2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101918A precise measurement of a muon $(g-2)$ experiment recently reported a deviation from the Standard Model. This implies the need to an extension of the model and suggests underlying mechanisms. We hypothesize that the influence of higher dimensional gravity causes this $(g-2)$ deviation. This effect would appear as Kaluza-Klein modes and Nambu-Goldstone modes on a 3-brane. These classical effects produce new contributions to the magnetic moment. In this paper, we perform a consistency check by comparing the results derived from the Born and Schr{ö}dinger approximations. This comparison reveals a similarity between KK-dilaton modes and the brane stretching effect.8 pages, 2 figures, minor corrections, title changed, accepted for Progress of Theoretical PhysicsHigh Energy Physics - PhenomenologyAstrophysicsGeneral Relativity and Quantum CosmologyHigh Energy Physics - Theorytext