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

Second-Order Optimality Conditions in Cone-Constrained Vector Optimization with Arbitrary Nondifferentiable Functions

In this paper, we introduce a new second-order directional derivative and a second-order subdifferential of Hadamard type for an arbitrary nondifferentiable function. We derive several second-order optimality conditions for a local and a global minimum and an isolated local minimum of second-order in unconstrained optimization. In particular, we obtain two types results with generalized convex functions. We also compare our conditions with the results of the recently published paper [Bednavrik, D., Pastor, K.: On second-order conditions in unconstrained optimization. Math. Program. Ser A, {\bf 113}, 283--291 (2008)] and a lot of other works, published in high level journals, and prove that they are particular cases of our necessary and sufficient ones. We prove that the necessary optimality conditions concern more functions than the lower Dini directional derivative, even the optimality conditions with the last derivative can be applied to a function, which does not belong to some special class. At last, we apply our optimality criteria for unconstrained problems to derive necessary and sufficient optimality conditions for the cone-constrained vector problems.Comment: 24 pages. arXiv admin note: substantial text overlap with arXiv:1311.236

Creation of two vortex-entangled beams in a vortex beam collision with a plane wave

Physics of photons and electrons carrying orbital angular momentum (OAM) is an exciting field of research in quantum optics and electron microscopy. Usually, one considers propagation of these vortex beams in a medium or external fields and their absorption or scattering on fixed targets. Here we consider instead a beam-beam collision. We show that elastic scattering of a Bessel vortex beam with a counterpropagating plane wave naturally leads to two vortex-entangled outgoing beams. The vortex entanglement implies that the two final particles are entangled not only in their orbital helicities but also in opening angles of their momentum cones. Our results are driven by kinematics of vortex-beam scattering and apply to particle pairs of any nature: e-gamma, e^+e^-, ep, etc. This collisional vortex entanglement can be used to create pairs of OAM-entangled particles of different nature, and to transfer a phase vortex, for example, from low-energy electrons to high-energy protons.Comment: 4 pages, 2 figures; v2: title modified, introduction rewritten and expanded, results unchange