to the LF [^9].

In contrast, asymmetric initial states (such as quark-gluon) *are* capable of distinguishing forward and backward directions in the HPF, and so *are* (at least in principle) able to generate detectable lab-frame asymmetries in $\alpha$. It is important to realise that such asymmetries could be seen even for Lorentz- and rotationally-invariant $2\rightarrow 3$ new-physics processes having final state momenta which are co-planar in the HPF. It is differences between the forward and backward boosts from parton distribution functions which would drive such an asymmetry, *exploiting* the dependence of $\alpha$ on longitudinal boosts. Given the asymmetry is generated by this mechanism, there is some motivation for biasing the signal region to events in which the three-jet system has a high absolute rapidity.

In summary: the three-jet variable which we have called $\alpha$ can (in principle) detect parity-violating effects in a broad class of new-physics models at the LHC. As the particular variable we used to illustrate our search is just one of many that could have been chosen, we make no claims of optimality – indeed we have highlighted many situations in which it has no sensitivity to anomalous parity violation whatsoever. Nonetheless, we have: (i) demonstrated that 