Análise e gestão de risco de vendas a crédito

Mestrado em Contabilidade e Gestão de Instituições Financeiras

Are there hidden scalars in LHC Higgs results?

The Higgs boson recently discovered at the Large Hadron Collider has shown to have couplings to the remaining particles well within what is predicted by the Standard Model. The search for other new heavy scalar states has so far revealed to be fruitless, imposing constraints on the existence of new scalar particles. However, it is still possible that any existing heavy scalars would preferentially decay to final states involving the light Higgs boson thus evading the current LHC bounds on heavy scalar states. Moreover, decays of the heavy scalars could increase the number of light Higgs bosons being produced. Since the number of light Higgs bosons decaying to Standard Model particles is within the predicted range, this could mean that part of the light Higgs bosons could have their origin in heavy scalar decays. This situation would occur if the light Higgs couplings to Standard Model particles were reduced by a concomitant amount. Using a very simple extension of the SM - the two-Higgs doublet model we show that in fact we could already be observing the effect of the heavy scalar states even if all results related to the Higgs are in excellent agreement with the Standard Model predictions.

Scaling law in Saddle-node bifurcations for one-dimensional maps: A complex variable approach

The study of transient dynamical phenomena near bifurcation thresholds has attracted the interest of many researchers due to the relevance of bifurcations in different physical or biological systems. In the context of saddle-node bifurcations, where two or more fixed points collide annihilating each other, it is known that the dynamics can suffer the so-called delayed transition. This phenomenon emerges when the system spends a lot of time before reaching the remaining stable equilibrium, found after the bifurcation, because of the presence of a saddle-remnant in phase space. Some works have analytically tackled this phenomenon, especially in time-continuous dynamical systems, showing that the time delay, tau, scales according to an inverse square-root power law, tau similar to (mu-mu (c) )(-1/2), as the bifurcation parameter mu, is driven further away from its critical value, mu (c) . In this work, we first characterize analytically this scaling law using complex variable techniques for a family of one-dimensional maps, called the normal form for the saddle-node bifurcation. We then apply our general analytic results to a single-species ecological model with harvesting given by a unimodal map, characterizing the delayed transition and the scaling law arising due to the constant of harvesting. For both analyzed systems, we show that the numerical results are in perfect agreement with the analytical solutions we are providing. The procedure presented in this work can be used to characterize the scaling laws of one-dimensional discrete dynamical systems with saddle-node bifurcations.