  A 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{\"o}dinger approximations. This comparison reveals a similarity
between KK-dilaton modes and the brane stretching effect.
