DREENA-A Model: Adaptive QGP Tomography

• DREENA-A is a computational framework that simulates quark-gluon plasma tomography by dynamically adapting arbitrary temperature profiles to model both radiative and collisional parton energy loss.
• It uses a parameter-free kernel with fixed physical constants and optimized Monte Carlo sampling to enable direct, model-independent comparisons across various hydrodynamic simulations.
• The model delivers unified predictions for high-p⊥ observables like RAA and v2, offering actionable insights into the QGP's spatial anisotropy and evolution.

The DREENA-A model (“Dynamical Radiative and Elastic ENergy loss Approach – Adaptive”) is a state-of-the-art computational framework in high-energy nuclear physics designed for precision quark-gluon plasma (QGP) tomography via high-$p_\perp$ observables. Originating from theoretical developments in the description of in-medium parton energy loss, DREENA-A distinguishes itself through its capability to incorporate fully arbitrary temperature profiles into the dynamical energy loss formalism. This allows systematic connection between the evolving, spatially nonuniform QGP medium and hard probes (light and heavy flavor jets), while maintaining parameter-free predictions for suppression ($R_{AA}$) and high-$p_\perp$ azimuthal anisotropy ($v_2$) observables. By doing so, DREENA-A provides a unified avenue for constraining not only parton–medium interactions but also fundamental properties of the bulk QCD matter created in heavy-ion collisions.

1. Theoretical Foundations and Model Architecture

At its core, DREENA-A implements a dynamical energy loss formalism rooted in finite-size, finite-temperature field theory, treating QGP scattering centers as dynamical (moving) partons rather than static obstacles. Both collisional and radiative energy loss mechanisms are computed within a single microscopic framework, incorporating:

• Generalized Hard-Thermal-Loop (HTL) resummation, addressing infrared divergences naturally.
• Running QCD coupling and finite electric and magnetic screening effects (e.g., Debye mass, magnetic mass).
• Nonperturbative effects and multi-gluon fluctuations (Poisson expansion for radiative component).
• Path-length fluctuations and arbitrary high-dimensional temperature fields.
• Parameter-free kernel: all physical constants and couplings are fixed to standard literature values; the only input is the temperature profile $T(\vec{x},\tau)$.

This structure enables DREENA-A to directly exploit differences in medium evolution models (such as those produced by different hydrodynamic simulations) without targeted parameter tuning or fitting.

2. Mathematical Formalism and Observable Computation

The calculation of medium-modified hadron spectra proceeds via a generic pQCD convolution:

$$E_f \frac{d^3 \sigma_q(H_Q)}{dp_f^3} = \left[E_i \frac{d^3 \sigma(Q)}{dp_i^3}\right] \otimes P(E_i \rightarrow E_f) \otimes D(Q \rightarrow H_Q)$$

where $P(E_i \rightarrow E_f)$ encompasses the radiative and collisional energy loss probability distribution for a given space-time path length and temperature field. The temperature along a parton’s trajectory is given by

$$T(x_0, y_0, \varphi, \tau) = T_{\text{profile}}(x_0 + \tau\cos\varphi,\, y_0 + \tau\sin\varphi,\,\tau)$$

Since $T$ feeds into all energy loss rates, changing $T_{\text{profile}}$ immediately affects jet quenching predictions.

Key observables are extracted as:

$$R_{AA}(p_\perp) = \frac{1}{2\pi}\int_0^{2\pi}R_{AA}(p_\perp,\varphi) d\varphi$$

$$v_2(p_\perp) = \frac{(1/2\pi)\int_0^{2\pi}\cos(2\varphi) R_{AA}(p_\perp,\varphi)\,d\varphi}{R_{AA}(p_\perp)}$$

These definitions naturally encode the response of hard probes to the global medium anisotropy and local fluctuating temperature fields.

3. Adaptive Integration of Temperature Profiles

DREENA-A’s distinguishing capability is its adaptive intake of temperature profiles. Any temperature evolution, whether derived from optical Glauber models, IP-Glasma, EKRT, or full $3+1$D hydrodynamic simulations, can serve as input:

• The model evaluates $T(\vec{x},\tau)$ along the parton's (randomized) production point and emission angle.
• Energy loss integrals are evaluated along these fluctuating paths for each particle, sampling the full space–time evolution (including both spatial and temporal non-uniformity, and transverse expansion).
• This flexibility allows systematic comparison of theoretical predictions across initial condition models and hydrodynamic scenarios, directly connecting measured $R_{AA}$ and $v_2$ to specific bulk medium properties.

4. Applications Across Probes, Energies, and Systems

Designed as a multipurpose QGP tomography tool, DREENA-A generates predictions for:

• Light-flavor (charged hadrons) and heavy-flavor (D, B mesons) observables, exploiting the heavy–light flavor consistency of dynamical energy loss.
• Collision systems and centralities (Pb+Pb at LHC, Au+Au at RHIC, smaller systems), covering the full spectrum of system sizes and initial spatial profiles.
• Wide range of collision energies, enabling quantitative cross-system comparison.

For each case, the model computes double-differential or integrated observables, facilitating benchmarking direct to experiment without re-tuning energy loss parameters.

5. Comparative Context and Key Insights

A comparison with the preceding DREENA-C and DREENA-B frameworks clarifies the incremental advantages:

Framework	Medium Evolution	Temperature Profile	$v_2$ Prediction Quality	Parameter-Free Kernel
DREENA-C	Static	Constant	Overestimates	Yes
DREENA-B	$1+1$D Bjorken expansion	Analytic, 1D	Improved (but not full)	Yes
DREENA-A	Arbitrary (e.g., 3+1D hydro)	Adaptive/Realistic	Fully data-driven	Yes

Including a fully adaptive $T(\vec{x},\tau)$ allows direct isolation of the medium evolution impact. For example, in DREENA-A, $v_2$ is reduced relative to constant-$T$ estimates due to time-dependent spatial anisotropy and temperature gradients—better matching experimental data and clarifying the so-called $v_2$ puzzle.

A salient analytic result uncovered in high-$p_\perp$ DREENA-A calculations (Stojku et al., 2021) is that

$$\frac{v_2}{1-R_{AA}} \xrightarrow{p_\perp\to\mathrm{large}} \langle jT_2\rangle$$

where $\langle jT_2\rangle$ is the time-averaged jet–temperature anisotropy, providing a direct tomographic mapping from experimental observables to bulk medium geometry.

6. Computational Features and Performance

Despite the increased complexity from arbitrary temperature evolution, DREENA-A maintains computational efficiency via:

• Adaptive tabulation and interpolation of expensive integrands (e.g., Debye mass, running coupling).
• Optimized equidistant smearing over transverse plane and azimuthal directions.
• Reordered multi-dimensional Monte Carlo sampling for efficient convolution over parton emission points, paths, and gluon emissions.
• Parameter-free execution: all physical parameters arise from established literature, not from observable-specific fits.

This allows global studies across system sizes and energies, producing jointly consistent $R_{AA}$ and $v_2$ results.

7. Significance in QGP Tomography and Future Directions

DREENA-A represents the current pinnacle in the DREENA framework hierarchy, enabling:

• Direct, model-independent tests of the relationship between QGP space–time evolution and jet quenching observables.
• Isolation of medium evolution effects in hard probe suppression without adjusting energy loss parameters.
• Parameter-free comparison of various hydrodynamical initializations by systematically supplying their temperature profiles.
• Extraction of bulk QGP properties (e.g., spatial anisotropy, temperature gradients) via data-driven inversion of high-$p_\perp$ observables (the “QGP tomography” program).

A plausible implication is that as experimental precision improves, the DREENA-A methodology, with its flexibility and parameter-free kernel, will play a central role in constraining the pre-equilibrium QCD dynamics and validating hydrodynamical models jointly from low- and high-$p_\perp$ data.

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In summary, DREENA-A fuses a robust, dynamical, parameter-free energy loss formalism with maximal flexibility in QGP temperature evolution modeling, enabling high-precision, systematic, and model-independent extraction of QGP geometric and dynamical properties from high-$p_\perp$ measurements. Its unique integration of both soft and hard sector constraints via direct comparison with data positions it as a premier tool for ongoing and future QGP tomography studies (Stojku et al., 2020, Zigic et al., 2021, Stojku et al., 2021).