Thermalization in Weakly Coupled Nonabelian Plasmas (1107.5050v1)

Abstract: We investigate how relativistic, nonabelian plasmas approach equilibrium in a general context. Our treatment is entirely parametric and for small Yang-Mills coupling $\alpha$. First we study isotropic systems with an initially nonequilibrium momentum distribution. We consider both the case of initially very high occupancy and initially very low occupancy. Then we consider systems which are anisotropic. We consider both weak anisotropy and large anisotropy, and allow the occupancy to be parametrically large or small. Writing the typical momentum of an initial excitation as Q and the final temperature as T, full equilibration occurs in a time t ~ \alpha^{-2}/T for T > Q, and t ~ \alpha^{-2} Q^{1/2} T^{-3/2} for T < Q, unless the initial system is sufficiently anisotropic and T > \alpha^{2/3} Q, in which case equilibration occurs somewhat faster, t ~ \alpha^{-13/7} Q^{5/7} T^{-12/7} (or \alpha^{-2}/T if that is longer).

• The paper establishes key thermalization mechanisms in nonabelian plasmas using perturbative analyses of elastic scattering, inverse splitting, and the LPM effect.
• It employs parametric models to contrast isotropic and anisotropic equilibration, highlighting how instabilities like Nielsen-Olesen and Weibel modify momentum distributions.
• The findings offer critical insights for early universe reheating and heavy-ion collisions, paving the way for advanced non-perturbative studies.

Overview of Thermalization in Weakly Coupled Nonabelian Plasmas

The paper by Aleksi Kurkela and Guy D. Moore, titled "Thermalization in Weakly Coupled Nonabelian Plasmas," presents a rigorous paper of the equilibration process in nonabelian plasmas, particularly focusing on weakly coupled scenarios typical of QCD. The authors analyze the dynamics and time scales associated with thermalization using parametric models in systems characterized by small Yang-Mills coupling $\alpha$.

The authors aim to understand how nonabelian plasmas approach equilibrium, given their significance in cosmological events, such as reheating post-inflation, and in high-energy physics contexts like heavy ion collisions. Their approach is grounded in high-energy QCD principles with weak couplings facilitating a perturbative analysis.

Key Findings

The paper categorizes the processes of equilibration into cases based on occupancy and anisotropy:

1. Isotropic Systems:
   • Overoccupied Systems ($0 < c < 1$): These systems evolve through elastic scattering and number-changing processes leading to a cascade of excitations into a thermal distribution with a time scale of $\alpha^{-2+\frac{c}{4}}$. The authors find that large-scale excitations can facilitate faster thermalization via inverse splitting processes, leading to full equilibration at $\sim \alpha^{-2} T^{-1}$.
   • Extreme Overoccupancy ($c > 1$): The Nielsen-Olesen instability rapidly converts the system's distribution into one described by $c=1$, allowing the modes to grow quickly and redistribute energy into higher momentum scales.
   • Underoccupied Systems ($c < 0$): The primary mechanism involves the formation of a thermal bath of soft particles catalyzing the further breakdown of hard excitations in a time scale $\sim \alpha^{-2+\frac{3c}{8}}$. Energy loss from hard particles is dominated by the emission of softer excitations modified by the Landau-Pomeranchuk-Migdal (LPM) effect, leading to final equilibration when $T \sim \alpha^{-c/4} Q$.
2. Anisotropic Systems:
   • Weak Anisotropy: Initiated plasma instabilities contribute to momentum redistribution due to angular dependence, significantly altering equilibrium times and mechanisms compared to isotropic cases. These instabilities can dominate dynamics when $\epsilon > \alpha^{\frac{1+c}{3}}$ or $\epsilon > \alpha^{\frac{1-c}{3}}$, leading to early direction randomization of momenta.
   • Large Anisotropy (both oblate and prolate distributions): Dominated by Weibel instabilities causing significant directional changes and particle creation in narrower solid angle distributions. The authors propose critical thresholds where nonlinear dynamics infer significant changes to mode distributions before instabilities saturate. The paper delineates scenarios where thermalization is inhibited until unstable modes are sufficiently dampened or the system isotropizes.

Implications and Speculations

The paper lays a foundational understanding of equilibration dynamics in weakly coupled nonabelian plasmas, crucial for both theoretical considerations and interpretations of early universe cosmology and ultra-relativistic heavy-ion collisions. The breakdown timescales and mechanisms underscore the relevance of plasma instabilities, providing insight into kinetic theory predictions in high-density environments.

Future work might explore non-perturbative effects, potentially enhancing the qualitative descriptions where thermal field theory and effective kinetic models might underestimate complex interaction terms. Exploring further into real collision setups beyond perturbative regimes remains an intriguing and necessary aspect to bridge theoretical findings with experimental observations.

Conclusion

This detailed parametric analysis by Kurkela and Moore stands as a substantive reference to elucidate the intricacies of plasma equilibration through an array of dynamic processes, accommodating the spectrum from isotropic to highly anisotropic conditions. Understanding these mechanics is pivotal for progressing the paper of fundamental forces in extreme conditions, shaping future investigations in high-energy physics and related fields.