Transmutation of nonlocal scale in infinite derivative field theories

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-eff similar to M-s / N-alpha, where M-s is the fundamental scale beyond the Standard Model and 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.