\cdot {{\vec p^{{j_3}}}}$, computed from the three jet three-momenta ${{\vec p^{{j_1}}}}$, ${{\vec p^{{j_2}}}}$ and ${{\vec p^{{j_3}}}}$ ordered by the requirement $$\begin{aligned}
p_T({j_1})\ge p_T({j_2}) \ge p_T({j_3})\label{eq:ptordering}.\end{aligned}$$Though the scalar triple product has the beneficial property of changing sign under parity, $({{\vec p^{{j_1}}}}, {{\vec p^{{j_2}}}}, {{\vec p^{{j_3}}}}) \rightarrow (-{{\vec p^{{j_1}}}},- {{\vec p^{{j_2}}}},-{{\vec p^{{j_3}}}})$, it has the disbenefit that it varies not only with the directions but also linearly with the magnitudes of each of the momenta. We therefore choose instead to use a normalised variant whose dependence is primarily on the directions of the momenta:[^5] $$\begin{aligned}
   \frac{{{\vec p^{{j_1}}}}\times {{\vec p^{{j_2}}}}}{|{{\vec p^{{j_1}}}}\times {{\vec p^{{j_2}}}}|}
    \cdot \frac{{{\vec p^{{j_3}}}}}{ |{{\vec p^{{j_3}}}}|} = \sin\alpha.\end{aligned}$$ We have denoted this quantity ‘$\sin \alpha$’ since it may be interpreted as the sine of the angle $\alpha$ which momentum ${{\vec p^{{j_3}}}}$ makes with the plane spanned by ${{\vec p^{{j_1}}}}$ and ${{\vec p^{{j_2}}}}$, as shown in Figure \[fig:Alpha\]. Positive angles $\alpha$ occur if and only if ${{\vec p^{{j_3}}}}$ is on the same side of that plane as ${{\vec p^{{j_1}}}}\times {{\vec p^{{j_2}}}}$.

![Dependence of $\alpha$ on the longitudinal velocity $\beta$ of the three-jet system for the example configuration described in the text. \[fig:BetaDependence\] ](Figures/Plot_Plane.pdf){width="1.0\linewidth"}

![Dependence of $\alpha$ on the longitudinal velocity $\beta$ of 