Convergence of the Crank-Nicolson-Galerkin finite element method for a class of nonlocal parabolic systems with moving boundaries

The aim of this paper is to establish the convergence and error bounds to the fully discrete solution for a class of nonlinear systems of reaction-diffusion nonlocal type with moving boundaries, using a linearized Crank-Nicolson-Galerkin finite element method with polynomial approximations of any degree. A coordinate transformation which fixes the boundaries is used. Some numerical tests to compare our Matlab code with some existing moving finite elements methods are investigated

High scale impact in alignment and decoupling in two-Higgs doublet models

The two-Higgs doublet model (2HDM) provides an excellent benchmark to study physics beyond the Standard Model (SM). In this work we discuss how the behaviour of the model at high energy scales causes it to have a scalar with properties very similar to those of the SM -- which means the 2HDM can be seen to naturally favor a decoupling or alignment limit. For a type II 2HDM, we show that requiring the model to be theoretically valid up to a scale of 1 TeV, by studying the renormalization group equations (RGE) of the parameters of the model, causes a significant reduction in the allowed magnitude of the quartic couplings. This, combined with $B$-physics bounds, forces the model to be naturally decoupled. As a consequence, any non-decoupling limits in type II, like the wrong-sign scenario, are excluded. On the contrary, even with the very constraining limits for the Higgs couplings from the LHC, the type I model can deviate substantially from alignment. An RGE analysis similar to that made for type II shows, however, that requiring a single scalar to be heavier than about 500 GeV would be sufficient for the model to be decoupled. Finally, we show that not only a 2HDM where the lightest of the CP-even scalars is the 125 GeV one does not require new physics to be stable up to the Planck scale but this is also true when the heavy CP-even Higgs is the 125 GeV and the theory has no decoupling limit for the type I model.Comment: 28 pages, 19 figure

Implications of the LHC two-photon signal for two-Higgs-doublet models

We study the implications for Two Higgs Doublet Models of the recent announcement at the LHC giving a tantalizing hint for a Higgs boson of mass 125 GeV decaying into two photons. We require that the experimental result be within a factor of two of the theoretical Standard Model prediction, and analyze the type I and type II models as well as the lepton-specific and flipped models, subject to this requirement. It is assumed that there is no new physics other than two Higgs doublets. In all of the models, we display the allowed region of parameter space taking the recent LHC announcement at face value, and we analyze the $W^+W^-$, $ZZ$, $\bar{b}b$ and $\tau^+\tau^-$ expectations in these allowed regions. Throughout the entire range of parameter space allowed by the $\gamma\gamma$ constraint, the number of events for Higgs decays into $WW$, $ZZ$ and $b \bar b$ are not changed from the Standard Model by more than a factor of two. In contrast, in the Lepton Specific model, decays to $\tau^+ \tau^-$ are very sensitive across the entire $\gamma \gamma$-allowed region.Comment: Latex, 6 pages, 4 figures; v2 - added 2 reference

Mass-degenerate Higgs bosons at 125 GeV in the Two-Higgs-Doublet Model

The analysis of the Higgs boson data by the ATLAS and CMS Collaborations appears to exhibit an excess of h --> gamma\gamma events above the Standard Model (SM) expectations; whereas no significant excess is observed in h --> ZZ* --> {four lepton} events, albeit with large statistical uncertainty due to the small data sample. These results (assuming they persist with further data) could be explained by a pair of nearly mass-degenerate scalars, one of which is a SM-like Higgs boson and the other is a scalar with suppressed couplings to W+W- and ZZ. In the two Higgs doublet model, the observed \gamma\gamma and ZZ* --> {four lepton} data can be reproduced by an approximately degenerate CP-even (h) and CP-odd (A) Higgs boson for values of \sin(\beta-\alpha) near unity and 0.7 < \tan\beta < 1. An enhanced \gamma\gamma signal can also arise in cases where m_h ~ m_H, m_H ~ m_A, or m_h ~ m_H ~ m_A. Since the ZZ* --> {four lepton} signal derives primarily from a SM-like Higgs boson whereas the \gamma\gamma signal receives contributions from two (or more) nearly mass-degenerate states, one would expect a slightly different invariant mass peak in the ZZ* --> {four lepton} and \gamma\gamma channels. The phenomenological consequences of such models can be tested with additional Higgs data that will be collected at the LHC in the near future.Comment: 18 pages, 19 pdf figures, v2: references added, v3&v4: added refs and explanation