We calculate the next to the leading order Casimir effect for a real scalar field, within φ 4 theory, confined between two parallel plates in three spatial dimensions with the Dirichlet boundary condition. In this paper we introduce a systematic perturbation expansion in which the counterterms automatically turn out to be consistent with the boundary conditions. This will inevitably lead to nontrivial position dependence for physical quantities, as a manifestation of the breaking of the translational invariance. This is in contrast to the usual usage of the counterterms in problems with nontrivial boundary conditions, which are either completely derived from the free cases or at most supplemented with the addition of counterterms only at the boundaries. Our results for the massive and massless cases are different from those reported elsewhere. Secondly, and probably less importantly, we use a supplementary renormalization procedure, which makes the usage of any analytic continuation techniques unnecessary.
We consider the standard model (SM) extended by a gauge singlet fermion as cold dark matter (SFCDM) and a gauge singlet scalar (singlet Higgs) as a mediator. The parameter space of the SM is enlarged by seven new ones. We obtain the total annihilation cross section of singlet fermions to the SM particles and singlet Higgs at tree level. Regarding the relic abundance constraint obtained by WMAP observations, we study the dependency on each parameter separately, for dark matter masses up to 1 TeV. In particular, the coupling of SFCDM to singlet Higgs gs, the SFCDM mass m ψ , the second Higgs mass m h 2 , and the Higgs bosons mixing angel θ are investigated accurately. Three other parameters play no significant role. For a maximal mixing of Higgs bosons or at resonances, gs is applicable for the perturbation theory at tree level. We also obtain the scattering cross section of SFCDM off nucleons and compare our results with experiments which have already reported data in this mass range; XENON100, LUX, COUPP and PICASSO collaborations. Our results show that the SFCDM is excluded by these experiments for choosing parameters which are consistent with perturbation theory and relic abundance constraints. * Electronic address: mettefaghi@qom.ac.ir † Electronic address: r.moazzemi@qom.ac.ir
In this paper we compute the leading order Casimir energy for the electromagnetic field (EM) in an open ended perfectly conducting rectangular waveguide in three spatial dimensions by a direct approach. For this purpose we first obtain the second quantized expression for the EM field with boundary conditions which would be appropriate for a waveguide. We then obtain the Casimir energy by two different procedures. Our main approach does not contain any analytic continuation techniques. The second approach involves the routine zeta function regularization along with some analytic continuation techniques. Our two approaches yield identical results. This energy has been calculated previously for the EM field in a rectangular waveguide using an indirect approach invoking analogies between EM fields and massless scalar fields, and using complicated analytic continuation techniques, and the results are identical to ours. We have also calculated the pressures on different sides and the total Casimir energy per unit length, and plotted these quantities as a function of the cross-sectional dimensions of the waveguide. We also present a physical discussion about the rather peculiar effect of the change in the sign of the pressures as a function of the shape of the cross-sectional area.
In models of anapole dark matter (DM), the DM candidate is a Majorana fermion whose primary interaction with standard model (SM) particles is through an anapole coupling to off-shell photons. As such, at tree-level, anapole DM undergoes p-wave annihilation into SM charged fermions via a virtual photon. But, generally, Majorana fermions are polarizable, coupling to two real photons. This fact admits the possibility that anapole DM can annihilate into two photons in an s-wave process. Using an explicit model, we compute both the tree-level and diphoton contributions to the anapole DM annihilation cross section. Depending on model parameters, the s-wave process can either rival or be dwarfed by the p-wave contribution to the total annihilation cross section. Subjecting the model to astrophysical upper bounds on the s-wave annihilation mode, we rule out the model with large s-wave annihilation.
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