QCD antenna radiative spectrum in dense media within the Improved Opacity Expansion

TL;DR

This work extends the theory of jet–medium interactions by computing the double differential soft-gluon spectrum from a color-singlet $q\bar q$ antenna traversing a dense QCD medium within the Improved Opacity Expansion (IOE). By simultaneously incorporating single hard and multiple soft scatterings, the authors analytically reduce the full antenna cross-section to tractable expressions and reveal that rare hard (Molière) scatterings significantly alter the spectrum at large emission angles, accelerating color decoherence. The analysis decomposes the spectrum into LO and NLO interference contributions, with explicit in-in, in-out, and out-out components, and introduces regime-specific matching scales $Q_b$ and $Q_r$ to connect multiple soft scattering and single hard scattering limits. Numerical results show substantial NLO corrections (up to ~50%), with the decoherence pattern governed by a combination of the decoherence factor $\Delta_{\rm med}$ and kernel corrections, providing direct input for jet quenching phenomenology. The findings clarify the role of color decoherence in QCD matter and offer a framework for incorporating IOE-based antenna spectra into phenomenological models and Monte Carlo generators for heavy-ion collisions.

Abstract

We compute the double differential inclusive spectrum for the emission of a soft gluon from a color-singlet $q\bar q$ pair traversing a dense QCD medium. Our results extend the existing literature by simultaneously incorporating both single hard and multiple soft gluon exchanges between the jet and the medium -- an essential ingredient for a complete phenomenological description of jet quenching. Using the Improved Opacity Expansion framework, we provide an analytically tractable treatment, reducing the full cross-section to a set of simple expressions. Our analysis demonstrates that rare hard (Molière) scatterings significantly modify the gluon spectrum at large angles, accelerating the loss of color coherence between the initial quarks. We further quantify whether the modifications are driven by an overall weakening of the interference term, or by more detailed modifications to the fragmentation pattern. Our results provide a direct input for phenomenological jet quenching studies, offering new insights into the role of color decoherence in QCD matter.

Figures (7)

• Figure 1: Three separate contributions to the QCD antenna gluon emission spectrum in Eq. \ref{['eq:AntennaSpectrumDef']}: two direct terms $\mathcal{R}_q$ (left), $\mathcal{R}_{\bar{q}}$ (middle) and interference term $\mathcal{J}$ (right). The gray box denotes the presence of a background medium with a finite extension.
• Figure 2: Time dependence of the decoherence factor $\left(1-\Delta_{\rm med}\right)$ defined in Eq. \ref{['eq:CoherenceFDef']} for three different opening angles: $\theta_{q\bar{q}} = 0.05,\, 0.1\,,0.25$. The solid lines represent the decoherence factor calculated using the full dipole potential defined in Eq. \ref{['eq:DipolePotentialGW']}, while the dashed lines use the harmonic oscillator potential defined in the text just above Eq. \ref{['eq:KLO']}.
• Figure 3: Diagram corresponding to gluon emission off a single quark inside a medium, illustrating the calculation in Eq. \ref{['eq:QuarkGluonSpectrum']}.
• Figure 4: Antenna radiation spectrum at LO, with $\Delta_{\rm med}$ calculated using the harmonic oscillator approximation (black curves) and using the full dipole potential in Eq. \ref{['eq:DipolePotentialGW']} (red curve). The two black curves correspond to different choices of matching scale in the expansion of the decoherence factor $\Delta_{\rm med}$ to leading-order (Eq. \ref{['eq:decoherence_factor_expansion']}) --- the solid line has $\log(Q_1^2/\mu_{\ast}^2) = 1$ and the dashed line has $Q_2 = 5\,Q_1$. A shaded band is drawn between the solid and dashed curves. Each pair of panels corresponds to a different value of $\theta_{q\bar{q}}$, the left one to $\omega=0.05,\omega_c$ and the right one to $\omega = \omega_c$.
• Figure 5: Antenna radiation spectrum at LO with $\Delta_{\rm med}$ calculated in the harmonic approximation, choosing the matching scale such that $\log{Q_{\Delta}^2/\mu_{\ast}^2}=1$ (black), at LO with $\Delta_{\rm med}$ calculated using the full dipole potential as in Eq. \ref{['eq:DipolePotentialGW']} (blue) and at LO+NLO (red). Each pair of panels corresponds to a different value of $\theta_{q\bar{q}}$, the left one to $\omega=0.05,\omega_c$ and the right one to $\omega = \omega_c$. The plot below each pair of panels shows the ratio between the NLO correction and the LO+NLO result.