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We extend our previous work on scattering amplitudes [1] to hadroncollisions. We provide a general formalism for the computation of eikonalamplitudes squared for the radiation of soft and energy-ordered gluons offthree hard-legs at finite-N$_c$ to any order in the perturbative expansion.Examples of three-hard legs processes include vector/Higgs boson production inassociation with a single hard jet and dijet production in DIS. Explicitexpressions for the radiation of up to four gluons are provided as anillustration of the formalism.

Eikonal amplitudes for three-hard legs processes at finite-N$_c$