Gravity-Matter Sum Rules in models with a single extra-dimension

TL;DR

This paper derives general sum rules for Kaluza-Klein gravitons in extra-dimensional models, ensuring unitarity and reducing high-energy growth of scattering amplitudes, thus broadening the understanding of extra-dimensional theories.

Contribution

It establishes universal sum rules for KK-graviton wave functions and masses, extending previous results to a wider class of models beyond the Randall-Sundrum scenario.

Findings

Sum rules ensure cancellations in KK-graviton production amplitudes.

These relations prevent unitarity violation at high energies.

Results are applicable to a broad category of extra-dimensional models.

Abstract

We prove a set of sum rules needed for KK-graviton pair production from matter in orbifolded extra-dimensional models. The sum rules can be found in full generality by considering the properties of solutions to the Sturm-Liouville problem, which describes the wave functions and the masses of the KK-gravitons in four dimensions. They ensure cancellations in the amplitudes of the processes mentioned above which considerably reduce their growth with $s$ in the high-energy limit. This protects extra-dimensional theories from the low-scale unitarity problems that plague other theories with massive spin-2 particles. We argue that such relations are valid for a broader category of models thus generalizing our previous results that were limited to the large $\mu$ limit of the Randall-Sundrum model.