JETSCAPE Collaboration Framework

• JETSCAPE Collaboration is a modular, extensible framework that integrates multiple models for simulating ultra-relativistic heavy ion and pp collisions.
• Its architecture supports plug-and-play modules for initial conditions, hard scattering, hydrodynamic evolution, energy loss, and hadronization.
• The framework employs advanced Bayesian inference and machine learning to extract QGP transport coefficients and validate against experimental observables.

The JETSCAPE Collaboration is an interdisciplinary effort focused on the development, validation, and application of a modular, extensible event generator framework for ultra-relativistic heavy ion collisions. Its core contribution is the JETSCAPE (Jet Energy-loss Tomography with a Statistically and Computationally Advanced Program Envelope) framework, which enables the integration of multiple state-of-the-art models across all stages of heavy ion and proton–proton (pp) collisions, including initial state construction, hard scattering, hydrodynamics, energy loss mechanisms, and hadronization. This unified, multi-model framework supports rigorous, data-driven studies of jet quenching phenomena, jet–medium interactions, and the extraction of QGP transport coefficients via Bayesian inference and active machine learning strategies.

1. JETSCAPE Framework Architecture

The JETSCAPE framework is designed as a highly modular, task-based computational envelope, employing signal-slot communication and graph-based representations of parton showers. The architecture supports seamless plug-and-play of model modules and wrappers, encapsulating all relevant stages of event generation:

• Initial Conditions: Modules such as TRENTO (TrentoInitial) and GubserHydro provide initial matter density and geometry.
• Hard Scattering: Simulated using parton or PythiaGun, leveraging PYTHIA8 for initial scatterings with multi-parton interactions and initial state radiation.
• Hydrodynamics: Multiple options are provided, including Brick (static medium), Gubser (analytic 2+1D), and interfaces to external codes like MUSIC for viscous hydrodynamic evolution.
• Pre-Equilibrium Dynamics: Free-streaming modules can be enabled for pre-hydrodynamic evolution.
• Energy Loss Models: Several modules cover different physical regimes, notably:
  • MATTER for high virtuality, virtuality-ordered parton showers.
  • LBT (Linear Boltzmann Transport), MARTINI (AMY-based in-medium showering), AdS/CFT, and CUJET for low virtuality or strong coupling regimes.
• Hadronization: PYTHIA-based modules (ColoredHadronization, ColorlessHadronization) and Hybrid Hadronization, which interpolate between string fragmentation and recombination mechanisms.

The framework is controlled via a C++ wrapper and a strongly parameterized XML configuration, allowing definition of physical settings (collision energy, $p_T^\text{hat}$ limits, random seeds, switching scales $Q_0$, etc.) and model interconnections. Key XML tags include <Hard>, <Eloss>, <JetHadronization>, and <Random>.

2. Multi-Stage Jet Evolution and Energy Loss Modeling

JETSCAPE advances a multi-stage paradigm in jet quenching theory, where the evolution of a jet is split according to parton virtuality (or transverse resolution scale):

• High Virtuality: The MATTER module employs a Sudakov-form-factor-controlled, virtuality-ordered parton shower with medium modifications. The key validity regime is $Q^2 \gg \sqrt{\hat{q} E}$, incorporating both vacuum and in-medium splitting functions. The Sudakov form factor is written schematically as:

$$S(Q, Q_0) = \exp \left[ -\int_{Q_0}^{Q} \frac{d\mu^2}{\mu^2} \int dz \frac{\alpha_s}{2\pi}\left(P(z) + \Delta P_\text{med}(z, \mu^2)\right) \right]$$

• Low Virtuality: When $Q^2$ drops below a switching scale $Q_0$ (default: $1–2~\mathrm{GeV}^2/c^2$), modules such as LBT, MARTINI, or AdS/CFT take over. LBT covers elastic and inelastic scatterings (with recollision/recoil tracking), MARTINI employs AMY formalism for in-medium rates, and AdS/CFT provides strong-coupling drag descriptions.
• Hybrid Hadronization: After shower termination, hadronization is applied via colored or colorless string fragmentation, or hybrid recombination–string fragmentation, the latter allowing interpolation between vacuum and in-medium regimes.

This design enables objective, side-by-side comparisons and validation of different energy-loss models under otherwise identical evolution conditions, as well as the use of multiple models in parallel with switching determined by local virtuality, energy, and (optionally) temperature.

3. Monte Carlo Event Generation and Computational Workflow

Event generation proceeds via a Monte Carlo strategy, simulating full collision events from initial hard scatterings to the final hadron state. The process is typically structured as follows:

• Configuration/Initialization: Compilation and module activation via CMake switches, specification of settings via XML (e.g., $\sqrt{s}$, $p_T^\text{hat}$ limits, $Q_0$, random seeds).
• Module Attachment: Shared pointer management of physics modules in C++. Example configuration in code:

  auto jetscape = make_shared<JetScape>("./jetscape_init.xml", nEvents); jetscape->Add(make_shared<PythiaGun>()); jetscape->Add(make_shared<Brick>()); auto jlossmanager = make_shared<JetEnergyLossManager>(); auto jloss = make_shared<JetEnergyLoss>(); auto matter = make_shared<Matter>(); jloss->Add(matter); jlossmanager->Add(jloss); jetscape->Add(jlossmanager);

• Event Simulation: Execution of the wrapper code (e.g., ./bin/PythiaGun), with stochastic sampling over millions of events, accumulation of cross section weights, and event output using writer modules (including gzipped ASCII).
• Analysis: Post-processing via provided tools for final state hadron extraction, FastJet clustering, or ROOT-based physics analysis, enabling validation against experimental observables such as inclusive jet spectra, jet shapes, fragmentation functions, and substructure variables.

4. Bayesian Inference, Parameter Extraction, and Model Calibration

JETSCAPE incorporates advanced Bayesian analysis as a core methodology for extracting QGP properties, especially the jet transport parameter $\hat{q}$, from experimental data:

• Parameterization: $\hat{q}$ is modeled as a function of temperature $T$, parton energy $E$, and virtuality $\mu^2$. A representative expression incorporates both the Hard Thermal Loop (HTL) baseline and a virtuality-dependent modulation:

$\hat{q}(\mu^2) = f(\mu^2) \hat{q}^\mathrm{HTL}$

with

$$f(\mu^2) = N \frac{\exp \left[ c_3 \left(1 - \frac{\mu^2}{2 M E} \right)\right] - 1} {1 + c_1 \log \left( \frac{\mu^2}{Q_0^2} \right) + c_2 \log^2 \left( \frac{\mu^2}{Q_0^2} \right)}$$

where $N$ is fixed so $f(Q_0^2) = 1$, $M$ is the proton mass, and $c_1$, $c_2$, $c_3$, $Q_0$ are inference parameters.

• Inference Workflow: Gaussian Process Emulators interpolate between compute-intensive simulation points ("design points" sampled via Latin hypercube). Bayesian inference (often Markov Chain Monte Carlo) is applied to combined datasets (inclusive hadron $R_{AA}$, jet $R_{AA}$, and jet substructure observables), with systematic Bayesian calibration of all free parameters. Active learning is used for computational efficiency, allocating more design points where emulator uncertainty is high.
• Findings and Tensions: Joint inference on jet and hadron data exposes tension in $\hat{q}$ posteriors: low-$p_T$ hadrons favor larger $\hat{q}$, while high-$p_T$ jets/hadrons prefer lower values. The tension suggests the parameterization of $\hat{q}$ may not fully describe energy or virtuality dependence and that additional theoretical uncertainties should be incorporated in future analyses.

5. Validation, Physics Results, and Community Benchmarks

JETSCAPE places a strong emphasis on quantitative validation:

• pp Baselines: The PP19 tune for pp collisions demonstrates agreement across multiple jet and hadron observables (inclusive jet cross sections, jet shapes, fragmentation functions, and dijet mass), with deviations comparable to standard event generators such as PYTHIA8. Key configuration: vacuum evolution with MATTER ($\hat{q}_0=0$), $\text{eCMforHadronization} = \sqrt{s}/2$, parton kinematics set by $p_T^\text{hat}$ and energy cuts.
• A+A Observables: Multi-stage models reproduce nuclear modification factors, elliptic flow coefficients, and substructure observables (e.g., jet fragmentation, $z_g$, $r_g$). The integration of LBT/MARTINI/AdS/CFT at low virtuality allows detailed investigation of model-dependent effects, with emphasis on qualitative and quantitative changes due to model differences (e.g., recoil effects in LBT, higher twist vs. AMY formulations).
• Photon-Jet and Heavy Flavor Studies: Photon-jet correlations (momentum imbalance $x_J$, azimuth $\Delta\phi$) and heavy-flavor tagged jet studies (e.g., $D^0$ $R_{AA}$ and $v_2$) are enabled with no additional parameter tuning, attesting to the framework's predictive power and consistency across various final-state probes.
• In-Medium Hadronization: The Hybrid Hadronization module enables paper of recombination effects and medium-induced changes in hadron chemistry. The $\Lambda/K$ ratio and proton-to-pion ratio as a function of medium path length highlight the role of recombination and flow in the QGP.

6. Implications, Future Directions, and Community Engagement

JETSCAPE's modular, extensible design, robust statistical methodology, and public release policy position it as the community standard for heavy-ion event generation and phenomenological QCD studies:

• Ongoing Development: Current priorities include incorporation of additional physics modules (e.g., hadronic rescattering with SMASH, explicit medium recoil), more robust multi-dimensional switching between energy loss models, and a full-featured manual.
• Model Refinement: Tensions in $\hat{q}$ extracted from different observables motivate refinement of virtuality and energy dependence in transport modeling, detailed paper of coherence effects, and the inclusion of further theoretical uncertainties and systematic effects (such as nuclear shadowing).
• Benchmarking and Validation: Reproduction of a broad suite of experimental measurements across RHIC and LHC energies is central; community-driven parameter improvement and validation is supported via open GitHub development and feedback.
• Bayesian and Machine Learning Advances: Active learning and surrogate model uncertainty quantification are being further developed to address the computational cost and improve the interpretability of model–data comparisons.

The JETSCAPE Collaboration's systematic integration of multi-scale physics, modular modeling, and rigorous statistical analysis represents a significant advance in the quantitative extraction of QGP properties and establishes a foundation for next-generation studies of jet quenching and jet–medium interaction.