Vittorio Del Duca, Claude Duhr, Rayan Haindl, Achilleas Lazopoulos and Martin Michel.
We provide here the quadruple collinear splitting amplitudes and the 3-parton splitting tensors for both a quark parent and a gluon parent, computed in arXiv:1912.06425 (quark parent) and arXiv:2007.05345 (gluon parent), in electronic form (Mathematica files). Each file corresponds to the quantity defined in the original publication, within the equation mentioned below.
The indices carried by the momentum fractions z1, z2, z3, z4 and the sub-energies s12, s13, s14, s23, s24, s34 follow the parton labeling conventions of arXiv:1912.06425 and arXiv:2007.05345. For convenience, we use an abbreviated notation to collect sums of the kinematic variables, e.g. z123 = z1+z2+z3 and s123 = s12 + s13 + s23. The gluon-initated splitting amplitudes contain the Minkowski metric gg and transverse momenta kikj, where i,j=1,...,4 and e.g. k1k2 and k2k1 denote a different ordering of the Lorentz indices. The splitting tensors contain sub-energies sP3 and sP4 where P denotes the on-shell momentum of the parton that splits into two partons in the wider context of strongly-ordered limits.
We provide the coefficients of the 3-parton splitting tensors for both a quark parent and a gluon parent. The constraints have been applied to replace z(12) = 1-z3-z4 and k(12) = -k3-k4.