the three-jet system for the example configuration described in the text. \[fig:BetaDependence\] ](Figures/Plot_BetaStarDependence){width="0.93\linewidth"}

Note that magnitude of $\sin\alpha$ is not invariant under longitudinal boosts of the system of three jets. Even the sign of $\alpha$ can be altered by longitudinal boosts for certain jet momenta. Consider, for example, a co-planar set of jet momenta such as ${{\vec p^{{j_1}}}}=(3,0,0)$, ${{\vec p^{{j_2}}}}=(0,2,0)$ and ${{\vec p^{{j_3}}}}=(1,1,0)$. As these are co-planar they have $\alpha=0$. If those momenta are then given a longitudinal boost, the value of $\sin\alpha$ ceases to be zero, but boosts in one direction generate equal and opposite values of $\alpha$ to boosts in the other direction.[^6] Consequently, any search for a new physics process which generates an $\alpha$-asymmetry in the frame of the hard process must contend with the possibility that such an asymmetry might be partly ‘washed away’ by the longitudinal boosts which relate the hard-process frame (HPF) to the lab frame (LF). Evidently, the sort of processes most easily washed away would be those which have three co-planar (or almost co-planar) final-state momenta in the HPF and are generated from initial states (such as gluon-gluon or quark-quark) whose hard processes have symmetrically distributed longitudinal boosts.

Given that a large 