Renormalization Group Evolution for In-medium Energy Correlators

Abstract: We present a first-principles analysis of the renormalization group (RG) evolution of the two-point energy-energy correlator (EEC) in light-quark and gluon jets propagating through nuclear matter. Our work focuses on the analytic structure of the RG equations in the thin-medium regime, highlighting how collinear emissions in the presence of a dense QCD medium reshape the EEC observables. We work in the opacity expansion of the SCET$_{\rm G}$ formalism, where the propagating quarks and gluons interact with the medium via Glauber gluon exchanges. We compute the corresponding one-loop jet functions using the medium-induced splitting kernels at first order in opacity and perform resummation at leading logarithmic (LL) order. In particular, we identify an experimentally accessible regime of jet energies and EEC angles where one can directly investigate the medium-induced scale evolution and extract the corresponding opacity-one correction to the anomalous dimensions. Furthermore, we demonstrate analytically, using the method of regions, the Coulomb-logarithmic enhancement regulated by plasma screening for EEC. We compare our theoretical predictions with experimental data in $p$-Pb collisions and make projections for O-O collisions to test whether energy correlators could serve as sensitive probe of the quark-gluon plasma (QGP) dynamics in small collision systems, offering a robust and model-independent avenue for constraining jet evolution in QCD matter.