Non-Abelian plasma instabilities: SU(3) vs. SU(2) (1012.0298v2)

Abstract: We present the first 3+1 dimensional simulations of non-Abelian plasma instabilities in gauge-covariant Boltzmann-Vlasov equations for the QCD gauge group SU(3) as well as for SU(4) and SU(5). The real-time evolution of instabilities for a plasma with stationary momentum-space anisotropy is studied using a hard-loop effective theory that is discretized in the velocities of hard particles. We find that the numerically less expensive calculations using the group SU(2) essentially reproduce the nonperturbative dynamics of non-Abelian plasma instabilities with higher rank gauge groups provided the mass parameters of the corresponding hard-loop effective theories are the same. In particular we find very similar spectra for the turbulent cascade that forms in the strong-field regime, which is associated with an approximately linear growth of energy in collective fields. The magnitude of the linear growth however turns out to increase with the number of colors.

• The paper demonstrates that non-Abelian plasma instabilities undergo an initial exponential growth phase before saturating into a linear regime as non-Abelian effects dominate.
• The paper reveals that the energy density growth in collective fields scales linearly with the number of colors, as confirmed by comparisons across SU(2) to SU(5).
• The paper identifies a turbulent cascade in the strong-field regime with a power-law spectral index near 2, offering insights into energy transport in quark-gluon plasmas.

Insights into Non-Abelian Plasma Instabilities in Higher SU(N) Gauge Groups

The paper presents rigorous investigations into the dynamics of non-Abelian plasma instabilities, focusing on their behavior across different SU(N) gauge groups—specifically SU(2), SU(3), SU(4), and SU(5). The research utilizes 3+1 dimensional simulations within the gauge-covariant Boltzmann-Vlasov framework, with the primary aim of understanding the influence of the number of colors on plasma instabilities in a quark-gluon plasma exhibiting momentum-space anisotropy.

Summary of Methodology

The paper leverages a discretized form of the hard-loop effective theory, which is critical for modeling weakly coupled quark-gluon plasmas. This approach allows for the examination of plasma instabilities using gauge groups beyond the commonly studied SU(2). The configuration space is represented by cubic lattices while the velocity space is discretized, enabling the simulation of the real-time evolution of instabilities.

Initially, the work verifies that the SU(2) simulations adequately capture nonperturbative dynamics, given that the mass parameters of the associated hard-loop effective theories remain consistent. The simulations were initialized with small gauge fields to explore both the Abelian growth phase and the subsequent non-Abelian self-interaction dominated regime.

Key Findings

1. Exponential Growth and Linear Dynamics:
   • The simulations confirm that during the initial phase, plasma instabilities exhibit exponential growth, which is saturated when non-Abelian interactions become significant. Following this saturation, a linear growth of energy density in collective fields is observed.
2. Influence of the Number of Colors:
   • It is observed that the energy grown in collective modes increases with the number of colors, N$_c$, suggesting a linear relationship. Specifically, for SU(2) through SU(5), the growth rate scales approximately proportional to N$_c$.
3. Spectral Analysis:
   • A turbulent cascade forms in the strong-field regime, characterized by a power-law distribution with a spectral index $\nu \approx 2$. This finding aligns with the conceptual understanding of energy transport from low to higher momentum modes, a haLLMark of non-Abelian cascading behavior.

Implications and Future Directions

The findings have substantial implications for understanding early dynamics in high-energy nuclear collisions, notably those at facilities like the LHC. The ability to simulate plasma instabilities in physically relevant gauge groups such as SU(3) provides a more refined theoretical backing to the initial conditions of quark-gluon plasma isotropization and thermalization observed in experiments.

Moreover, this work sets the stage for further exploration into more complex initial conditions and their effects on plasma behavior, particularly as higher energy scales are probed in future collider experiments. The observed scaling relations with N$_c$ may also inspire theoretical advancements in large N$_c$ QCD and related fields, enhancing our grasp of strong-field QCD dynamics.

The paper's exploration of non-Abelian phenomena through comprehensive numerical simulations expands the toolkit for theoretical physicists, offering new avenues to validate models against experimental data and deepen the overall understanding of quark-gluon plasma. Future research might focus on initializing simulations with more realistic conditions drawn from experimental data or exploring the transition from the weak coupling regime to nonperturbative QCD domains.