The Higgs mass in the MSSM infrared fixed point scenario

In the infrared fixed point (IFP) scenario of the minimal supersymmetric model (MSSM), the top-quark mass and other physical quantities of the low-energy theory are insensitive to the values of the parameters of the theory at some high energy scale. In this framework we evaluate the light CP-even Higgs mass, $m_h$, taking into account some important effects that had not been previously considered. In particular, the supersymmetric correction to the relation between the running and the physical top-quark masses lowers the value of $\tan\beta$, thereby implying a lower predicted value of $m_h$. Assuming a supersymmetric threshold of $M_S\leq 1$ TeV and $M_t=175$ GeV, we find an upper bound of $m_h\le 97\pm 2$ GeV; the most plausible value of $m_h$ lies somewhat below the upper bound. This places the Higgs boson in the IFP scenario well within the reach of the LEP-2 Higgs search.Comment: 18 pages, LaTeX, 5 ps figures, uses psfig.sty. Final version, some comments and a figure added, references correcte

QLC relation and neutrino mass hierarchy

Latest measurements have revealed that the deviation from a maximal solar mixing angle is approximately the Cabibbo angle, i.e. QLC relation. We argue that it is not plausible that this deviation from maximality, be it a coincidence or not, comes from the charged lepton mixing. Consequently we have calculated the required corrections to the exactly bimaximal neutrino mass matrix ansatz necessary to account for the solar mass difference and the solar mixing angle. We point out that the relative size of these two corrections depends strongly on the hierarchy case under consideration. We find that the inverted hierarchy case with opposite CP parities, which is known to guarantee the RGE stability of the solar mixing angle, offers the most plausible scenario for a high energy origin of a QLC-corrected bimaximal neutrino mass matrix. This possibility may allow us to explain the QLC relation in connection with the origin of the charged fermion mass matrices.Comment: 7 pages, 0 figure

Analysis of the velocity tracking control problem for the 3D evolutionary Navier-Stokes equations

The velocity tracking problem for the evolutionary Navier–Stokes equations in three dimensions is studied. The controls are of distributed type and are submitted to bound constraints. The classical cost functional is modified so that a full analysis of the control problem is possible. First and second order necessary and sufficient optimality conditions are proved. A fully discrete scheme based on a discontinuous (in time) Galerkin approach, combined with conforming finite element subspaces in space, is proposed and analyzed. Provided that the time and space discretization parameters, τ and h, respectively, satisfy τ ≤ Ch2, the L2(ΩT ) error estimates of order O(h) are proved for the difference between the locally optimal controls and their discrete approximations. Finally, combining these techniques and the approach of Casas, Herzog, and Wachsmuth [SIAM J. Optim., 22 (2012), pp. 795–820], we extend our results to the case of L1(ΩT ) type functionals that allow sparse controls.This author was partially supported by the Spanish Ministerio de Economía y Competitividad under projects MTM2011-22711 and MTM2014-57531-

New Production Mechanism of Neutral Higgs Bosons with Right scalar tau neutrino as the LSP

Motived by the neutrino oscillation data, we consider the lightest tau sneutrino $\tilde \nu_{\tau_1}$ (which is mostly the right tau sneutrino) to be the lightest supersymmetric particle (LSP) in the framework of the minimal supersymmetric Standard Model. Both the standard and the non-standard trilinear scalar coupling terms are included for the right tau sneutrino interactions. The decay branching ratio of $\tilde \nu_{\tau_2} \to \tilde \nu_{\tau_1}+ h^0$ can become so large that the production rate of the lightest neutral Higgs boson ($h^0$) can be largely enhanced at electron or hadron colliders, either from the direct production of $\tilde \nu_{\tau_2}$ or from the decay of charginos, neutralinos, sleptons, and the cascade decay of squarks and gluinos, etc. Furthermore, because of the small LSP annihilation rate, $\tilde \nu_{\tau_1}$ can be a good candidate for cold dark matter.Comment: 11 pages, RevTex, 3 eps figures. We clarify the theoretical framework of this study, with a note added in the end, and correct an equation, with updated figure

Optimal Control of the Thermistor Problem in Three Spatial Dimensions

This paper is concerned with the state-constrained optimal control of the three-dimensional thermistor problem, a fully quasilinear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the heating of a conducting material by means of direct current. Local existence, uniqueness and continuity for the state system are derived by employing maximal parabolic regularity in the fundamental theorem of Pr\"uss. Global solutions are addressed, which includes analysis of the linearized state system via maximal parabolic regularity, and existence of optimal controls is shown if the temperature gradient is under control. The adjoint system involving measures is investigated using a duality argument. These results allow to derive first-order necessary conditions for the optimal control problem in form of a qualified optimality system. The theoretical findings are illustrated by numerical results

The frequency map for billiards inside ellipsoids

The billiard motion inside an ellipsoid Q \subset \Rset^{n+1} is completely integrable. Its phase space is a symplectic manifold of dimension $2n$, which is mostly foliated with Liouville tori of dimension $n$. The motion on each Liouville torus becomes just a parallel translation with some frequency $\omega$ that varies with the torus. Besides, any billiard trajectory inside $Q$ is tangent to $n$ caustics $Q_{\lambda_1},...,Q_{\lambda_n}$, so the caustic parameters $\lambda=(\lambda_1,...,\lambda_n)$ are integrals of the billiard map. The frequency map $\lambda \mapsto \omega$ is a key tool to understand the structure of periodic billiard trajectories. In principle, it is well-defined only for nonsingular values of the caustic parameters. We present four conjectures, fully supported by numerical experiments. The last one gives rise to some lower bounds on the periods. These bounds only depend on the type of the caustics. We describe the geometric meaning, domain, and range of $\omega$. The map $\omega$ can be continuously extended to singular values of the caustic parameters, although it becomes "exponentially sharp" at some of them. Finally, we study triaxial ellipsoids of \Rset^3. We compute numerically the bifurcation curves in the parameter space on which the Liouville tori with a fixed frequency disappear. We determine which ellipsoids have more periodic trajectories. We check that the previous lower bounds on the periods are optimal, by displaying periodic trajectories with periods four, five, and six whose caustics have the right types. We also give some new insights for ellipses of \Rset^2.Comment: 50 pages, 13 figure

The abundance of moduli, modulini and gravitinos produced by the vacuum fluctuation

Moduli, modulini and the gravitino have gravitational-strength interactions, and thermal collisions after reheating create all of them with roughly the same abundance. With their mass of order 100\GeV, corresponding to gravity-mediated supersymmetry breaking, this leads to the well-known bound \gamma T\sub R\lsim 10^9\GeV on the reheat temperature, where $\gamma\leq 1$ is the entropy dilution factor. The vacuum fluctuation also creates these particles, with abundance determined by the solution of the equation for the mode function. Taking the equation in each case to be the one corresponding to a free field, we consider carefully the behaviour of the effective mass during the crucial era after inflation. It may have a rapid oscillation, which does not however affect the particle abundance. Existing estimates are confirmed; the abundance of modulini and (probably) of moduli created from the vacuum is less than from thermal collisions, but the abundance of gravitinos may be much bigger, leading to a tighter bound on $T\sub R$ if supersymmetry breaking is gravity-mediated. It is noted that in the case of gauge-mediated supersymmetry breaking, the abundance of the gravitino may be sufficient to make it a dark matter candidate.Comment: 14 pages. v3 as it will appear in PL

Analysis of optimal control problems of semilinear elliptic equations by BV-functions

Optimal control problems for semilinear elliptic equations with control costs in the space of bounded variations are analysed. BV-based optimal controls favor piecewise constant, and hence ’simple’ controls, with few jumps. Existence of optimal controls, necessary and sufficient optimality conditions of first and second order are analysed. Special attention is paid on the effect of the choice of the vector norm in the definition of the BV-seminorm for the optimal primal and adjoined variables.The first author was partially supported by Spanish Ministerio de Economía, Industria y Competitividad under research projects MTM2014-57531-P and MTM2017-83185-P. The second was partially supported by the ERC advanced grant 668998 (OCLOC) under the EUs H2020 research program

Optimal control of semilinear elliptic equations in measure spaces

Optimal control problems in measure spaces governed by semilinear elliptic equations are considered. First order optimality conditions are derived and structural properties of their solutions, in particular sparsity, are discussed. Necessary and sufficient second order optimality conditions are obtained as well. On the basis of the sufficient conditions, stability of the solutions is analyzed. Highly nonlinear terms can be incorporated by utilizing an L∞(Ω) regularity result for solutions of the first order necessary optimality conditions.This author’s research was supported by Spanish Ministerio de Economía y Competitividad under project MTM2011-22711

Gowdy waves as a test-bed for constraint-preserving boundary conditions

Gowdy waves, one of the standard 'apples with apples' tests, is proposed as a test-bed for constraint-preserving boundary conditions in the non-linear regime. As an illustration, energy-constraint preservation is separately tested in the Z4 framework. Both algebraic conditions, derived from energy estimates, and derivative conditions, deduced from the constraint-propagation system, are considered. The numerical errors at the boundary are of the same order than those at the interior points.Comment: 5 pages, 1 figure. Contribution to the Spanish Relativity Meeting 200