Related papers: Computable conditions for order-2 $CP$ symmetry in…
The second-order differential equation describes harmonic oscillators, as well as currents in LCR circuits. This allows us to study oscillator systems by constructing electronic circuits. Likewise, one set of closed commutation relations…
The spontaneous CP-violation in three kinds of extension of the standard model are investigated. We find that if no additional symmetry is introduced to reduce the number of coefficients, then all three extended models possess the…
We show that the quasi-exactly solvable eigenvalues of the Schr\"odinger equation for the PT-invariant potential $V(x) = -(\zeta \cosh 2x -iM)^2$ are complex conjugate pairs in case the parameter M is an even integer while they are real in…
We discuss the extrema of the Two Higgs Doublet Model with different physical properties. We have found necessary and sufficient conditions for realization of the extrema with different properties as the vacuum state of the model. We found…
A class of three-dimensional models which satisfy supersymmetric intertwining relations with the simplest - oscillator-like - variant of shape invariance is constructed. It is proved that the models are not amenable to conventional…
We study the potential of Weinberg's $\mathbb{Z}_2\times\mathbb{Z}_2$-symmetric three-Higgs-doublet model (3HDM). The potential is designed to accommodate CP violation in the scalar sector within a gauge theory, while at the same time…
We discuss the feasibility of spontaneous CP violation being induced by radiative corrections in 2HDM's, emphasizing on a consistent treatment at 1-loop level. Specifically, we analyze the cases of gaugino/higgsino effect on MSSM, and a new…
Second order integrals of motion for 3d quantum mechanical systems with position dependent masses (PDM) are classified. Namely, all PDM systems are specified which, in addition to their rotation invariance, admit at least one second order…
We review CP properties of the Two-Higgs-Doublet model. In particular, we show that spontaneous CP violation occurs in the parameter space on the border between regions allowing explicit CP violation and those where there is another…
We consider a class of linear ODEs of second order with variable coefficients and construct its Lie algebra of Lie group of equivalence transformations. Further we find invariants and differential invariants of this Lie algebra and by using…
Second-order optimality conditions of the bilevel programming problems are dependent on the second-order directional derivatives of the value functions or the solution mappings of the lower level problems under some regular conditions,…
We prove the existence of a model companion of the two-sorted theory of $c$-nilpotent Lie algebras over a field satisfying a given theory of fields. We describe a language in which it admits relative quantifier elimination up to the field…
We consider a Composite Higgs Model (CHM) with two isospin doublet Higgs fields arising as pseudo Nambu-Goldstone bosons from a ${\rm SO}(6)\to {\rm SO}(4)\times {\rm SO}(2)$ breaking. The main focus of this work is to explicitly compute…
This paper talk about the complexity of computation by Turing Machine. I take attention to the relation of symmetry and order structure of the data, and I think about the limitation of computation time. First, I make general problem named…
We find set of necessary and sufficient conditions for CP conservation in the most general 2HDM in terms of observable quantities. This set contains two relatively easily testable simple conditions instead of usually discussed three more…
The controllability condition for finite dimensional quantum systems, the Lie Algebra Rank Condition, has been stated assuming that the right invariant differential system under consideration is bilinear. We remark that this assumption is…
In this brief review, we comment on the concept of shape invariant potentials, which is an essential feature in many settings of $N=2$ supersymmetric quantum mechanics. To motivate its application within supersymmetric quantum cosmology, we…
We generalize our previous model to an O(N) symmetric two-dimensional model which possesses chiral symmetry breaking and superconducting (Cooper pair condensates) phases at large-N. At zero temperature and density, the model can be solved…
We give two conditionally exactly solvable inverse power law potentials whose linearly independent solutions include a sum of two confluent hypergeometric functions. We notice that they are partner potentials and multiplicative shape…
The differential branching ratio, forward-backward asymmetry, CP asymmetry and lepton polarization for a B-meson to decay to strange hadronic final states and a $\tau^+\tau^-$ pair in a CP softly broken two Higgs doublet model are computed.…