Correctors for the Neumann problem in thin domains with locally periodic oscillatory structure

In this paper we are concerned with convergence of solutions of the Poisson equation with Neumann boundary conditions in a two-dimensional thin domain exhibiting highly oscillatory behavior in part of its boundary. We deal with the resonant case in which the height, amplitude and period of the oscillations are all of the same order which is given by a small parameter $\epsilon > 0$. Applying an appropriate corrector approach we get strong convergence when we replace the original solutions by a kind of first-order expansion through the Multiple-Scale Method.Comment: to appear in Quarterly of Applied Mathematic

Discrete and continuous symmetries in multi-Higgs-doublet models

We consider the Higgs sector of multi-Higgs-doublet models in the presence of simple symmetries relating the various fields. We construct basis invariant observables which may in principle be used to detect these symmetries for any number of doublets. A categorization of the symmetries into classes is required, which we perform in detail for the case of two and three Higgs doublets.Comment: 13 pages, RevTex, references adde

h→Zγh \rightarrow Z \gamma in the complex two Higgs doublet model

The latest LHC data confirmed the existence of a Higgs-like particle and made interesting measurements on its decays into $\gamma \gamma$, $Z Z^\ast$, $W W^\ast$, $\tau^+ \tau^-$, and $b \bar{b}$. It is expected that a decay into $Z \gamma$ might be measured at the next LHC round, for which there already exists an upper bound. The Higgs-like particle could be a mixture of scalar with a relatively large component of pseudoscalar. We compute the decay of such a mixed state into $Z \gamma$, and we study its properties in the context of the complex two Higgs doublet model, analysing the effect of the current measurements on the four versions of this model. We show that a measurement of the $h \rightarrow Z \gamma$ rate at a level consistent with the SM can be used to place interesting constraints on the pseudoscalar component. We also comment on the issue of a wrong sign Yukawa coupling for the bottom in Type II models.Comment: 31 pages, 15 figure

A reappraisal of the wrong-sign hbb‾hb\overline{b} coupling and the study of h→Zγh \rightarrow Z \gamma

It has been pointed out recently that current experiments still allow for a two Higgs doublet model where the $h b \bar{b}$ coupling ($k_D m_b/v$) is negative; a sign opposite to that of the Standard Model. Due to the importance of delayed decoupling in the $h H^+ H^-$ coupling, $h \rightarrow \gamma \gamma$ improved measurements will have a strong impact on this issue. For the same reason, measurements or even bounds on $h \rightarrow Z \gamma$ are potentially interesting. In this article, we revisit this problem, highlighting the crucial importance of $h \rightarrow VV$, which can be understood with simple arguments. We show that the impacts on $k_D<0$ models of both $h \rightarrow b \bar{b}$ and $h \rightarrow \tau^+ \tau^-$ are very sensitive to input values for the gluon fusion production mechanism; in contrast, $h \rightarrow \gamma \gamma$ and $h \rightarrow Z \gamma$ are not. We also inquire if the search for $h \rightarrow Z \gamma$ and its interplay with $h \rightarrow \gamma \gamma$ will impact the sign of the $h b \bar{b}$ coupling. Finally, we study these issues in the context of the Flipped two Higgs doublet model.Comment: 13 pages, pdf figure