  Anomalous self-interactions of non-abelian gauge fields can be described by
higher dimensional operators featuring gauge-invariant combinations of the
field strengths. In the case of QCD, the gluon self-interactions start to be
modified at dimension six by operators of the type $GGG$, with $G$ the gluon
field strength tensor, possibly leading to deviations in all observables and
measurements that probe strong interactions at very small distances. In this
work we consider the sensitivity to the triple gluon operator of a series of
observables at the LHC in di-jet, three- and multi-jet final states and
heavy-quark production. We critically re-examine the robustness of
long-standing as well as more recent proposals addressing issues such as the
validity of the EFT expansion and the impact of higher order QCD corrections.
Our results support the conclusion that multi-jet observables can reliably
bound these anomalous interactions to the level that their impact on other key
observables at the LHC, involving for example top quark and Higgs production,
can be safely neglected. We also highlight the potential of using previously
suggested angular observables in three-jet events at the LHC to further
constrain these interactions.
