# Transmutation of nonlocal scale in infinite derivative field theories

## TL;DR

This paper demonstrates a connection between ultraviolet and infrared scales in ghost-free infinite derivative field theories, showing how a new infrared scale emerges from the ultraviolet scale depending on the number of points and the choice of entire functions.

## Contribution

It introduces a novel scale transmutation mechanism in infinite derivative theories, linking UV and IR regimes through N-point amplitudes and specific entire functions.

## Key findings

- Infrared scale M_eff depends on ultraviolet scale M_s and number of points N.
- The scale transmutation is demonstrated in scalar toy models with cubic interactions.
- Potential phenomenological implications include macroscopic nonlocal regions.

## 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. $M_{\rm eff}\sim M_s/N^\alpha,$ 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.