PT Journal AU Llanes Jurado, J Rodrigo, G Torres Bobadilla, WJ TI From Jacobi off-shell currents to integral relations SO Journal of High Energy Physics JI J. High Energy Phys. PY 2017 BP 122 EP 22pp VL 12 IS 12 DI 10.1007/JHEP12(2017)122 LA English DE NLO Computations; QCD Phenomenology AB In this paper, we study off-shell currents built from the Jacobi identity of the kinematic numerators of gg -> X with X = ss, q (q) over bar, gg. We find that these currents can be schematically written in terms of three-point interaction Feynman rules. This representation allows for a straightforward understanding of the Colour-Kinematics duality as well as for the construction of the building blocks for the generation of higher-multiplicity tree-level and multi-loop numerators. We also provide one-loop integral relations through the Loop-Tree duality formalism with potential applications and advantages for the computation of relevant physical processes at the Large Hadron Collider. We illustrate these integral relations with the explicit examples of QCD one-loop numerators of gg -> ss. ER