Probing the QCD Phase Structure with Dileptons from SIS to LHC Energies

This study utilizes the Dynamical QuasiParticle Model and Parton--Hadron--String Dynamics transport approach to demonstrate that thermal QGP dilepton radiation becomes a dominant signal over correlated charm decays in central heavy-ion collisions at energies below 25–30 GeV, highlighting the potential of RHIC-BES and FAIR experiments to directly observe QGP electromagnetic radiation and probe the QCD phase structure.

The Gist

Imagine trying to understand what happens inside a star or a black hole, but instead of looking at light, you are looking at the very building blocks of matter: quarks and gluons. This paper is like a detective story where scientists use "messenger particles" called dileptons (pairs of electrons and their antimatter twins) to peek inside the hottest, densest collisions of atomic nuclei ever created in a lab.

Here is the story of what they found, broken down into simple concepts:

1. The Big Experiment: Smashing Atoms Like Cars

Scientists smash heavy atoms (like Gold) together at incredible speeds.

• The Goal: To melt the atoms so their insides (quarks and gluons) flow freely, creating a "soup" called Quark-Gluon Plasma (QGP). This is the state of matter that existed just after the Big Bang.
• The Challenge: It's hard to see this soup because it's hidden inside a chaotic mess of other particles.
• The Solution: They use dileptons as messengers. Unlike other particles that get stuck in the soup, dileptons are like ghosts; they pass right through the mess without getting hit, carrying a perfect snapshot of the conditions inside when they were born.

2. The Two Models: The "Blueprint" and the "Movie"

To understand these messengers, the authors used two computer models working together:

• The Blueprint (DQPM): This is like a detailed architectural plan for the "soup." It tells them what the quarks and gluons look like when they are hot and dense, based on previous calculations from supercomputers (Lattice QCD).
• The Movie (PHSD): This is the animation software. It takes the blueprint and simulates the actual crash, showing how the soup forms, expands, cools down, and turns back into normal particles. It tracks every single particle from the moment of impact until the end.

3. The Discovery: A Tiny Core at Low Speeds

Usually, scientists think you need a massive amount of energy to create this "soup." However, this study found something surprising:

• The Finding: Even at relatively "slow" collision speeds (compared to the fastest ones), a tiny, deconfined core of the soup still forms.
• The Analogy: Imagine trying to melt an ice cube. You usually think you need a roaring fire. But this study says, "Even if you just hold the ice cube in your warm hand, a tiny, tiny drop of water forms in the very center."
• The Detail: At the lowest energy they tested, this soup core was less than 1% of the total energy, but it was there.

4. The "Chemical Pressure" (Baryon Chemical Potential)

The paper introduces a new variable: Baryon Chemical Potential ($\mu_B$).

• The Analogy: Think of this as the "crowdedness" or "pressure" of matter.
  • At high speeds (like at the LHC or top RHIC energies), the collision is so violent that the matter flies apart instantly. The "pressure" drops to almost zero, and the soup is very hot but not very crowded.
  • At lower speeds (like at the FAIR or RHIC-BES facilities), the collision is less violent. The matter stays packed together longer. It's like a crowded subway car that doesn't empty out immediately. The "pressure" ($\mu_B$) is very high.
• The Result: The study shows that as you lower the collision energy, the "pressure" inside the soup gets higher and higher. This is crucial because it helps scientists map out the "phase diagram" of matter—essentially a weather map for the universe's building blocks.

5. The "Ghost" vs. The "Heavy Truck"

One of the main goals was to figure out how much of the signal comes from the "soup" (QGP) versus other sources, like heavy particles (Charm quarks) decaying.

• The High-Speed Zone (LHC/RHIC): At the highest energies, the signal is dominated by heavy particles (like heavy trucks on a highway) and the soup is hard to separate from them.
• The Medium-Speed Zone (The Sweet Spot): The study found a "sweet spot" at energies around 25–30 GeV.
  • The Analogy: Imagine you are trying to hear a whisper (the soup) in a noisy room. At very high speeds, the room is filled with loud trucks (heavy charm decays) that drown out the whisper. But at these medium speeds, the trucks slow down, and the whisper becomes louder than the trucks.
  • The Claim: In central collisions at these specific energies, the signal from the hot soup actually exceeds the signal from the heavy particle decays. This makes these specific energy ranges the best place to "hear" the soup directly.

6. The Conclusion: A New Map

The paper concludes that by using these messenger particles (dileptons) and their advanced computer models, scientists can now:

1. Confirm that a tiny bit of the "Big Bang soup" forms even at lower energies.
2. See how the "pressure" of matter changes as we slow down the collisions.
3. Identify the perfect energy range (around 25–30 GeV) where the "soup" signal is strongest and easiest to isolate from background noise.

This gives future experiments (like those at FAIR in Germany or RHIC in the US) a clear target: focus on these specific energies to get the cleanest picture of the universe's earliest moments.

Technical Summary

Technical Summary: Probing the QCD Phase Structure with Dileptons from SIS to LHC Energies

Problem Statement
This study investigates the properties of strongly interacting matter at finite temperature ($T$) and baryon chemical potential ($\mu_B$) created in relativistic heavy-ion collisions. The primary objective is to probe the Quantum Chromodynamics (QCD) phase structure using dilepton observables. A central challenge addressed is the quantification of the Quark-Gluon Plasma (QGP) contribution to the dilepton spectrum across a broad energy range, specifically determining the conditions under which thermal QGP radiation becomes distinguishable from hadronic sources and heavy-flavor decays.

Methodology
The authors employ a multi-stage theoretical framework combining equilibrium and non-equilibrium descriptions:

1. Equilibrium QGP Description (DQPM): The non-perturbative QGP is modeled using the Dynamical QuasiParticle Model (DQPM). This approach describes the QGP in terms of massive quarks and gluons with finite spectral widths, formulated within a two-particle irreducible (2PI) propagator representation. The model is constrained to reproduce lattice-QCD results for the equation of state (EoS) at $\mu_B = 0$. It provides $\mu_B$-dependent quasiparticle properties, transport coefficients, and thermal dilepton rates, accounting for both elastic and inelastic partonic processes ($q + \bar{q} \to e^+e^-$, $q + \bar{q} \to g + e^+e^-$, $q + g \to q + e^+e^-$).
2. Dynamical Evolution (PHSD): The space-time evolution of the collision is simulated using the off-shell Parton–Hadron–String Dynamics (PHSD) transport approach. This framework consistently propagates partonic and hadronic degrees of freedom based on Kadanoff–Baym theory, ensuring conservation of energy-momentum and quantum numbers. It incorporates chiral-symmetry restoration effects, leading to in-medium modifications of hadronic spectral functions and strange hadron properties.
3. Dilepton Sources: The total dilepton yield in PHSD is calculated by summing contributions from:
   • Hadronic decays (including $\pi^0, \eta, \omega, \phi, \Delta$ Dalitz decays).
   • Bremsstrahlung ($NN, \pi N$).
   • QGP thermal radiation.
   • Primary Drell–Yan (DY) production.
   • Semileptonic decays of correlated charm ($D\bar{D}$) and bottom ($B\bar{B}$) pairs.

Key Contributions

• $\mu_B$ Dependence in PHSD: The paper presents, for the first time, the baryon-chemical-potential dependence of QGP thermal dilepton radiation within the PHSD framework.
• Low-Energy QGP Formation: The study demonstrates that a small deconfined QGP core can emerge even at low collision energies, specifically at $\sqrt{s_{NN}} \simeq 3.5$ GeV.
• Excitation Functions: The authors provide detailed excitation functions for dilepton yields across the energy range from SIS (1.23 AGeV) to LHC (5.02 TeV), comparing theoretical predictions with experimental data from HADES, STAR, and ALICE.

Results

• Space-Time Evolution: At high energies ($\sqrt{s_{NN}} = 200$ GeV), the early-time evolution is dominated by partonic matter, carrying up to 90% of the midrapidity energy. As collision energy decreases, this fraction drops significantly. However, even at $\sqrt{s_{NN}} = 3.5$ GeV, a QGP component comprising less than 1% of the total energy is formed.
• Chemical Potential Probing: At $\sqrt{s_{NN}} = 3.5$ GeV, partonic dileptons probe matter at large baryon chemical potentials ($\mu_B \gtrsim 0.6$ GeV) but only slightly above the critical energy density. Conversely, at $\sqrt{s_{NN}} = 200$ GeV, $\mu_B$ at midrapidity rapidly approaches zero.
• Spectral Agreement: The PHSD results show good agreement with experimental dilepton data from HADES (SIS energies), STAR (RHIC-BES and top RHIC energies), and ALICE (LHC energies).
  • At SIS energies (1–2 AGeV), the low-mass region is dominated by hadronic processes (bremsstrahlung, Dalitz decays), with $\rho$-meson broadening playing a decisive role in reproducing spectral shapes.
  • At intermediate and high energies, the vector meson contribution dominates the low-mass region ($M_{ee} < 0.7$ GeV/$c^2$), while the intermediate-mass region ($1.2 < M_{ee} < 3$ GeV/$c^2$) is dominated by QGP radiation and correlated heavy-flavor decays.
• Competition between Sources: The excitation function indicates that thermal QGP radiation exceeds dileptons from correlated charm decays in central Au+Au collisions at $\sqrt{s_{NN}} \lesssim 25\text{--}30$ GeV. For minimum-bias collisions, this crossover occurs at $\sqrt{s_{NN}} \sim 20$ GeV.
• Drell-Yan Contribution: Primary Drell–Yan production contributes significantly to the intermediate-mass region at intermediate collision energies. However, the authors note that these estimates carry sizable uncertainties due to limited phase space and sensitivity to parton distribution functions, suggesting they should be regarded as upper estimates.

Significance and Claims
The paper claims that the RHIC Beam Energy Scan (BES) and FAIR energies are particularly promising for the direct observation of QGP electromagnetic radiation. This is because, in this energy window, the thermal QGP contribution can exceed the background from correlated charm decays in central collisions. The authors assert that after subtracting heavy-flavor and Drell–Yan contributions, intermediate-mass dileptons provide direct access to very hot QGP matter. Furthermore, the study highlights that precise dilepton measurements in $p+p$ collisions are essential to constrain and subtract the DY contribution from $A+A$ spectra, thereby improving the extraction of the QGP signal. The work supports the use of dileptons as penetrating probes to establish the QCD phase structure under extreme conditions of temperature and baryon density.