Transmutation of nonlocal scale in infinite derivative field theories

Abstract

In this paper we will show an ultraviolet-infrared connection for ghost-free infinite derivative field theories where the Lagrangians are made up of exponentials of entire functions. In particular, for $N$-point amplitudes a new scale emerges in the infrared from the ultraviolet, i.e., ${M}_{\mathrm{eff}}\ensuremath{\sim}{M}_{s}/{N}^{\ensuremath{\alpha}}$, where ${M}_{s}$ is the fundamental scale beyond the Standard Model and $\ensuremath{\alpha}>0$ depends on the specific choice of an entire function and on whether we consider zero or nonzero external momenta. We will illustrate this by first considering a scalar toy model with a cubic interaction and subsequently a scalar toy model inspired by ghost-free infinite derivative theories of gravity. We will briefly discuss some phenomenological implications, such as making the nonlocal region macroscopic in the infrared.