In-Medium Parton Cascades in QGP

• In-medium parton cascades are QCD branching processes in dense quark-gluon plasma that unify vacuum and medium-induced effects to modify jet fragmentation.
• Democratic branching drives turbulent energy transport, leading to jet quenching and angular broadening as evidenced by experimental observations.
• Theoretical frameworks combining modified DGLAP evolution, transport equations, and Monte Carlo simulations provide precise tools to extract QGP transport coefficients.

In-medium parton cascades refer to the quantum chromodynamics (QCD) branching and transport processes undergone by highly energetic quarks and gluons as they traverse hot, dense QCD matter—most notably, the quark–gluon plasma (QGP) produced in nucleus–nucleus collisions. Experimental evidence from RHIC and the LHC has shown that the QCD medium induces substantial modifications to the traditionally vacuum fragmentation process, altering jet energy, angular profiles, and hadron composition. Theoretical developments, building upon standard DGLAP evolution and incorporating medium-induced radiative and collisional effects, have established a rich phenomenology described by modified fragmentation functions, transport equations, and scaling laws. These features—jet quenching, enhanced angular broadening, altered hadrochemistry, and turbulent energy flow—provide essential probes of the microscopic properties of the QGP.

1. Medium-Modified Parton Cascade Evolution

The evolution of parton cascades in a medium is formulated by supplementing the standard DGLAP splitting probabilities with an additional term that accounts for medium-specific processes. The total in-medium splitting probability reads

$$P^{\mathrm{tot}}(z) = P^{\mathrm{vac}}(z) + P^{\mathrm{med}}(z, t)$$

with $P^{\mathrm{vac}}(z)$ the vacuum DGLAP splitting function and $P^{\mathrm{med}}(z, t)$ obtained from the spectrum of medium-induced gluon radiation. In the multiple-scattering approximation,

$$P^{\mathrm{med}}(z, t) \simeq 2\pi t \frac{dI^{\mathrm{med}}}{dz dt}$$

so the medium-induced emission spectrum acts as an additional source of splittings.

Energy–momentum conservation at each branching, modified virtuality evolution, and the unification of vacuum and medium-induced branchings in a single DGLAP-type formalism provide a transparent and robust framework. At high energy and virtuality standard (vacuum-like) behavior is naturally recovered; at lower scales, medium corrections dominate, enhancing the probability for multiple democratic branchings and soft emissions.

2. Democratic Branching and Turbulent Energy Transport

A defining property of in-medium cascades is the democratic (quasi-democratic) nature of gluon branchings: in contrast with vacuum showers, where asymmetric (soft-dominated) splittings are enhanced, medium-induced branchings favor nearly equal energy sharing. The splitting rate for a gluon with energy $\omega$ and splitting fraction $z$ is

$$P_{\mathrm{br}}(z, t) = \frac{\alpha_s}{2\pi} \frac{P_{g \to g}(z)}{\tau_{\mathrm{br}}(z, \omega)}$$

with

$$\tau_{\mathrm{br}}(z, \omega) = \sqrt{ \frac{z(1-z) \omega}{\hat{q}} }$$

where $\hat{q}$ is the jet quenching parameter.

This almost symmetric splitting kernel drives the development of a turbulent cascade, in which the energy spectrum at small $x = \omega/E$ exhibits a universal scaling behavior

$D(x) \propto \frac{1}{\sqrt{x}}$

as first described in the context of wave turbulence in in-medium cascades (Blaizot et al., 2013, Blaizot et al., 2015). This scaling is a direct consequence of a balance between gain and loss terms across the cascade, and translates into the efficient transfer of energy from leading partons to very soft quanta at large angles—an essential component in explaining experimental dijet asymmetry.

3. Transport, Broadening, and Nonradiative Effects

In addition to radiative branching, a hard parton encounters both transverse and longitudinal momentum exchanges, governed by the jet transport coefficients $\hat{q}$ (for transverse broadening) and $\hat{e}$, $\hat{e}_2$ (for longitudinal drag and diffusion). The combined effect of multiple scatterings is captured by the master equation

$$\frac{\partial \phi}{\partial L^-} = D_{L1} \frac{\partial}{\partial l_q^-} + \frac{1}{2} D_{L2} \frac{\partial^2}{\partial (l_q^-)^2} + \frac{1}{2} D_{T2} \nabla_{l_{q\perp}}^2 \phi$$

where $D_{L1}$, $D_{L2}$ and $D_{T2}$ are the transport coefficients for drag, longitudinal diffusion, and transverse broadening respectively (Qin et al., 2012). This framework unifies elastic energy loss and diffusive processes, which, together with radiative contributions, shape both the angular and longitudinal fragmentation patterns observed in the final state.

4. Color Decoherence and Angular Modifications

Color decoherence and the destruction of interference are fundamental mechanisms through which the medium alters not just energy loss rates but the angular and azimuthal structure of parton showers. The rate and angular distribution of medium-induced gluon emission from a color antenna (e.g., a $q\bar{q}$ pair) is sensitive to the degree of color coherence maintained between emitters. The decoherence parameter

$$\Delta_{\text{med}} \approx 1 - \exp \left( -\frac{1}{12} \hat{q} \theta_{q\bar{q}} L^3 \right)$$

encapsulates the onset of anti-angular ordering: in the limit of an opaque medium the destructive interference between antennas is lost and emissions proceed incoherently, generating substantial radiation at large angles (Apolinário et al., 2015). A critical outcome is the breakdown of angular ordering—a haLLMark of QCD coherence in vacuum—leading to enhanced population of the jet periphery and large-angle broadening.

5. Experimental Signatures and Observables

Experimental measurements at RHIC and the LHC provide direct evidence for the key signatures predicted by in-medium cascading dynamics:

• Suppression of high-$p_T$ hadrons and jets (jet quenching), as quantified by the nuclear modification factor $R_{AA}$, is a direct manifestation of energy loss via in-medium cascades.
• Hadronic composition effects: K/π and p/π ratios increase by 50–100% relative to vacuum, indicative of a softened cascade and altered hadrochemistry (0804.2021).
• Angular broadening and energy flow at large angles: Significant jet energy emerges as soft particles at large angles (θ ~ 0.6–0.7 radians), reflecting the turbulent transport and color decoherence of the in-medium cascade (Neufeld et al., 2011).
• Dijet asymmetry: The observed asymmetry in dijet energies in Pb–Pb collisions can be traced to the outflow of jet energy via quasi-democratic medium-induced branchings (Blaizot et al., 2013, Iancu, 2013).

Advanced jet reconstruction techniques—including γ-tagged jets (CMS), full jet and hadron-jet correlation analyses (ALICE, ATLAS)—enable the isolation and measurement of medium-modified fragmentation functions. Systematic uncertainties achieved are on the 10–40% level, with ongoing improvements anticipated as LHC detector capabilities advance.

6. Monte Carlo Implementations and Modeling Frameworks

Modern simulation approaches incorporate probabilistic treatments of both collisional and radiative interactions, accounting for quantum interference and the Landau–Pomeranchuk–Migdal (LPM) effect. Probabilistic algorithms update the parton formation time with each scattering, ensuring proper quantum coherence and energy–momentum conservation. Monte Carlo models can be validated against analytical BDMPS-Z results by confirming the path-length squared ($L^2$) scaling of the energy loss (Coleman-Smith et al., 2011). Simulations now routinely integrate both vacuum and medium effects, and account for the time-evolution of the QGP (including expansion and temperature dependence) (Martin et al., 2015, Adhya et al., 2022).

Mean-field and path-integral formalisms are used to handle color rotations and the stochastic evolution of partons, with explicit combinatoric analysis of color structures necessary for predictions of multi-partonic cascades. The inclusion of realistic interaction models and decoherence parameters is critical for the high-precision prediction of jet substructure and for the extraction of medium transport coefficients from data (Andres et al., 29 Aug 2025).

7. Theoretical and Phenomenological Implications

The unified DGLAP-based treatment, modified by medium-induced radiation and realistic scattering rates, provides a transparent bridge between vacuum and in-medium fragmentation, enabling systematic investigation of jet quenching phenomena. The emergence of universal scaling relations—such as the quark-to-gluon ratio in the inertial range and the turbulent energy transport spectrum—provides concrete predictions linking QCD perturbative dynamics to observables in relativistic heavy-ion collisions (Mehtar-Tani et al., 2018).

Key implications include:

• Robust criteria for the onset of decoherence and anti-angular radiation in QGP tomography.
• Sensitivity of cascade evolution to the time-dependent and spatial profile of the medium, impacting the extraction of transport coefficients from jet $v_2$ and rapidity-dependent $R_{AA}$ (Adhya et al., 2022).
• Potential for precision constraints on models of QGP thermalization and for discriminating between radiative and collisional energy loss mechanisms via studies of angular and multiplicity correlations in heavy-flavor jets (Rohrmoser et al., 2016).

In-medium parton cascades therefore constitute a cornerstone for both theoretical advances in non-equilibrium QCD and practical extraction of QGP properties from experimental data, underpinning the contemporary program of jet tomography in heavy-ion physics.