Manifestation of infrared instabilities in high energy processes in non-Abelian gauge theories

Abstract

We show that a high frequency standing wave in SU(2) gauge theory is unstable against decay into long wavelength modes. This provides a nonperturbative mechanism for energy transfer from initial high momentum modes to final states with low momentum excitations. The Abelian case does not manifest such instability. Our analysis is supported by lattice simulations.

Wave packet dynamics in Yang-Mills theory

“…Thus, one understands why the instability persists even for very small relative polarizations, as seen in Figure 8. As a further check on our understanding of this limit, the cases with very small θ c in Figures 8 and 9 display the similar exponential growth found in [2].…”

“…Larger values of σ require longer times for the development of comparable nonlinearities. This is analogous to the case of the standing wave configuration where the largest Lyapunov exponent is a linear function of the amplitude [2].…”

Quantum Scattering and Classical Solutions

“…This is in contrast to plane waves, which exist everywhere in spacetime. Since the plane waves of Müller et al [5] have finite, nonzero amplitude, they also contain the equivalent of an infinite number of particles. It is quite possible that the behavior of wave packets representing a finite number of particles is very different.…”

“…In light of this new formalism, I will discuss the implications of some recent numerical simulations in classical field theory for high energy two-particle scattering. In particular, in 4-dimensional pure SU(2) Yang-Mills theory, Gong, Matinyan, Müller and Trayanov [5] have found an instability of high frequency standing waves of pure glue to decay to low frequency modes. When interpreted within our formalism, this result leads to the speculation that multiparticle scattering in SU(2) gauge theories may be unsuppressed (at least exponentially) at high energies.…”

Real-time evolution of soft QCD in ultra-relativistic heavy-ion collisions

“…It avoids the problem with the lattice dispersion since the discretized k-space is fixed after the boost. The adiabatic increase of the coupling constant avoids the excitation of instable high frequent modes in the color fields [32]. However, it requires large initial distances between the nuclei because the charge fluctuation µ converges slowly against a final constant value before the collision.…”