Mudit Rai, Lisong Chen, Daniel Boyanovsky

We implement a dynamical resummation method (DRM) as an extension of the dynamical renormalization group to study the time evolution of infrared dressing in nongauge 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 $\propto {t}^{-\mathrm{\Delta}}$. The DRM confirms this decay, yields the dressed state, and determines that the anomalous dimension $\mathrm{\Delta}$ 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, 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 axionlike particles coupled to fermion fields do not feature infrared divergences and provide a criterion for infrared divergences in effective field theories valid for nongauge theories up to one loop.