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In this work, some of the NLO QCD corrections for pp → V V jj +X are presented. A program in Mathematica based on the structure of FeynCalc which automatically simplifies a set of amplitudes up to the hexagon level of rank 5 has been created for this purpose. We focus on two different topologies. The first involves all the virtual contributions needed for quadruple electroweak vector boson production, i.e. pp → V V V V + X. In the second, the remaining “bosonic” corrections to electroweak triple vector boson production with an additional jet (pp → V V V j+X) are computed. We show the factorization formula of the infrared divergences of the bosonic contributions for VVVV and VVVj production with V ∈ (W,Z, γ). Stability issues associated with the evaluation of the hexagons up to rank 5 are studied. The CPU time of the FORTRAN subroutines rounds the 2 milliseconds and seems to be competitive with other more sophisticated methods. Additionally, in appendix A the master equations to obtain the tensor coefficients up to the hexagon level in the external momenta convention are presented including the ones needed for small Gram determinants.
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