Related papers: Solving the Hierarchy Problem Discretely
In the underlying Planck scale theory we introduce a certain type of discrete symmetry, which potentially brings the stability of the weak-scale hierarchy under control. Under the discrete symmetry the $\mu $-problem and the tadpole problem…
We find that massless Higgs doublets at the GUT scale can be the natural result of a discrete symmetry. Such a mechanism does not require elaborate fine tuning or complicated particle content. The same discrete symmetry will also protect…
We present a cosmological solution to the electroweak hierarchy problem. After discussing general features of cosmological approaches to naturalness, we extend the Standard Model with two light scalars very weakly coupled to the Higgs and…
Nonrelativistic scalar field theories can exhibit a natural cascading hierarchy of scales, protected by a hierarchy of polynomial shift symmetries. Using a simple model, we argue that a high-energy cross-over to such nonrelativistic…
The use of discrete symmetries, especially abelian ones, in physics beyond the standard model of particle physics is discussed. A method is developed how a general, abelian, discrete symmetry can be obtained via spontaneous symmetry…
In this paper, a model is proposed to solve the gauge hierarchy problem. Beyond the standard model, we introduce an extra scalar field that non-minimally couples to gravity. The fundamental scale is set at weak scale and Planck scale…
A cosmological scenario is proposed, which simultaneously solves the mass hierarchy and the small dark energy problem. In the present scenario an effective gravity mass scale (inverse of the Newton's constant) increases during the…
Singular perturbation theory plays a central role in the approximate solution of nonlinear differential equations. However, applying these methods is a subtle art owing to the lack of globally applicable algorithms. Inspired by the fact…
Assuming that no other conventional new physics is found immediately at the LHC, we investigate how just the consistent solution of the scalar mass hierarchy problem points towards the minimal necessary field content. We show that to…
Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential…
This paper proposes a novel method for designing finite-horizon discrete-valued switching signals in linear switched systems based on discreteness-promoting regularization. The inherent combinatorial optimization problem is reformulated as…
We introduce a discrete delayed exponential depending on sequence of matrices. This discrete matrix gives a representation of a solution to the Cauchy problem for a discrete linear system with pure delay with sequence of matrices. We…
We show that the little hierarchy problem can be solved in the no-scale supergravity framework. In this model the supersymmetry breaking scale is generated when the electroweak symmetry breaking condition is satisfied and therefore, unlike…
We discuss two possible extensions to the standard model in which an inert singlet scalar state that only interacts with the Higgs boson is added together with some fermions. In one model the fermions provide for a see-saw mechanism for the…
We report on the presence of families of exact solutions for a complex scalar field that behaves according to the rules of discrete $Z_N$ symmetry. Since the family of models is exactly solved, the results appear to be of interest to…
The hierarchy problem is associated with renormalization and decoupling. We can account for the smallness of the scalar mass against loop corrections and its insensitivity to ultraviolet physics through the decoupling of heavy fields. It is…
In this paper we investigate the discrete version of the classical hanging chain problem. We generalize the problem, by allowing for arbitrary mass and length of each link. We show that the shape of the chain can be obtained by solving a…
We argue that identifying the electroweak Higgs particle with the extra components of the gauge field in $4+d$ dimensions provides a solution to the hierarchy problem. The absence of ultraviolate quadratic divergences is due to the fact…
In models with spontaneous symmetry breaking by scalar fields in large group representations, we observe that some of the scalar masses can be loop-suppressed with respect to the naive expectation from symmetry selection rules. We present…
We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…