Abstract
We compute the quantum chromodynamics (QCD) corrections to the decay of a neutralino to gluinos and partons at next-to-next-to-next-to-leading order (N$^{3}$LO) in the strong coupling constant α$_{s}$, integrated separately over the phase-space of two, three, four or five particles in the final state. The resulting matrix elements are related to the quark-gluon antenna functions, completing the set of integrated antenna functions in final-final kinematics required for the extension of the antenna subtraction scheme to N$^{3}$LO. For a model with massless partons (quarks and gluons) and an arbitrary number of adjoint fermions, we obtained the following new results to $ \mathcal{O}\left({\alpha}_s^3\right) $: the inclusive cross section for the decay of a neutralino, the renormalization of the effective coupling of a neutralino to a gluino and gluon(s), the gluino collinear anomalous dimension, the gluino contribution to the parton collinear anomalous dimensions and the neutralino-gluino-gluon(s) vertex form factors. A special case of this model is the $$ \mathcal{N} $$ = 1 super Yang-Mills theory, where we can relate some of our findings to known results.
Chen, Xuan