A theoretical framework aims to bring three parts of high-energy jet physics into the same calculation: soft radiation produced in vacuum, energy lost inside a quark–gluon plasma, and the loss of color coherence between parts of a jet. The work is built around threshold factorization, a way of separating the different radiation scales that matter when a jet is produced close to an energy threshold.
Its central proposal is that the medium can be folded into the starting condition of the calculation rather than changing the ultraviolet evolution that follows. In the model, medium-induced energy loss and color decoherence enter through a soft-collinear boundary condition, while the later evolution remains vacuum-like under the stated time-scale hierarchy.
A calculation built in layers
In the threshold limit, where N is much greater than 1, the jet function is refactorized into collinear pieces and soft-collinear operators made from light-like Wilson lines. Terms suppressed by powers of 1/N are left out, so the construction applies within that approximation.
The analytic calculation first determines the one-loop anomalous dimension for a single collinear mode, which describes how that component changes with the resolution scale. More complicated, higher-multiplicity configurations are then handled with nonlinear evolution equations rather than by calculating every configuration independently.
In the large-Nc limit, where the number of color charges is treated as large, the coupled hierarchy of operators closes into a color-singlet dipole equation. The authors identify this equation with the BMS/BK equation, giving the nonlinear part of the framework a tractable form.
What changes inside the plasma
For the dense, weakly coupled and extended plasma considered in the study, the proposed medium-modified boundary condition reproduces the BDMPS-Z radiation spectrum. Within the model, that includes the Landau–Pomeranchuk–Migdal effect, in which emissions are influenced by interference over the medium, as well as the color coherence of a two-pronged jet.
The treatment divides a two-pronged system into two regimes according to the medium coherence angle. Below that angle, the pair is treated as a single color charge for energy-loss purposes. Above it, the medium resolves the two prongs, and the model treats their energy loss independently.
A background-field formulation underpins the medium matching. It separates fast and slow gauge-field modes according to their light-cone momentum component.
The coherence scale keeps shrinking
After the evolution is resummed, the modeled decoherence angle falls exponentially with the amount of evolution. In practical terms, the angular range over which the two prongs retain their shared color coherence becomes progressively smaller as the calculation evolves.
The asymptotic analysis gives numerical coefficients of about 2.44 for the leading term and 1.20 for a subleading term in that coherence-angle behavior. These are asymptotic analytical results without reported error intervals.
The authors also draw a formal connection with small-x gluon saturation. They assign analogous roles to the nonlinear high-energy-QCD operators used in saturation studies and to the operators governing medium color decoherence. The comparison is theoretical: it links the structures of the equations rather than validating either description with data.
A softer suppression in an illustrative model
The framework is used in an approximate calculation of inclusive jet suppression, expressed through R_AA. In that illustration, including the nonlinear term is associated with substantial taming of the suppression of the modeled jet spectrum at large transverse momentum. The result is qualitative and model-dependent; the study does not report a measured effect size.
That example is not a complete phenomenological prediction. The simplified large-medium treatment leaves out subsequent branchings of primary emitted gluons, and the paper notes that a full treatment would need to include multiple branching processes. More generally, the framework depends on the threshold approximation, the large-Nc closure and the assumed separation between the hard process and the medium.
The document is an arXiv preprint marked as prepared for submission to JHEP. Its analytical and illustrative results still need to be tested through full numerical evolution with realistic medium boundary conditions and through quantitative comparison with jet-suppression and jet-substructure measurements.
Paper data and sources
Original title: Color Coherence and the Soft Structure of QCD Jets in Vacuum and the QGP
Authors: Paul Caucal, Yacine Mehtar-Tani
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text