Cone-Dependent Jet Collisional Energy Loss in Finite QCD Medium

TL;DR

This work develops a compact HTL-resummed framework for jet collisional energy loss in a finite-size QCD medium by defining the jet energy inside a cone of radius $R$ and computing the out-of-cone energy transfer. It extends the finite-size HTL calculation from a single parton to jets, explicitly separating the primary-jet and recoiling medium contributions and interpolating between the partonic limit ($R\to0$) and full cone recovery ($R\to\pi$). The authors implement improvements beyond strict HTL by using a self-consistent Debye mass $\mu_E(T)$ and a running coupling $\alpha_S(Q^2)$, and provide detailed numerical results for light and heavy flavor jets, including the impact of medium response from the $\omega<0$ sector. Key findings are a pronounced non-linear $R$-dependence of the elastic out-of-cone loss, a potential to dominate over radiative energy loss at large jet radii, near-linear path-length scaling with modest finite-size corrections, and a non-negligible medium-response contribution (up to ~15% for certain $R$). These results offer a quantitative baseline for incorporating cone-restricted elastic energy transport and recoil in jet-quenching phenomenology.

Abstract

We derive a compact HTL-resummed expression for the leading-order jet collisional energy loss in a finite-size, finite-temperature QCD medium. Defining the jet energy inside a cone of radius $R$, we obtain the out-of-cone elastic energy loss with an explicit separation between contributions from the primary jet parton and recoiling medium partons. The result reproduces the known partonic limit as $R\!\to\!0$, vanishes for $R\!\to\!π$, and applies to both light- and heavy-flavor jets. Numerically, the elastic component shows a pronounced non-linear $R$ dependence relative to the radiative baseline, and its importance increases with $R$, becoming comparable to or exceeding the radiative contribution for sufficiently large jet radii. The path-length dependence remains close to linear for all $R$, while the medium-response contribution can exceed $10\%$ for realistic jet radii.

Figures (4)

• Figure 1: Fractional energy loss $\Delta E^{(R)}/E$ of light-quark jets as a function of jet (parton) energy $E$ for a medium path length $L=4~\mathrm{fm}$. Solid curves show the collisional contribution and dashed curves show the radiative contribution Karmakar:2024fkn. Results are shown for a parton ($R=0$) and for jets with cone radii $R=0.2$, $0.4$, and $0.6$, as indicated in the legend.
• Figure 2: Collisional fractional energy loss and its cone dependence for light-, charm-, and bottom-quark--initiated jets at $L=4~\mathrm{fm}$. Left panel: $\Delta E^{(R)}_{el}/E$ as a function of $E$ at fixed cone radius $R=0.4$. Right panel: ratio $\Delta E^{(R)}_{el}/\Delta E^{(0)}_{el}$ as a function of the jet cone radius $R$ at fixed energies $E=10$, $50$, and $200~\mathrm{GeV}$ (line styles), shown for light-, charm-, and bottom-quark--initiated jets (colors).
• Figure 3: Collisional fractional energy loss $\Delta E^{(R)}_{el}/E$ as a function of path length $L$ for light-quark--initiated jets with $E=50~\mathrm{GeV}$. Solid curves correspond to the finite-size calculation and dashed curves to the infinite-medium (large-$L$) limit. Results are shown for a parton ($R=0$) and for jets with cone radii $R=0.2$, $0.4$, and $0.6$, as indicated in the legend.
• Figure 4: Medium-response effect (in percent) for collisional energy loss of light-quark--initiated jets, defined as $\frac{\Delta E^{(R)}_{\rm el,no\,resp}-\Delta E^{(R)}_{\rm el}}{\Delta E^{(R)}_{\rm el}}$, where $\Delta E^{(R)}_{\rm el}$ denotes the collisional energy loss including medium response. Left: medium-response effect as a function of jet (parton) energy $E$ at fixed path length $L=5~\mathrm{fm}$. Right: medium-response effect as a function of path length $L$ at fixed energy $E=100~\mathrm{GeV}$. Curves correspond to the light-quark parton limit ($R=0$) and to jets with cone radii $R=0.2$, $0.4$, and $0.6$, as indicated in the legend.