Revisiting Radiation Patterns in $e^+e^-$ Collisions

We propose four simple event-shape variables for semi-inclusive $e^+e^- \to 4$-jet events. The observables and cuts are designed to be especially sensitive to subleading aspects of the event structure, and allow to test the reliability of phenomenological QCD models in greater detail. Three of them, $\theta_{14}$, $\theta^*$, and $C_2^{(1/5)}$, focus on soft emissions off three-jet topologies with a small opening angle, for which coherence effects beyond the leading QCD dipole pattern are expected to be enhanced. A complementary variable, $M_L^2/M_H^2$, measures the ratio of the hemisphere masses in 4-jet events with a compressed scale hierarchy (Durham $y_{23}\sim y_{34}$), for which subleading $1\to 3$ splitting effects are expected to be enhanced. We consider several different parton-shower models, spanning both conventional and dipole/antenna ones, all tuned to the same $e^+e^-$ reference data, and show that a measurement of the proposed observables would allow for additional significant discriminating power between the models.