Fixed point scenario in the Two Higgs Doublet Model inspired by degenerate vacua

We consider the renormalisation group flow of Higgs and Yukawa couplings within the simplest non--supersymmetric two Higgs doublet extension of the Standard Model (SM). In this model the couplings are adjusted so that the multiple point principle (MPP) assumption, which implies the existence of a large set of degenerate vacua at some high energy scale $\Lambda$, is realised. When the top quark Yukawa coupling at the scale $\Lambda$ is large, the solutions of RG equations in this MPP inspired 2 Higgs Doublet Model (2HDM) converge to quasi--fixed points. We analyse the Higgs spectrum and couplings in the quasi--fixed point scenario and compute a theoretical upper bound on the lightest Higgs boson mass. When the scale $\Lambda$ is low, the coupling of the SM--like Higgs scalar to the top quark can be significantly larger in the considered model than in the SM, resulting in the enhanced production of Higgs bosons at the LHC.Comment: 16 pages, 3 figures, CERN preprint number added, references update

Systoles of Arithmetic Hyperbolic Surfaces and 3-manifolds

Our main result is that for all sufficiently large $x_0>0$, the set of commensurability classes of arithmetic hyperbolic 2- or 3-orbifolds with fixed invariant trace field $k$ and systole bounded below by $x_0$ has density one within the set of all commensurability classes of arithmetic hyperbolic 2- or 3-orbifolds with invariant trace field $k$. The proof relies upon bounds for the absolute logarithmic Weil height of algebraic integers due to Silverman, Brindza and Hajdu, as well as precise estimates for the number of rational quaternion algebras not admitting embeddings of any quadratic field having small discriminant. When the trace field is $\mathbf{Q}$, using work of Granville and Soundararajan, we establish a stronger result that allows our constant lower bound $x_0$ to grow with the area. As an application, we establish a systolic bound for arithmetic hyperbolic surfaces that is related to prior work of Buser-Sarnak and Katz-Schaps-Vishne. Finally, we establish an analogous density result for commensurability classes of arithmetic hyperbolic 3-orbifolds with small area totally geodesic $2$-orbifolds.Comment: v4: 17 pages. Revised according to referee report. Final version. To appear in Math. Res. Let

Design of optimized three-dimensional thrust nozzle contours

Design of optimized three-dimensional thrust nozzle contour

Fully Coherent X-ray Pulses from a Regenerative Amplifier Free Electron Laser

We propose and analyze a novel regenerative amplifier free electron laser (FEL) to produce fully coherent x-ray pulses. The method makes use of narrow-bandwidth Bragg crystals to form an x-ray feedback loop around a relatively short undulator. Self-amplified spontaneous emission (SASE) from the leading electron bunch in a bunch train is spectrally filtered by the Bragg reflectors and is brought back to the beginning of the undulator to interact repeatedly with subsequent bunches in the bunch train. The FEL interaction with these short bunches not only amplifies the radiation intensity but also broadens its spectrum, allowing for effective transmission of the x-rays outside the crystal bandwidth. The spectral brightness of these x-ray pulses is about two to three orders of magnitude higher than that from a single-pass SASE FEL.Comment: 11 pages, 6 figure

A numerical study of the correspondence between paths in a causal set and geodesics in the continuum

This paper presents the results of a computational study related to the path-geodesic correspondence in causal sets. For intervals in flat spacetimes, and in selected curved spacetimes, we present evidence that the longest maximal chains (the longest paths) in the corresponding causal set intervals statistically approach the geodesic for that interval in the appropriate continuum limit.Comment: To the celebration of the 60th birthday of Rafael D. Sorki

Double wells, scalar fields and quantum phase transitions in ions traps

Since Hund's work on the ammonia molecule, the double well potential has formed a key paradigm in physics. Its importance is further underlined by the central role it plays in the Landau theory of phase transitions. Recently, the study of entanglement properties of many-body systems has added a new angle to the study of quantum phase transitions of discrete and continuous degrees of freedom, i.e., spin and harmonic chains. Here we show that control of the radial degree of freedom of trapped ion chains allows for the simulation of linear and non-linear Klein-Gordon fields on a lattice, in which the parameters of the lattice, the non-linearity and mass can be controlled at will. The system may be driven through a phase transition creating a double well potential between different configurations of the ion crystal. The dynamics of the system are controllable, local properties are measurable and tunnelling in the double well potential would be observable.Comment: 6 pages, 5 figure