Unified description of longitudinal and transverse parton dynamics in cold nuclear matter

We present a unified description of longitudinal momentum evolution and transverse-momentum broadening in cold nuclear matter using soft collinear effective theory with Glauber gluon interactions (SCET${}_{\mathrm{G}}$). In a finite nucleus, Landau–Pomeranchuk–Migdal interference couples medium-induced energy loss to the transverse scale resolved by the observable. Our framework combines RG evolution of impact-parameter-dependent energy loss with BFKL-type rapidity evolution of the collision kernel, improved by kinematical constraints and running coupling. With a common set of cold-nuclear-matter parameters, it accounts for the main nuclear modification patterns in semi-inclusive DIS and Drell–Yan production and provides predictions for TMD hadron multiplicities at the EIC. We also discuss the one-point energy correlator in DIS, whose energy weighting suppresses the leading final-state energy-loss contribution. In the EIC kinematics studied, the residual dynamical corrections are small, leaving the nuclear modification dominated by the initial-state nuclear parton distributions.