Recently, a family of interesting analytical brane solutions were found in f (R) gravity with f (R) = R + α R 2 in Bazeia et al. (Phys Lett B 729:127 2014). In these solutions, the inner brane structure can be turned on by tuning the value of the parameter α. In this paper, we investigate how the parameter α affects the localization and the quasilocalization of the tensorial gravitons around these solutions. It is found that, in a range of α, despite the brane having an inner structure, there is no graviton resonance. However, in some other regions of the parameter space, although the brane has no internal structure, the effective potential for the graviton Kaluza-Klein (KK) modes has a singular structure, and there exist a series of graviton resonant modes. The contribution of the massive graviton KK modes to Newton's law of gravity is discussed briefly.

Stringent limits are set on the long-lived lepton-like sector of the phenomenological minimal supersymmetric standard model (pMSSM) and the anomaly-mediated supersymmetry breaking (AMSB) model. The limits are derived from the results presented in a recent search for long-lived charged particles in proton–proton collisions, based on data collected by the CMS detector at a centre-of-mass energy of 8 TeV at the Large Hadron Collider. In the pMSSM parameter sub-space considered, 95.9 % of the points predicting charginos with a lifetime of at least 10 ns are excluded. These constraints on the pMSSM are the first obtained at the LHC. Charginos with a lifetime greater than 100 ns and masses up to about 800 GeV in the AMSB model are also excluded. The method described can also be used to set constraints on other models.

It is known that by introducing the Yukawa coupling between the fermion and the background scalar field, a bulk spin-half fermion can be localized on general Randall-Sundrum braneworlds generated by a kinklike background scalar. However, this localization mechanism does not work anymore for Randall-Sundrum braneworlds generated by a scalar whose configuration is an even function of the extra dimension. In this paper, we present a new localization mechanism for spin-half fermions for such a class of braneworld models, in which extra dimension has the topology $S^1/Z_2$. By two examples, it is shown that the new localization mechanism produces interesting results. In the first model with the brane generated by two scalars, the zero mode of the left-handed fermion is localized on the brane and there is a mass gap between the fermion zero mode and excited KK modes. In the second model with the brane generated by a dilaton scalar, the zero mode of the left- or right-chiral fermion can be localized on the brane and there is no mass gap.Comment: 8 pages, 2 figure