Do 1/r potentials require massless particles ?

TL;DR

This paper explores whether long-range 1/r potentials can exist without massless particles, suggesting they might arise in certain broken scalar field theories due to zero-momentum propagator effects.

Contribution

It proposes that infinitesimally weak 1/r potentials could originate in a simple broken scalar theory, challenging the notion that massless particles are necessary for such potentials.

Findings

1/r potential may emerge in broken scalar theories due to zero-momentum propagator effects

The potential could be infinitesimally weak but long-range

Implications for lattice simulations and phenomenology are discussed

Abstract

Long-range 1/r potentials play a fundamental role in physics. Their ultimate origin is usually traced back to the existence of genuine massless particles as photons or gravitons related to fundamental properties of continuum quantum field theories such as gauge invariance. In this Letter, it is argued that, in principle, an asymptotic, infinitesimally weak 1/r potential might also occur in the cutoff version of a simple, one-component spontaneously broken \Phi^4 theory, after taking into account the peculiar nature of the zero-momentum limit of the connected scalar propagator. Physical interpretation, phenomenological implications and proposals for a new generation of lattice simulations are also discussed.