Brane world corrections to scalar vacuum force in RSII-p, R. Linares, H. A. Morales-Tecotl, O. Pedraza, Phys.Rev.D78:066013 (2008), arXiv:0804.2042 [hep-ph].
Vacuum force is an interesting low energy test for brane worlds due to its dependence on fields modes and its role in submillimeter gravity experiments. In this work, we generalize a previous model example: the scalar field vacuum force between two parallel plates lying in the brane of a Randall-Sundrum scenario extended by p compact dimensions (RSII-p). Upon use of Greens function technique, for the massless scalar field, the 4D force is obtained from a zero mode while leading order corrections due to the noncompact dimension turn out attractive and depend on the separation between plates as l-(6+p). For the massive scalar field, a quasilocalized mode yields the 4D force with attractive corrections behaving like l-(10+p). Corrections are negligible with respect to 4D force for anti-de Sitter (AdS(5+p)) radius much less than ?10-6??m. In the massless case we also determined, numerically, the corrections due to compact dimensions. To avoid conflict with experimental data we get R?0.4???m, 0.3???m for the cases p=1, 2, respectively. Although the p=0 case is not physically viable due to the different behavior in regard to localization for the massless scalar and electromagnetic fields it yields a useful comparison between the dimensional regularization and Greens function techniques as we describe in the discussion.