Infrared dressing in real time: emergence of anomalous dimensions

TL;DR

This paper introduces a dynamical resummation method to analyze infrared dressing in non-gauge theories, revealing universal power-law decay and entanglement properties of dressed states, with implications for effective field theories.

Contribution

It extends the dynamical renormalization group to study infrared dressing, deriving a universal anomalous dimension and analyzing entanglement entropy in non-gauge theories.

Findings

Power law decay of survival probability $ o t^{- riangle}$

Anomalous dimension $ riangle$ is universal, determined by spectral density slope

Infrared divergences absent in certain effective field theories of axion-like particles

Abstract

We implement a dynamical resummation method (DRM) as an extension of the dynamical renormalization group to study the time evolution of infrared dressing in non-gauge theories. Super renormalizable and renormalizable models feature infrared divergences similar to those of a theory at a critical point, motivating a renormalization group improvement of the propagator that yields a power law decay of the survival probability $\propto t^{-\Delta}$. The (DRM) confirms this decay, yields the dressed state and determines that the anomalous dimension $\Delta$ is completely determined by the slope of the spectral density at threshold independent of the ultraviolet behavior, suggesting certain universality for infrared phenomena. The dressed state is an entangled state of the charged and massless quanta. The entanglement entropy is obtained by tracing over the unobserved massless quanta. Its time evolution is determined by the (DRM), it is infrared finite and describes the information flow from the initial single particle to the asymptotic multiparticle dressed state. We show that effective field theories of massless axion-like particles coupled to fermion fields do not feature infrared divergences, and provide a criterion for infrared divergences in effective field theories valid for non-gauge theories up to one loop.