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In this work, we derive an expression for the correction in the Newton's lawof gravitation due to the gravitational Kaluza-Klein states in a general thickstring-like braneworld scenario in six dimensions. In order to analyzecorrections to Newton's law we study the gravity fluctuations in a 3-braneplaced in a transverse resolved conifold and use suitable numerical methods toattain the massive spectrum and the corresponding eigenfunctions. Suchbraneworld model has a resolution parameter which removes the conicalsingularity. The correction has an exponentially suppressed mass term anddepends on the values of the eigenfunctions and warp factors computed at thecore peak of the brane. The spectrum is real and monotonically increased, asdesired. However, the resolution parameter must assume moderate values to havephysically acceptable states. Moreover, the trapped massless mode regains the4D gravity and it is displaced from the origin, sharing similar profile withthe energy density of brane for small values of resolution parameter. Finally,for the singular conifold, we found that a non-first eigenstate is a resonantmode. Such excited state is the largest contributor to corrections in theNewtonian potential.

Graviton KK resonant mode in the correction of the Newton's law from 6D braneworlds