Transport coefficients of strongly interacting quark-gluon plasma including elastic and inelastic scattering within the dynamical quasiparticle model

This study extends the dynamical quasiparticle model to include inelastic gluon-radiation processes, finding that while these radiative channels systematically reduce transport coefficients like shear viscosity and electric conductivity compared to elastic-only results, the effect remains moderate in the thermal regime and yields predictions compatible with lattice-QCD estimates at zero baryon chemical potential.

The Gist

Imagine the universe, just a fraction of a second after the Big Bang, was filled with a super-hot, super-dense soup of tiny particles called quarks and gluons. Scientists call this the Quark-Gluon Plasma (QGP). It's not a liquid or a gas in the usual sense; it's a "strongly interacting" fluid where these particles are constantly bumping into each other, sticking together, and flying apart.

To understand how this cosmic soup flows, scientists use "transport coefficients." Think of these as the rules of the road for the soup:

• Viscosity: How "thick" or "sticky" the soup is (like honey vs. water).
• Conductivity: How easily electricity moves through it.
• Diffusion: How quickly particles spread out.

The Big Question: Do "Side Trips" Matter?

For a long time, researchers calculated these rules by only looking at elastic collisions.

• The Analogy: Imagine a crowded dance floor where everyone is bumping into each other and bouncing off (elastic). If two people bump, they just change direction and keep dancing. No one leaves the floor, and no one joins in.

However, in the real world of this plasma, particles can do something more complex: inelastic collisions.

• The Analogy: Imagine that during a bump, a dancer gets so excited they accidentally kick a third person onto the dance floor, or they throw a piece of their own energy (a "gluon") into the crowd. This is a 2-to-3 process: two particles collide, and three come out (the original two plus a new "radiated" particle).

The paper asks: Does this "side trip" of creating new particles significantly change the rules of the road (the transport coefficients)?

The Study: The "Dynamical Quasiparticle Model" (DQPM)

The authors used a specific simulation tool called the Dynamical Quasiparticle Model (DQPM).

• The Metaphor: Think of the DQPM as a very sophisticated video game engine. It doesn't treat particles as tiny, hard billiard balls. Instead, it treats them as "clouds" or "fuzzy blobs" with mass and a specific "width" (how long they last before changing). This model is tuned to match real-world data from supercomputers (Lattice QCD) that simulate the laws of physics at zero density.

In this study, the researchers upgraded their video game engine. They took the existing rules (bouncing off each other) and added the new rule: particles can also radiate energy and create extra particles during a collision.

What They Found

The researchers ran the simulation across a wide range of temperatures and densities (simulating everything from the early universe to the conditions created in heavy-ion collision experiments).

1. The "Side Trips" are Rare
They found that while the "radiative" collisions (2-to-3) definitely happen, they are much less frequent than the simple "bouncing" collisions (2-to-2).

• Analogy: On that crowded dance floor, 99 times out of 100, people just bump and bounce. Only occasionally does someone get so energetic they kick a third person onto the floor. The "bouncing" is the dominant force.

2. The Soup Gets Slightly Less "Sticky"
Because the new "side trip" collisions happen, the particles interact more often overall. In physics, more interactions mean particles get "relaxed" or slowed down faster.

• Result: When they added these new rules, the calculated viscosity (stickiness), conductivity, and diffusion coefficients all went down slightly.
• Why? It's like adding a few extra obstacles to a hallway. People (particles) can't move as freely as before, so the "flow" properties change.

3. The Change is Small, But Real
Here is the most important takeaway: The change was moderate.

• Because the "side trips" are rare compared to the "bouncing," the overall behavior of the soup didn't change dramatically. The "sticky" factor (viscosity) didn't turn into "slippery" overnight. The new rules just provided a small correction to the old ones.
• The new rules only became really important for particles moving at very high speeds (high momentum), but in the "thermal" soup (where most particles are), the simple bouncing rules still do 90% of the work.

Why This Matters

• At Zero Density (The Early Universe): Their results match well with other supercomputer calculations, giving scientists confidence that their model is accurate.
• At High Density (Future Experiments): The paper provides new predictions for what happens when there are lots of "baryons" (protons and neutrons) in the mix. This is crucial for upcoming experiments (like the Beam Energy Scan) that are trying to map out the "phase diagram" of the universe—essentially, figuring out how matter behaves under extreme pressure and density.

The Bottom Line

The authors successfully added a new, complex layer of physics (particles radiating energy) to their model of the early universe's soup. They found that while this new layer does make the soup slightly less viscous and slightly more conductive, it doesn't rewrite the whole story. The simple "bouncing" collisions are still the main drivers of how this cosmic soup flows.

This study confirms that previous calculations were robust, but now scientists have a more complete, slightly more accurate "rulebook" for simulating the universe's most extreme states of matter.

Technical Summary

Technical Summary: Transport Coefficients of Strongly Interacting Quark-Gluon Plasma with Inelastic Scattering

Problem Statement
Transport coefficients—specifically shear viscosity ($\eta$), bulk viscosity ($\zeta$), electric conductivity ($\sigma_Q$), and baryon diffusion ($\kappa_B$)—are critical for characterizing the non-equilibrium evolution of the quark-gluon plasma (QGP) created in relativistic heavy-ion collisions. While the Dynamical Quasiparticle Model (DQPM) has successfully described these coefficients based on elastic ($2 \to 2$) scattering, the impact of inelastic processes, particularly gluon radiation ($2 \to 3$), remains to be fully quantified within this framework. Previous DQPM studies at zero baryon chemical potential ($\mu_B = 0$) indicated that inelastic rates are suppressed relative to elastic ones, but a systematic investigation of these effects across the temperature ($T$) and baryon chemical potential ($\mu_B$) plane, including their influence on transport properties, was lacking.

Methodology
The authors extend the DQPM framework to include radiative $2 \to 3$ scattering channels alongside the established elastic $2 \to 2$ baseline.

• Model Framework: The DQPM treats the QGP as a system of massive, strongly interacting quasiparticles (quarks, antiquarks, and gluons) with complex self-energies. The real parts of the self-energies define dynamically generated thermal masses, while the imaginary parts determine spectral widths. Model parameters are constrained by lattice QCD (lQCD) thermodynamics at $\mu_B = 0$ and extended to finite $\mu_B$ via a scaling hypothesis.
• Scattering Amplitudes: The study explicitly calculates leading-order Feynman diagrams for inelastic processes ($q+q \to q+q+g$, $q+g \to q+g+g$, and corresponding antiquark/gluon channels) using effective DQPM propagators and vertices. These propagators account for the finite width and mass of the partons.
• Relaxation Time Approximation (RTA): Transport coefficients are evaluated using the RTA of kinetic theory. The relaxation times ($\tau_i$) for quarks and gluons are derived from the total interaction rates ($\Gamma_i$), which are computed by integrating the squared matrix elements over phase space. Two scenarios are compared:
  1. $\tau^{-1} = \Gamma_{2\to2}$ (elastic only).
  2. $\tau^{-1} = \Gamma_{2\to2} + \Gamma_{2\to3}$ (elastic + inelastic).
• Scope: Calculations are performed as functions of $T$ and $\mu_B$, covering the range relevant for beam-energy-scan programs (e.g., RHIC-BES, FAIR, NICA).

Key Contributions and Results

1. Interaction Rates: The momentum-averaged interaction rates for $2 \to 3$ gluon-radiation processes are found to be orders of magnitude smaller than elastic $2 \to 2$ rates across the explored $(T, \mu_B)$ range. This suppression is attributed to the large effective thermal masses of the partons in the DQPM, which restrict the available phase space for inelastic transitions, particularly for thermal momenta ($p \sim T$).
2. Impact on Relaxation Times: The inclusion of inelastic channels systematically reduces the relaxation times compared to the elastic-only case. However, because the inelastic rates are sub-dominant, this reduction is moderate.
3. Transport Coefficients:
   • Shear Viscosity ($\eta/s$): The inclusion of $2 \to 3$ channels leads to a systematic but small reduction in $\eta/s$. The effect is more pronounced at higher momenta but remains a quantitative correction rather than a qualitative change in temperature dependence. At $\mu_B = 0$, the results are compatible with available lQCD estimates for pure SU(3) gauge theory.
   • Bulk Viscosity ($\zeta/s$): The impact of radiative channels on $\zeta/s$ is even more limited. The integral defining bulk viscosity is heavily weighted by a non-conformal factor that suppresses contributions from the high-momentum region where radiative processes are most relevant. Consequently, the temperature dependence of $\zeta/s$ remains essentially unchanged.
   • Electric Conductivity ($\sigma_Q/T$) and Baryon Diffusion ($\kappa_B/T^2$): Similar to the viscosities, the inclusion of inelastic processes results in a moderate reduction of these coefficients due to decreased relaxation times. The finite $\mu_B$ effects are mild, with no qualitative changes in the temperature dependence observed between $\mu_B = 0$ and $\mu_B = 0.4$ GeV.

Significance and Claims
The paper claims that while radiative inelastic processes are physically present and systematically reduce transport coefficients by shortening relaxation times, their contribution within the strongly interacting QGP described by the DQPM is a sub-leading correction rather than a dominant mechanism.

• Robustness of Previous Results: The study validates the robustness of previous DQPM transport calculations based solely on elastic scattering, confirming that the omission of $2 \to 3$ channels does not lead to qualitative errors in the thermal regime.
• Predictive Power: The results provide updated microscopic inputs for hydrodynamic and transport simulations of heavy-ion collisions at finite net-baryon density. Specifically, the predictions for $\eta/s$, $\zeta/s$, $\sigma_Q/T$, and $\kappa_B$ at finite $\mu_B$ serve as model constraints for interpreting beam-energy-scan data.
• Limitations: The authors note that the current treatment within RTA does not constitute a full solution of the linearized inelastic collision operator (which would require explicit inclusion of inverse $3 \to 2$ processes and detailed balance). They speculate that inverse processes are further suppressed due to thermal phase space restrictions but acknowledge this as a direction for future work.