Jet Substructure Modifications in QGP

Updated 13 November 2025

Jet substructure modifications are changes in the internal structure of high-energy QCD jets caused by interactions with quark–gluon plasma, including energy loss and medium-induced radiation.
Key observables such as jet mass, angularities, and groomed momentum fractions provide insights into the interplay of radiative energy loss, elastic broadening, and medium response.
Advanced Monte Carlo models and bias-reduction strategies enable the precise extraction of QGP transport properties, facilitating improved understanding of jet–medium interactions.

Jet substructure modifications refer to the changes induced in the internal structure of QCD jets when high-energy partons traverse a dense QCD medium such as the quark–gluon plasma (QGP). These modifications encode essential information about jet–medium interactions, including partonic energy loss, medium-induced radiation, color decoherence, and the hydrodynamic response of the plasma. Through precise measurements and sophisticated Monte Carlo and analytic techniques, the study of these modifications enables quantitative tomographic extraction of QGP transport properties.

1. Theoretical Foundations of Jet Substructure Modification

Jet substructure observables are sensitive to both perturbative and nonperturbative mechanisms that affect QCD parton showers in a medium. Core processes include:

Radiative energy loss: High-energy partons lose energy via medium-induced gluon emissions, governed by the transport coefficient $\hat q$ .
Elastic broadening and drag: Collisions with medium constituents impart transverse momentum broadening ( $\hat q$ ) and energy loss ( $\hat e$ ).
Color decoherence and medium resolution: The ability of the QGP to resolve substructures is controlled by the decoherence parameter $S_2(t) = \exp[ -(1/12)\hat q\theta^2 t^3 ]$ and the critical angle $\theta_c \sim (\hat q L^3)^{-1/2}$ ; only splittings with $t_f < t_d(\theta)$ are resolved as separate emitters (Tywoniuk et al., 2018).
Medium response (wake): Jets deposit energy and momentum into the QGP, creating a hydrodynamic wake that manifests as a correlated excess of soft, large-angle hadrons within or around the jet cone.

These effects are intertwined, and their interplay determines the modification patterns observed in jet substructure observables, such as the jet mass, angularities, splittings (e.g., $z_g$ , $r_g$ ), and N-subjettiness ratios.

2. Experimental Probes: Observables, Methods, and Grooming

Modern jet substructure studies employ a suite of observables and analysis techniques:

Key Observables

Jet mass: $m^2 = (\sum_i p^\mu_i)^2$ ; sensitive to the radiation pattern’s hardness and angular spread.
Angularities: $\lambda_\beta = \sum_i z_i \theta_i^\beta$ , where $\theta_i$ is the angular distance from the jet axis.
Groomed substructure: Soft Drop algorithm traverses the C/A clustering tree and imposes

$\frac{\min(p_{T,1}, p_{T,2})}{p_{T,1}+p_{T,2}} > z_{\rm cut} \left( \frac{\Delta R_{12}}{R} \right)^\beta$

The first splitting that passes defines the groomed momentum fraction $z_g$ and opening angle $r_g = \Delta R_{12}$ (Brewer et al., 2021, Lapidus et al., 2017).

Jet shape: $\rho(r)$ , the $p_T$ fraction at a radial distance $r$ within the jet; probes the energy flow at different angular scales (Santos, 2021, Chang et al., 2018, Chien et al., 2018).
N-subjettiness: $\tau_N = \frac{1}{p_{T,{\rm jet}}} \sum_i p_{T,i} \min_k [\Delta R_{ik}]$ , with the discriminant $\tau_{21} = \tau_2/\tau_1$ distinguishing 2-prong from 1-prong substructure (Santos, 2021).

Jet Grooming and Area Subtraction

Grooming: Removes soft, wide-angle radiation to suppress underlying event and pileup. The grooming aggressiveness is set by $z_{\rm cut}$ and $\beta$ (Larkoski et al., 2014).
Constituent subtraction: Removes thermal and underlying-event background by sequentially subtracting soft background four-momenta from jet constituents, maintaining positive $m^2$ , and fidelity at the hadron level (2207.14814).

3. Mechanisms of Modification: Quenching, Bias, and Medium Response

Selection Bias

Inclusive jet samples after quenching are biased toward jets that underwent the least energy loss (“survivor bias”), as only those above the $p_T$ threshold remain. This masks true modification patterns:

Quenched-cut sample: $\Delta R$ and $r_g$ distributions appear unmodified between $pp$ and $AA$ because jets that lost substantial energy are underrepresented.
Unquenched-cut or boson-tagged sample: Using a selection based on a colorless boson ( $Z$ or $\gamma$ ) $p_T$ alleviates this bias, revealing strong enhancements at large $\Delta R$ and $r_g$ due to medium response and large-angle deflections (Brewer et al., 2021, Tachibana et al., 19 Jun 2025, Collaboration et al., 2023).

Medium-Induced Radiation and Recoil

Radiative modifications: Enhanced soft gluon emissions (RAD scenario) result in increased frequency of wide-angle, low- $z_g$ splittings; observed as a tilt of the $z_g$ spectrum toward small values and a shift of $r_g$ to larger angles (Lapidus et al., 2017, Chien et al., 2018).
Medium recoil: Elastic recoils (medium response) inject soft momentum at wide angles, producing:
- Enhancement in the high-mass and large-angle tails of Soft Drop observables under mild grooming.
- Strong broadening of the jet shape at $r\sim$ 0.3 (Chang et al., 2018, Milhano et al., 2017, Duan et al., 23 Jun 2025).
- A distinctive rise of $dN/d\Delta R_{12}$ with increasing $\Delta R_{12}$ , and enhanced girth of subleading subjets at low $z_g$ (Milhano et al., 2017).

Grooming Parameter Dependence

Increasing grooming aggressiveness (higher $z_{\rm cut}$ , lower $\beta$ ) suppresses soft, large-angle wake hadrons, reducing medium-response-induced enhancements in $r_g$ and $m_g$ distributions (Duan et al., 23 Jun 2025, Brewer et al., 2021).
Under strong grooming, modifications to $m_g/p_T$ become negligible, demonstrating that medium effects predominantly affect large-angle, soft structure.

4. Monte Carlo and Multistage Theoretical Descriptions

A range of Monte Carlo and semi-analytic approaches have been developed:

Hybrid and Strong-Coupling Models: Embed vacuum parton showers into hydrodynamically evolving backgrounds, then apply medium-induced energy loss via strong-coupling models with one or more free parameters (e.g., $\kappa_{\rm sc}$ ) (Brewer et al., 2021).
JEWEL: Perturbative parton showers with elastic and inelastic interactions, including explicit medium recoil. Proper grid- or constituent-level subtraction isolates genuine medium response (2207.14814, Chien et al., 2018).
YaJEM: Offers explicit control of radiative (FMED, RAD) vs. drag (DRAG) scenarios, showing distinctive signatures in soft-drop observables (Lapidus et al., 2017).
JETSCAPE Multistage: Virtuality-ordered (MATTER) at high $Q^2$ with reduced medium interaction (coherence suppression), transitions to transport-dominated (LBT) at low $Q^2$ . Only with modified coherence is the experimentally observed monotonic suppression of large- $r_g$ recovered, matching ATLAS and ALICE data (Tachibana et al., 2023, Collaboration et al., 2023).
AMPT: Demonstrates that elastic jet–medium scattering is primarily responsible for high- $m_g/p_T$ enhancement under weak grooming, with minimal modification of $z_g$ (Duan et al., 23 Jun 2025).

The interplay and tuning of these mechanisms are essential to simultaneously describe inclusive and boson-tagged jets, capturing both genuine and bias-driven modification patterns.

5. Characteristic Patterns in Data and Simulations

The main modification signatures identified experimentally and in theory are:

Observable	Inclusive Jet Selection	Boson-Tagged or Unbiased Selection
$\Delta R$ , $r_g$	No visible modification	Enhancement at large angles (30–50% increases in PbPb vs $pp$ for $\Delta R\gtrsim 0.2$ )
$z_g$	Little to no modification or slight tilt	Enhancement at low $z_g$ (soft, asymmetric splittings); sensitivity to quark jets in $\gamma$ -tagged samples
$m_g/p_T$	Enhancement in the high-mass tail under mild grooming; none under strong grooming	Greater enhancement for events with large energy loss
Quark/Gluon discrimination	Degrades by ~10–15% in presence of soft background/recoil	Stronger modification in quark jets, minimized in gluon jets; $\gamma$ -tagged jets provide maximal sensitivity

These patterns are robust across different heavy-ion collision energies, centralities, and model frameworks, provided medium response and bias are accurately incorporated.

6. Extraction Strategies, Systematic Uncertainties, and Future Directions

Bias avoidance: Employ boson-tagged jet selections (using $p_T^{Z}$ or $p_T^{\gamma}$ as the proxy for the unquenched jet $p_T$ ) to eliminate survivor bias and access the full modification pattern (Brewer et al., 2021, Tachibana et al., 19 Jun 2025).
Grooming tuning: Vary $z_{\rm cut}$ and $\beta$ to disentangle core modifications from large-angle medium response (Duan et al., 23 Jun 2025).
Background correction: Precise constituent subtraction is mandatory to accurately interpret jet–medium response and compare to experimental data (2207.14814, Alon et al., 2011).
Quark vs. gluon sensitivity: Quark jets exhibit more pronounced medium-induced modifications, particularly when selected via $\gamma$ -tagged events; gluon jets show monotonic narrowing and smaller $m_g$ shifts (Tachibana et al., 19 Jun 2025).
Dimensionality reduction & ML: A minimal set of observables (Soft Drop girth, $\tau_{2,1}$ , a dynamical grooming scale) capture nearly all medium-modified information, enabling efficient data analyses and transfer of discriminant taggers between $pp$ and $AA$ (Romão et al., 2023).
Open problems: Precise separation of intrinsic jet quenching from wake/medium response, characterization of path-length dependence, and extraction of the angular structure of medium response remain ongoing challenges. Upcoming analyses will exploit high-statistics data and additional theoretical developments to resolve these.

7. Implications for QCD Tomography and QGP Characterization

Jet substructure modifications serve as high-precision, multi-scale probes of the QGP. By correlating hard and soft components—using a combination of energy flow observables, grooming strategies, and bias-free event selection—researchers can:

Map the angular and energy distribution of energy loss.
Separate core jet modification from medium response.
Extract the transport coefficient $\hat q$ and test the limits of color coherence and decoherence theories.
Benchmark and improve the next generation of Monte Carlo and analytic jet quenching models.