Multi-Higgs models with CP symmetries of increasingly high order

When building CP-symmetric models beyond the Standard Model, one can impose CP-symmetry of higher order. This means that one needs to apply the CP-transformation more than two times to get the identity transformation, but still the model is perfectly CP-conserving. A multi-Higgs-doublet model based on CP-symmetry of order 4, dubbed CP4, was recently proposed and its phenomenology is being explored. Here, we show that the construction does not stop at CP4. We build examples of renormalizable multi-Higgs-doublet potentials which are symmetric under CP8 or CP16, without leading to any accidental symmetry. If the vacuum conserves CP-symmetry of order 2k, then the neutral scalars become CP-eigenstates, which are characterized not by CP-parities but by CP-charges defined modulo 2k. One or more lightest states can be the dark matter candidates, which are protected against decay not by the internal symmetry but by the exotic CP. We briefly discuss their mass spectra and interaction patterns for CP8 and CP16.Comment: 13 pages; v2: extra comments and references; v3: extra clarifications, matches published versio

Resonant Cyclotron Scattering and Comptonization in Neutron Star Magnetospheres

Resonant cyclotron scattering of the surface radiation in the magnetospheres of neutron stars may considerably modify the emergent spectra and impede efforts to constraint neutron star properties. Resonant cyclotron scattering by a non-relativistic warm plasma in an inhomogeneous magnetic field has a number of unusual characteristics: (i) in the limit of high resonant optical depth, the cyclotron resonant layer is half opaque, in sharp contrast to the case of non-resonant scattering. (ii) The transmitted flux is on average Compton up-scattered by ~ $1+ 2 beta_T$, where $\beta_T$ is the typical thermal velocity in units of the velocity of light; the reflected flux has on average the initial frequency. (iii) For both the transmitted and reflected fluxes the dispersion of intensity decreases with increasing optical depth. (iv) The emergent spectrum is appreciably non-Plankian while narrow spectral features produced at the surface may be erased. We derive semi-analytically modification of the surface Plankian emission due to multiple scattering between the resonant layers and apply the model to anomalous X-ray pulsar 1E 1048.1--5937. Our simple model fits just as well as the ``canonical'' magnetar spectra model of a blackbody plus power-law.Comment: 37 pages, 10 figures, accepted by MNRAS, minor change

A Beautiful Blonde: a Nash coordination game

In a memorable scene from the …lm ”A Beautiful Mind,” John Nash explains to his friends how to direct their attentions to women in a bar. Game theorists who have seen the …lm point out that the proposed solution is not a Nash equilibrium. Here we determine the Nash equilibria to the attention game. The symmetric mixed strategy equilibrium has resembles a common property resource problem. It has perverse comparative static properties that are not borne out by experimental data. Finally, we discuss alternative ways of formulating the game.coordination, Nash equilibrium, mixed strategy equilibrium, common property resource problem, comparative statics.

Phase diagram for the ν=0\nu=0 quantum Hall state in monolayer graphene

The $\nu=0$ quantum Hall state in a defect-free graphene sample is studied within the framework of quantum Hall ferromagnetism. We perform a systematic analysis of the pseudospin anisotropies, which arise from the valley and sublattice asymmetric short-range electron-electron (e-e) and electron-phonon (e-ph) interactions. The phase diagram, obtained in the presence of generic pseudospin anisotropy and the Zeeman effect, consists of four phases characterized by the following orders: spin-polarized ferromagnetic, canted antiferromagnetic, charge density wave, and Kekul\'{e} distortion. We take into account the Landau level mixing effects and show that they result in the key renormalizations of parameters. First, the absolute values of the anisotropy energies become greatly enhanced and can significantly exceed the Zeeman energy. Second, the signs of the anisotropy energies due to e-e interactions can change upon renormalization. A crucial consequence of the latter is that the short-range e-e interactions alone could favor any state on the phase diagram, depending on the details of interactions at the lattice scale. On the other hand, the leading e-ph interactions always favor the Kekul\'{e} distortion order. The possibility of inducing phase transitions by tilting the magnetic field is discussed.Comment: 25 pages, 19 figs; v2: nearly identical to the published version, some stylistic improvements, Tables I-IV added, anisotropy energies redefined as u -> u/2 for aesthetic reaso