Light quark and gluon jet quenching in heavy ion collisions is described within the overwhelming majority of models as resulting predominantly from pQCD-type gluon radiation,
but details of the underlying mechanisms differ greatly.
One key difference lies in the treatment of the Altarelli-Parisi, AP, splitting functions.
While in some models, such as Q-PYTHIA, the splitting functions are directly modified in the medium, this core component remains unchanged in others (e.g. YaJEM).
It has been shown that the shared momentum fraction $z_g$ can be made a Sudakov-safe measurement .
This quantity measures the $p_T$ ratio between the two dominant branches
as determined by the SoftDrop grooming process.
We will present the first study of $z_g$ measurements at top RHIC energy in p+p and Au+Au.
The focus will be on the specific di-jet selection introduced in our previous momentum imbalance measurement,
i.e. jets geometrically matched to ``hard core'' jets found using
only constituents above 2 GeV/$c$ and with a high tower above 5.5 GeV .
Such di-jet pairs were found to be significantly imbalanced with respect to p+p, yet regained balance when all soft constituents were included.
Individual examination of the splitting behavior of leading and recoil jet adds a new
dimension to this observation, and new input to energy loss models.
 A. J. Larkoski, S. Marzani and J. Thaler, Phys. Rev. D 91, no. 11, 111501 (2015) [arXiv:1502.01719 [hep-ph]].
 K. Kauder (STAR Collaboration), Nuclear and Particle Physics Proceedings, Hard Probes 2015