In this paper we investigate the innermost stable circular orbit (ISCO) (spin-aligned or anti-aligned orbit) for a classical spinning test particle with the pole-dipole approximation in the background of Kerr-Newman black hole in the equatorial plane. It is shown that the orbit of the spinning particle is related to the spin of the test particle. The motion of the spinning test particle will be superluminal if its spin is too large. We give an additional condition by considering the superluminal constraint for the ISCO in the black hole backgrounds. We obtain numerically the relations between the ISCO and the properties of the black holes and the test particle. It is found that the radius of the ISCO for a spinning test particle is smaller than that of a nonspinning test particle in the black hole backgrounds.

It is known that a five-dimensional free vector field $A_M$ cannot be localized on Randall-Sundrum (RS)-like thick branes—namely, the thick branes embedded in asymptotic anti–de Sitter spacetime. To localize a vector field on the RS-like thick brane, an extra coupling term should be introduced. We generalize the geometrical coupling mechanism by adding two mass terms ($\alpha R{g}^{MN}{A}_M{A}_N+\beta R^{MN}{A}_M{A}_N$) to the action. We decompose the fundamental vector field $A_M$ into three parts: transverse vector part ${\widehat{A}}_{\mu }$ and scalar parts $\varphi$ and $A_5$. Then we find that the transverse vector part ${\widehat{A}}_{\mu }$ decouples from the scalar parts. To eliminate the tachyonic modes of ${\widehat{A}}_{\mu }$, the two coupling parameters $\alpha$ and $\beta$ should satisfy a relation. Combining the restricted condition, we can get a combination parameter as $\gamma =\frac{3}{2}\pm \sqrt{1+12\alpha }$. Only if $\gamma >1/2$ can the zero mode of ${\widehat{A}}_{\mu }$ be localized on the RS-like thick brane. We also investigate the resonant character of the vector part ${\widehat{A}}_{\mu }$ for a general RS-like thick brane with a warp factor $A(z)=-\ln (1+k^2{z}^2)/2$ by choosing the relative probability method. The results show that the massive resonant Kaluza-Klein modes can exist only for $\gamma >3$. The number of resonant Kaluza-Klein states increases with the combination parameter $\gamma$, and the lifetime of the first resonant state can be as long as our Universe’s. This indicates that the vector resonances might be considered one of the candidates of dark matter. Combining the conditions of experimental observations, the constraint shows that the parameter $k$ has a lower limit with $k\gtrsim {10}^{-17}\mathrm{eV}$, the combination parameter $\gamma$ should be greater than 57, and, accordingly, the mass of the first resonant state should satisfy $m_1\gtrsim {10}^{-15}\mathrm{eV}$.

In this paper, we investigate thick branes generated by a scalar field in mimetic gravity theory, which is inspired by considering the conformal symmetry under the conformal transformation of an auxiliary metric. By introducing two auxiliary super-potentials, we transform the second-order field equations of the system into a set of first-order equations. With this first-order formalism, several types of analytical thick brane solutions are obtained. Then, tensor and scalar perturbations are analyzed. We find that both kinds of perturbations are stable. The effective potentials for the tensor and scalar perturbations are dual to each other. The tensor zero mode can be localized on the brane while the scalar zero mode cannot. Thus, the four-dimensional Newtonian potential can be recovered on the brane.

The 4.2\sigma 4.2 σ discrepancy in the (g-2) ( g − 2 ) of the muon provides a hint that may indicate that physics beyond the standard model is at play. A multi-TeV scale muon collider provides a natural testing ground for this physics. In this paper, we discuss the potential to probe the BSM parameter space that is consistent with solving the (g-2)_{\mu} ( g − 2 ) μ discrepancy in the language of the SMEFT, utilizing the statistical power provided by fitting event rates collected running at multiple energies. Our results indicate the importance of including interference between the BSM and the SM amplitudes, and illustrates how a muon collider running at a handful of lower energies and with less total collected luminosity can better significantly constrain the space of relevant SMEFT coefficients than would be possible for a single high energy run.