Renormalization Group Evolution for In-medium Energy Correlators

TL;DR

This work establishes a first-principles RG framework for the in-medium two-point energy-energy correlator (EEC) in jets traversing QCD matter using SCET$_{ m G}$ with Glauber exchanges. By computing medium-modified jet functions at finite opacity and performing leading-log resummation, it identifies an experimentally accessible regime where medium corrections appear as shifts to the EEC anomalous dimensions, regulated by the Debye mass through a Coulomb logarithm. The analysis yields analytic and numerical results for $p$-Pb data and realistic projections for O–O, showing characteristic small-angle suppression and large-angle enhancement due to medium-induced broadening and energy redistribution. The approach provides a model-independent baseline for constraining jet evolution in QCD matter and offers a path toward extracting medium properties from jet substructure observables with controlled theoretical uncertainties. Overall, the paper links medium parameters directly to RG evolution of an infrared-safe observable, enabling robust tests of QGP dynamics in small collision systems and guiding future extensions to higher orders and heavier flavors.

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.

Figures (11)

• Figure 1: An illustration of the EEC of exclusive jets in the vacuum and after it is modified in a thin medium. In the asymptotic region, the EEC in the vacuum takes a power-law form with the time-like anomalous dimension $\gamma(\alpha_s) = \sum_{n=0} \left(\frac{\alpha_s}{4\pi}\right)^{n+1}\gamma_T^{{\rm vac}, (n)}$. It is also known that medium correction significantly modify the large-angle behavior of EEC, as shown by the red solid line. In this paper, we identify an important medium-induced resummation effect in the region $\Lambda_{\rm QCD}/p_T \ll \theta\ll 1/\sqrt{p_T L_{\rm eff}}$, resulting in a medium correction $\Delta\gamma(\alpha_s)$ to the vacuum $\gamma(\alpha_s)$. This is illustrated by the red dashed line.
• Figure 2: Feynman diagrams that contributes to the TMD splitting functions at the amplitude level that are relevant for the calculation at opacity $N=1$. The red gluons are the Glauber gluon medium interactions.
• Figure 3: Left: numerical results for the non-contact contribution to the energy--energy correlator in the vacuum (black dashed line) and with medium correction at first order in opacity (black solid line) for $p_T = 200~\mathrm{GeV}$. The "brick" medium has a constant temperature $T=0.4$ GeV with maximum length $2$ fm and the medium-modified EEC shows the transition across the characteristic angular scales $\theta_{\mathrm{LPM}}$. Right: only plotting the medium-induced non-contact component (RR + RV channels) normalized by $\alpha_s^2 \rho_{\mathrm{eff}}L_{\rm eff}^3 \ln \frac{p_T}{L_{\rm eff} m_{\rm eff}^2}$, as motivated by the analytic calculation of exponentially decaying medium. Different lines correspond to the variations of the jet $p_T$, the effective path length, and the screening mass of the brick medium. They all collapses curves, corroborating the leading poser dependence on medium parameters and the presence of the Coulomb logarithm $\ln \frac{p_T}{L_{\rm eff}^+ m_{\rm eff}^2}$.
• Figure 4: Schematic illustration of the scale hierarchies relevant to the Coulomb logarithm and EEC evolution. The upper panel shows the vacuum case, where the EEC evolution is governed by collinear logarithms of radiation. The lower panel shows the in-medium case, where Glauber interactions introduce an additional Coulomb logarithm regulated by the Debye mass, modifying the evolution of the jet and the EEC.
• Figure 5: Left: the numerical calculation of jet energy loss with a screening mass $m_{\rm eff}$. A variations in the values of $R$, $m_{\rm eff}$, and $L_{\rm eff}$ in a constant brick medium confirms the scaling of the jet radiative energy loss as a function of $m_{\rm eff}L_{\rm eff}\tan\frac{R}{2}$. Right: for asymptotically high jet energy, the radiative energy loss of a jet is independent of jet $p_T$.