Electric Dipole Moments in Two-Higgs-Doublet Models

Electric dipole moments are extremely sensitive probes for additional sources of CP violation in new physics models. Specifically, they have been argued in the past to exclude new CP-violating phases in two-Higgs-doublet models. Since recently models including such phases have been discussed widely, we revisit the available constraints in the presence of mechanisms which are typically invoked to evade flavour-changing neutral currents. To that aim, we start by assessing the necessary calculations on the hadronic, nuclear and atomic/molecular level, deriving expressions with conservative error estimates. Their phenomenological analysis in the context of two-Higgs-doublet models yields strong constraints, in some cases weakened by a cancellation mechanism among contributions from neutral scalars. While the corresponding parameter combinations do not yet have to be unnaturally small, the constraints are likely to preclude large effects in other CP-violating observables. Nevertheless, the generically expected contributions to electric dipole moments in this class of models lie within the projected sensitivity of the next-generation experiments.Comment: 23+8 pages, 6 figures. v2: added new global analysis of the electron EDM, including the recent ThO result, and additional references. Version accepted for publication in JHE

Solving Hard Computational Problems Efficiently: Asymptotic Parametric Complexity 3-Coloring Algorithm

Many practical problems in almost all scientific and technological disciplines have been classified as computationally hard (NP-hard or even NP-complete). In life sciences, combinatorial optimization problems frequently arise in molecular biology, e.g., genome sequencing; global alignment of multiple genomes; identifying siblings or discovery of dysregulated pathways.In almost all of these problems, there is the need for proving a hypothesis about certain property of an object that can be present only when it adopts some particular admissible structure (an NP-certificate) or be absent (no admissible structure), however, none of the standard approaches can discard the hypothesis when no solution can be found, since none can provide a proof that there is no admissible structure. This article presents an algorithm that introduces a novel type of solution method to "efficiently" solve the graph 3-coloring problem; an NP-complete problem. The proposed method provides certificates (proofs) in both cases: present or absent, so it is possible to accept or reject the hypothesis on the basis of a rigorous proof. It provides exact solutions and is polynomial-time (i.e., efficient) however parametric. The only requirement is sufficient computational power, which is controlled by the parameter $\alpha\in\mathbb{N}$. Nevertheless, here it is proved that the probability of requiring a value of $\alpha>k$ to obtain a solution for a random graph decreases exponentially: $P(\alpha>k) \leq 2^{-(k+1)}$, making tractable almost all problem instances. Thorough experimental analyses were performed. The algorithm was tested on random graphs, planar graphs and 4-regular planar graphs. The obtained experimental results are in accordance with the theoretical expected results.Comment: Working pape

On Resumming Inflationary Perturbations beyond One-loop

It is well known that the correlation functions of a scalar field in a quasi-de Sitter space exhibit at the loop level cumulative infra-red effects proportional to the total number of e-foldings of inflation. Using the in-in formalism, we explore the behavior of these infra-red effects in the large N limit of an O(N) invariant scalar field theory with quartic self-interactions. By resumming all higher-order loop diagrams non-perturbatively, we show that the connected four-point correlation function, which is a signal of non-Gaussianity, is non-perturbatively enhanced with respect to its tree-level value.Comment: 17 pages, v2: minor corrections, to appear in jca

Intrinsic palindromic numbers

We introduce a notion of palindromicity of a natural number which is independent of the base. We study the existence and density of palindromic and multiple palindromic numbers, and we raise several related questions.Comment: 6 pages, Latex2