Kaluza-Klein tower thresholds and scheme dependence of the species scale

Abstract

We revisit the species scale in quantum gravity from the viewpoint of effective field theory (EFT). Two characterizations are commonly used: one defines it as the energy at which the perturbative description of quantum gravity breaks down, as inferred from the one-loop correction to the graviton propagator; the other identifies it with the suppression scale of higher-derivative operators in the gravitational effective action. We clarify the relation between these characterizations by analyzing the cutoff-scheme dependence of the one-loop tower contribution. For a large number of species, the leading tower-enhanced local correction is regulator dependent and should be interpreted as EFT matching data, while the subleading logarithmic contribution is universal within the class of proper-time cutoff profiles considered here. As a concrete application, we compute the full four-derivative one-loop corrections from Kaluza-Klein towers. Our results separate regulator-stable logarithmic data from scheme-dependent local threshold contributions, providing a controlled EFT interpretation of the relation between perturbative-breakdown and higher-derivative definitions of the species scale and explaining why their coefficient-level identification is not regulator independent.

52 pages, 2 figures, ancillary file included