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 common parametric characterizations relate it to the breakdown of perturbative gravity and to the suppression scale of higher-derivative gravitational operators. We examine their correspondence through local threshold corrections from infinite Kaluza–Klein (KK) towers. In four dimensions, we compute the four-derivative one-loop action of minimally coupled scalar and Dirac towers with KK spectra in graviton, radion, and photon backgrounds. Feynman diagrams determine the single-mode coefficients, while analytic summation with full threshold functions tests the logarithmic coefficient inferred from renormalization-group evolution. The leading contribution scales with the effective number of KK levels, reproducing the standard species-scale relation under the stated matching assumptions, but its coefficient depends on the cutoff profile and belongs to EFT matching data. In contrast, the subleading curvature-squared thresholds contain logarithms of the KK mass gap whose spin-dependent coefficients remain stable under changes of the cutoff profile within the class studied here.