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

TL;DR

This paper calculates high-order QCD corrections to neutralino decay into gluinos and partons, extending the antenna subtraction scheme to N$^3$LO and providing new theoretical results relevant for supersymmetric models.

Contribution

The paper extends the antenna subtraction scheme to N$^3$LO for neutralino decay, providing new integrated antenna functions and related theoretical results for massless partons and supersymmetric models.

Findings

Computed the N$^3$LO QCD corrections to neutralino decay.

Derived the gluino collinear anomalous dimension.

Related findings to $ ext{N}=1$ super Yang-Mills theory.

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.