Z_p scalar dark matter from multi-Higgs-doublet models

In many models, stability of dark matter particles is protected by a conserved Z_2 quantum number. However dark matter can be stabilized by other discrete symmetry groups, and examples of such models with custom-tailored field content have been proposed. Here we show that electroweak symmetry breaking models with N Higgs doublets can readily accommodate scalar dark matter candidates stabilized by groups Z_p with any $p \le 2^{N-1}$, leading to a variety of kinds of microscopic dynamics in the dark sector. We give examples in which semi-annihilation or multiple semi-annihilation processes are allowed or forbidden, which can be especially interesting in the case of asymmetric dark matter.Comment: 10 page

Minkowski space structure of the Higgs potential in 2HDM

The Higgs potential of 2HDM keeps its generic form under the group of transformation GL(2,C), which is larger than the usually considered reparametrization group U(2). This reparametrization symmetry induces the Minkowski space structure in the orbit space of 2HDM. Exploiting this property, we present a geometric analysis of the number and properties of stationary points of the most general 2HDM potential. In particular, we prove that charge-breaking and neutral vacua never coexist in 2HDM and establish conditions when the most general explicitly CP-conserving Higgs potential has spontaneously CP-violating minima. Our analysis avoids manipulation with high-order algebraic equations.Comment: 33 pages, 6 figures; v3: corrected a flaw in the proof of proposition 1

Extended Camassa-Holm Hierarchy and Conserved Quantities

An extension of the Camassa-Holm hierarchy is constructed in this letter. The conserved quantities of the hierarchy are studied and a recurrent formula for the integrals of motion is derived.Comment: 13 page