 + 4 *u*mb2^2*ma2 + 4*t*mb2*ma2^2 + 4*t*mb2^2*ma2 + 4*t*u*ma2^2 + 16*t*u* mb2*ma2 + 4*t*u*mb2^2 - 4*t*u^2*ma2 - 4*t*u^2*mb2 - 4*t^2*u*ma2 - 4*t^2*u*mb2 - 4*t^2*u^2 + 2*d*mb2*mb2^3 + 5*d*mb2^2*ma2^2 + 2*d* ma2^3*ma2 - 3*d*u*mb2*ma2^2 - 3*d*u*mb2^2*ma2 + d*u^2*mb2*ma2 - 3*d *t*mb2*ma2^2 - 3*d*t*mb2^2*ma2 - d*t*u*ma2^2 - 2*d*t*u*mb2*ma2 - d*t *u*mb2^2 + d*t*u^2*ma2 + d*t*u^2*mb2 + d*t^2*mb2*ma2 + d*t^2*u* ma2 + d*t^2*u*mb2 + d*t^2*u^2) ) + tau2 * ( - 1/2*Den( - 3 + d)*Den(mb2*ma2 - t*u)^3*Den(ma2 + mb2 - u - t)^ 2*Num(mb2 - u)*Num( - 2*mb2*ma2^2 - 4*mb2^2*ma2 + 4*u*mb2*ma2 + 2* t*mb2*ma2 + 2*t*u*ma2 + 4*t*u*mb2 - 4*t*u^2 - 2*t^2*u + d*mb2* ma2^2 + 2*d*mb2^2*ma2 - d*u*ma2^2 - 3*d*u*mb2*ma2 + d*u^2*ma2 - d*t* mb2*ma2 + d*t*u*ma2 - d*t*u*mb2 + d*t*u^2) ) + tau3 * ( - 1/2*Den( - 3 + d)*Den(mb2*ma2 - t*u)^3*Den(ma2 + mb2 - u - t)^ 2*Num(ma2 - t)*Num( - 4*mb2*ma2^2 - 2*mb2^2*ma2 + 2*u*mb2*ma2 + 4* t*mb2*ma2 + 4*t*u*ma2 + 2*t*u*mb2 - 2*t*u^2 - 4*t^2*u + 2*d*mb2* ma2^2 + d*mb2^2*ma2 - d*u*mb2*ma2 - 3*d*t*mb2*ma2 - d*t*mb2^2 - d*t *u*ma2 + d*t*u*mb2 + d*t^2*mb2 + d*t^2*u) ) + tau4 * ( - 1/2*Den( - 3 + d)*Den(mb2*ma2 - t*u)^3*Den(ma2 + mb2 - u - t)^ 2*Num(mb2 - u)^2*Num(ma2 - t)^2*d ) + tau5 * ( - 1/2*Den( - 3 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^ 2*Num(ma2 - t)*Num(3*mb2*ma2 + 2*mb2^2 - u*ma2 - 3*u*mb2 + u^2 - 2*t*mb2) ) + tau6 * ( - 1/2*Den( - 3 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^ 2*Num(mb2 - u)*Num(ma2 - t)*Num(ma2 + 2*mb2 - 2*u - t) ) + tau7 * ( + 1/2*Den( - 3 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^ 2*Num(mb2 - u)*Num(ma2^2 + 2*mb2*ma2 - u*ma2 - t*ma2 - t*u) ) + tau8 * ( + 1/2*Den( - 3 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^ 2*Num(mb2 - u)*Num(ma2 - t)^2 ) + tau9 * ( + 1/4*Den( - 3 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)* Num(mb2 - u)*Num(ma2 - t) ) + tau10 * ( + 1/4*Den( - 3 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)* Num(mb2 - u)*Num(ma2 - t) ); id A5 = + tau1 * ( - 1/2*Den( - 3 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^ 2*Num(mb2 - t)*Num(ma2 - u)*Num(ma2 + 2*mb2 - u - 2*t) ) + tau2 * ( - 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^2*Num( - 2*mb2*ma2^2 + 4*u*ma2^2 + 14*u*mb2*ma2 + 8*u* mb2^2 - 8*u^2*ma2 - 12*u^2*mb2 + 4*u^3 - 10*t*u*ma2 - 16*t*u*mb2 + 10*t*u^2 + 8*t^2*u + d*mb2*ma2^2 - d*u*ma2^2 - 4*d*u*mb2*ma2 - 2* d*u*mb2^2 + 2*d*u^2*ma2 + 3*d*u^2*mb2 - d*u^3 + 2*d*t*u*ma2 + 4*d*t *u*mb2 - 2*d*t*u^2 - 2*d*t^2*u) ) + tau3 * ( + 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^2*Num( - 2*mb2*ma2^2 + 2*u*mb2*ma2 - 4*t*ma2^2 - 12*t* mb2*ma2 - 8*t*mb2^2 + 10*t*u*ma2 + 12*t*u*mb2 - 6*t*u^2 + 12*t^2* ma2 + 16*t^2*mb2 - 12*t^2*u - 8*t^3 + d*mb2*ma2^2 - d*u*mb2*ma2 + d*t*ma2^2 + 3*d*t*mb2*ma2 + 2*d*t*mb2^2 - 3*d*t*u*ma2 - 3*d*t*u* mb2 + 2*d*t*u^2 - 3*d*t^2*ma2 - 4*d*t^2*mb2 + 3*d*t^2*u + 2*d*t^3) ) + tau4 * ( - 1/2*Den( - 3 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^ 2*Num(ma2 - t)*Num(3*mb2*ma2 + 2*mb2^2 - u*ma2 - 3*u*mb2 + u^2 - 2*t*mb2) ) + tau5 * ( - 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)^2*Num( - 3*ma2^2 - 8*mb2*ma2 - 8*mb2^2 + 6*u*ma2 + 8*u *mb2 - 3*u^2 + 8*t*ma2 + 16*t*mb2 - 8*t*u - 8*t^2 + d*ma2^2 + 2*d* mb2*ma2 + 2*d*mb2^2 - 2*d*u*ma2 - 2*d*u*mb2 + d*u^2 - 2*d*t*ma2 - 4*d*t*mb2 + 2*d*t*u + 2*d*t^2) ) + tau6 * ( - 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)^2*Num( - 5*ma2^2 - 16*mb2*ma2 - 8*mb2^2 + 9*u*ma2 + 12 *u*mb2 - 4*u^2 + 9*t*ma2 + 12*t*mb2 - 5*t*u - 4*t^2 + d*ma2^2 + 4*d *mb2*ma2 + 2*d*mb2^2 - 2*d*u*ma2 - 3*d*u*mb2 + d*u^2 - 2*d*t*ma2 - 3*d*t*mb2 + d*t*u + d*t^2) ) + tau7 * ( + 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)^2*Num(ma2 - u)^2 ) + tau8 * ( - 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)^2*Num(ma2 - t)*Num(ma2 - u) ) + tau9 * ( + 1/4*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)*Num( - 3*ma2 - 4*mb2 + 3*u + 4*t + d*ma2 + d*mb2 - d*u - d*t) ) + tau10 * ( + 1/4*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)*Num( - 5*ma2 - 4*mb2 + 5*u + 4*t + d*ma2 + d*mb2 - d*u - d*t) ); id A6 = + tau1 * ( - 1/2*Den( - 3 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^ 2*Num(ma2 - u)*Num(3*mb2*ma2 + 2*mb2^2 - 2*u*mb2 - t*ma2 - 3*t* mb2 + t^2) ) + tau2 * ( + 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^2*Num( - 2*mb2*ma2^2 - 4*u*ma2^2 - 12*u*mb2*ma2 - 8*u* mb2^2 + 12*u^2*ma2 + 16*u^2*mb2 - 8*u^3 + 2*t*mb2*ma2 + 10*t*u* ma2 + 12*t*u*mb2 - 12*t*u^2 - 6*t^2*u + d*mb2*ma2^2 + d*u*ma2^2 + 3* d*u*mb2*ma2 + 2*d*u*mb2^2 - 3*d*u^2*ma2 - 4*d*u^2*mb2 + 2*d*u^3 - d*t*mb2*ma2 - 3*d*t*u*ma2 - 3*d*t*u*mb2 + 3*d*t*u^2 + 2*d*t^2*u) ) + tau3 * ( - 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^2*Num( - 2*mb2*ma2^2 + 4*t*ma2^2 + 14*t*mb2*ma2 + 8*t* mb2^2 - 10*t*u*ma2 - 16*t*u*mb2 + 8*t*u^2 - 8*t^2*ma2 - 12*t^2*mb2 + 10*t^2*u + 4*t^3 + d*mb2*ma2^2 - d*t*ma2^2 - 4*d*t*mb2*ma2 - 2*d* t*mb2^2 + 2*d*t*u*ma2 + 4*d*t*u*mb2 - 2*d*t*u^2 + 2*d*t^2*ma2 + 3*d *t^2*mb2 - 2*d*t^2*u - d*t^3) ) + tau4 * ( - 1/2*Den( - 3 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^ 2*Num(mb2 - u)*Num(ma2 - t)*Num(ma2 + 2*mb2 - 2*u - t) ) + tau5 * ( - 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)^2*Num( - 5*ma2^2 - 16*mb2*ma2 - 8*mb2^2 + 9*u*ma2 + 12 *u*mb2 - 4*u^2 + 9*t*ma2 + 12*t*mb2 - 5*t*u - 4*t^2 + d*ma2^2 + 4*d *mb2*ma2 + 2*d*mb2^2 - 2*d*u*ma2 - 3*d*u*mb2 + d*u^2 - 2*d*t*ma2 - 3*d*t*mb2 + d*t*u + d*t^2) ) + tau6 * ( - 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)^2*Num( - 3*ma2^2 - 8*mb2*ma2 - 8*mb2^2 + 8*u*ma2 + 16* u*mb2 - 8*u^2 + 6*t*ma2 + 8*t*mb2 - 8*t*u - 3*t^2 + d*ma2^2 + 2*d* mb2*ma2 + 2*d*mb2^2 - 2*d*u*ma2 - 4*d*u*mb2 + 2*d*u^2 - 2*d*t*ma2 - 2*d*t*mb2 + 2*d*t*u + d*t^2) ) + tau7 * ( - 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)^2*Num(ma2 - t)*Num(ma2 - u) ) + tau8 * ( + 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)^2*Num(ma2 - t)^2 ) + tau9 * ( + 1/4*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)*Num( - 5*ma2 - 4*mb2 + 4*u + 5*t + d*ma2 + d*mb2 - d*u - d*t) ) + tau10 * ( + 1/4*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)*Num( - 3*ma2 - 4*mb2 + 4*u + 3*t + d*ma2 + d*mb2 - d*u - d*t) ); id A7 = + tau1 * ( + 1/2*Den( - 3 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^ 2*Num(mb2 - t)*Num(ma2 - u)^2 ) + tau2 * ( - 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^2*Num(ma2 - u)*Num(2*mb2*ma2 - 4*u*ma2 - 4*u*mb2 + 4*u^2 + 2*t*u - d*mb2*ma2 + d*u*ma2 + d*u*mb2 - d*u^2) ) + tau3 * ( + 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^2*Num( - 6*mb2*ma2^2 - 8*mb2^2*ma2 + 6*u*mb2*ma2 + 4* t*ma2^2 + 12*t*mb2*ma2 - 2*t*u*ma2 + 4*t*u*mb2 - 2*t*u^2 - 4*t^2* ma2 - 4*t^2*u + d*mb2*ma2^2 + 2*d*mb2^2*ma2 - d*u*mb2*ma2 - d*t* ma2^2 - 3*d*t*mb2*ma2 + d*t*u*ma2 - d*t*u*mb2 + d*t^2*ma2 + d*t^2 *u) ) + tau4 * ( + 1/2*Den( - 3 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^ 2*Num(mb2 - u)*Num(ma2^2 + 2*mb2*ma2 - u*ma2 - t*ma2 - t*u) ) + tau5 * ( + 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)^2*Num(ma2 - u)^2 ) + tau6 * ( - 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)^2*Num(ma2 - t)*Num(ma2 - u) ) + tau7 * ( - 1/2*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)^2* Num(ma2 - u)^2 ) + tau8 * ( - 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)^2*Num( - 5*ma2^2 - 8*mb2*ma2 + 5*u*ma2 + 5*t*ma2 + 3 *t*u + d*ma2^2 + 2*d*mb2*ma2 - d*u*ma2 - d*t*ma2 - d*t*u) ) + tau9 * ( - 1/4*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)*Num(ma2 - u) ) + tau10 * ( + 1/4*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)*Num(ma2 - u) ); id A8 = + tau1 * ( + 1/2*Den( - 3 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^ 2*Num(mb2 - t)*Num(ma2^2 + 2*mb2*ma2 - u*ma2 - t*ma2 - t*u) ) + tau2 * ( + 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^2*Num( - 6*mb2*ma2^2 - 8*mb2^2*ma2 + 4*u*ma2^2 + 12*u* mb2*ma2 - 4*u^2*ma2 + 6*t*mb2*ma2 - 2*t*u*ma2 + 4*t*u*mb2 - 4* t*u^2 - 2*t^2*u + d*mb2*ma2^2 + 2*d*mb2^2*ma2 - d*u*ma2^2 - 3*d*u*mb2 *ma2 + d*u^2*ma2 - d*t*mb2*ma2 + d*t*u*ma2 - d*t*u*mb2 + d*t* u^2) ) + tau3 * ( - 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^2*Num(ma2 - t)*Num(2*mb2*ma2 - 4*t*ma2 - 4*t*mb2 + 2*t*u + 4*t^2 - d*mb2*ma2 + d*t*ma2 + d*t*mb2 - d*t^2) ) + tau4 * ( + 1/2*Den( - 3 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)^ 2*Num(mb2 - u)*Num(ma2 - t)^2 ) + tau5 * ( - 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)^2*Num(ma2 - t)*Num(ma2 - u) ) + tau6 * ( + 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)^2*Num(ma2 - t)^2 ) + tau7 * ( - 1/2*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)^2*Num( - 5*ma2^2 - 8*mb2*ma2 + 5*u*ma2 + 5*t*ma2 + 3 *t*u + d*ma2^2 + 2*d*mb2*ma2 - d*u*ma2 - d*t*ma2 - d*t*u) ) + tau8 * ( - 1/2*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)^2* Num(ma2 - t)^2 ) + tau9 * ( + 1/4*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)*Num(ma2 - t) ) + tau10 * ( - 1/4*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)*Num(ma2 - t) ); id A9 = + tau1 * ( + 1/4*Den( - 3 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)* Num(mb2 - t)*Num(ma2 - u) ) + tau2 * ( - 1/4*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)*Num( - 6*mb2*ma2 - 4*u*ma2 - 4*u*mb2 + 4*u^2 + 10*t *u + d*mb2*ma2 + d*u*ma2 + d*u*mb2 - d*u^2 - 2*d*t*u) ) + tau3 * ( - 1/4*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)*Num( - 2*mb2*ma2 - 4*t*ma2 - 4*t*mb2 + 6*t*u + 4* t^2 + d*mb2*ma2 + d*t*ma2 + d*t*mb2 - 2*d*t*u - d*t^2) ) + tau4 * ( + 1/4*Den( - 3 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)* Num(mb2 - u)*Num(ma2 - t) ) + tau5 * ( + 1/4*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)*Num( - 3*ma2 - 4*mb2 + 3*u + 4*t + d*ma2 + d*mb2 - d*u - d*t) ) + tau6 * ( + 1/4*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)*Num( - 5*ma2 - 4*mb2 + 4*u + 5*t + d*ma2 + d*mb2 - d*u - d*t) ) + tau7 * ( - 1/4*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)*Num(ma2 - u) ) + tau8 * ( + 1/4*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)*Num(ma2 - t) ) + tau9 * ( - 1/8*Den( - 4 + d)*Den(mb2*ma2 - t*u) ) + tau10 * ( - 1/8*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Num( - 5 + d) ); id A10 = + tau1 * ( + 1/4*Den( - 3 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)* Num(mb2 - t)*Num(ma2 - u) ) + tau2 * ( - 1/4*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)*Num( - 2*mb2*ma2 - 4*u*ma2 - 4*u*mb2 + 4*u^2 + 6*t* u + d*mb2*ma2 + d*u*ma2 + d*u*mb2 - d*u^2 - 2*d*t*u) ) + tau3 * ( - 1/4*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)*Num( - 6*mb2*ma2 - 4*t*ma2 - 4*t*mb2 + 10*t*u + 4* t^2 + d*mb2*ma2 + d*t*ma2 + d*t*mb2 - 2*d*t*u - d*t^2) ) + tau4 * ( + 1/4*Den( - 3 + d)*Den(mb2*ma2 - t*u)^2*Den(ma2 + mb2 - u - t)* Num(mb2 - u)*Num(ma2 - t) ) + tau5 * ( + 1/4*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)*Num( - 5*ma2 - 4*mb2 + 5*u + 4*t + d*ma2 + d*mb2 - d*u - d*t) ) + tau6 * ( + 1/4*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)*Num( - 3*ma2 - 4*mb2 + 4*u + 3*t + d*ma2 + d*mb2 - d*u - d*t) ) + tau7 * ( + 1/4*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)*Num(ma2 - u) ) + tau8 * ( - 1/4*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Den(ma2 + mb2 - u - t)*Num(ma2 - t) ) + tau9 * ( - 1/8*Den( - 3 + d)*Den( - 4 + d)*Den(mb2*ma2 - t*u)*Num( - 5 + d) ) + tau10 * ( - 1/8*Den( - 4 + d)*Den(mb2*ma2 - t*u) );