  The nuclear modification of jet splitting in relativistic heavy-ion
collisions at RHIC and the LHC energies is studied based on the higher twist
formalism. Assuming coherent energy loss for the two splitted subjets, a
non-monotonic jet energy dependence is found for the nuclear modification of
jet splitting function: strongest modification at intermediate jet energies
whereas weaker modification for larger or smaller jet energies. Combined with
the smaller size and lower density of the QGP medium at RHIC than at the LHC,
this explains the CMS-STAR groomed jet puzzle -- strong nuclear modification of
the momentum sharing $z_g$ distribution at the LHC whereas no obvious
modification of the $z_g$ distribution at RHIC. In contrast, the observed
nuclear modification pattern of the groomed jet $z_g$ distribution cannot be
explained solely by independent energy loss of the two subjets. Our result may
be tested in future measurements of groomed jets with lower jet energies at the
LHC and larger jet energies at RHIC, for different angular separations between
the two subjets.
