Graviton KK resonant modes in the correction of Newton's law from six-dimensional braneworlds

In this work, we derive an expression for the corrections in Newton's law of gravitation due to gravitational Kaluza-Klein (KK) states in a general thick string-like braneworld scenario in six dimensions (6D). The correction has an exponentially suppressed mass term and depends on the values of the eigenfunctions and warp factors computed at the peak of the brane. Besides, we use suitable numerical methods to analyze such corrections in a 3-brane placed in a transverse Resolved Conifold (RC), wherein we attain the massive KK spectrum and its corresponding eigenfunctions. The spectrum is real and monotonically increasing. The RC model has a parameter, known as the resolution parameter, which removes the conical singularity and we conclude that such parameter must assume moderate values to have physically acceptable states. Moreover, the trapped massless mode regains the 4D gravity, and it is displaced from the origin, sharing a similar profile with the energy density of brane for small values of the resolution parameter. Finally, we found for the singular RC a resonant mode which is the seventh eigenfunction in the KK mass tower. Such an excited state is the most accountable massive mode in the computation of the deviations in the Newtonian potential. Moreover, the bounds to RC parameters are briefly discussed as a perspective to fit the current experimental data.