Radiation from a gluon-gluino colour-singlet dipole at N${}^3$LO

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 ${\alpha }_s$, 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 $\mathcal{O}({\alpha }_s^3)$: 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.

Comments: 55 pages, 2 figures, 5 tables, ancillary files