parity violating models to which our variable *is* sensitive do not need to abandon the equivalence principle, Lorentz invariance or isotropy, and (ii) noted that since $\alpha$ is defined in terms of only three objects the parity violating processes which $\alpha$ is sensitive to would probably include only those which couple to asymmetric initial states, such as quark-gluon.

In future work, it may be interesting to consider other event variables which depend on *two* or *four* (rather than three) final state momenta. A simple variable of the first sort might be the product $\Delta(\phi) \Delta(\eta)$ of the azimuthal and pseudorapidity differences between any two final state objects.[^10] Variables acting on four objects could show sensitivity to non-standard parity violating effects which do not need the initial state to provide an reference direction. One example would be the four-jet (longitudinal boost invariant) event-variable $\delta$ defined by: $$\begin{aligned}
    \delta \equiv \frac { 
        p^\mu({j_1})
    p^\nu({j_2})
    p^\sigma({j_3})
    p^\tau({j_4})
    \epsilon_{\mu\nu\sigma\tau} 
    } {
        p_T({j_1}) 
        p_T({j_2}) 
        p_T({j_3}) 
        p_T({j_4}) 
        }.
        \label{eq:delta}\end{aligned}$$ The numerator of $\delta$ is the archetypical Lorentz-invariant pseudoscalar, so is certainly invariant with respect to longitudinal boosts and capable of demonstrating non-standard parity violating effects. The numerator makes $\delta$ dimensionless, and is also invariant under longitudinal 