Alfredo Aranda

Improved Lindstedt–Poincaré method for the solution of nonlinear problems

Abstract We apply the Linear Delta Expansion (LDE) to the Lindstedt–Poincare (“distorted time”) method to find improved approximate solutions to nonlinear problems. We find that our method works very well for a wide range of parameters in the case of the anharmonic oscillator (Duffing equation), of the non linear pendulum and of more general anharmonic potentials. The approximate solutions found with this method converge more rapidly to the exact ones than in the simple Lindstedt–Poincare method.

Maximal neutrino mixing from a minimal flavor symmetry

The authors study a number of models, based on a non-Abelian discrete group, that successfully reproduce the simple and predictive Yukawa textures usually associated with U(2) theories of flavor. These models allow for solutions to the solar and atmospheric neutrino problems that do not require altering successful predictions for the charged fermions or introducing sterile neutrinos. Although Yukawa matrices are hierarchical in the models they consider, the mixing between second- and third-generation neutrinos is naturally large. They first present a quantitative analysis of a minimal model proposed in earlier work, consisting of a global fit to fermion masses and mixing angles, including the most important renormalization group effects. They then propose two new variant models: The first reproduces all important features of the SU(5) x U(2) unified theory with neither SU(5) nor U(2). The second demonstrates that discrete subgroups of SU(2) can be used in constructing viable supersymmetric theories of flavor without scalar universality even though SU(2) by itself cannot.

U(2) flavor physics without U(2) symmetry

Grupo de Fisica Teorica Universidade Catolica de Petropolis (UCP), Rua Barao do Amazonas 124, 25.685-000 Petropolis-RJThe authors present a model of fermion masses based on a minimal, non-Abelian discrete symmetry that reproduces the Yukawa matrices usually associated with U(2) theories of flavor. Mass and mixing angle relations that follow from the simple form of the quark and charged lepton Yukawa textures are therefore common to both theories. They show that the differing representation structure of the horizontal symmetry allows for new solutions to the solar and atmospheric neutrino problems that do not involve modification of the original charged fermion Yukawa textures, or the introduction of sterile neutrinos.

Presenting a new method for the solution of nonlinear problems

Abstract We present a method for the resolution of (oscillatory) nonlinear problems. It is based on the application of the linear delta expansion to the Lindstedt–Poincare method. By applying it to the Duffing equation, we show that our method substantially improves the approximation given by the simple Lindstedt–Poincare method.

Dirac neutrinos from flavor symmetry

We present a model where Majorana neutrino mass terms are forbidden by the flavor symmetry group Delta(27). Neutrinos are Dirac fermions and their masses arise in the same way as that of the charged fermions, due to very small Yukawa couplings. The model fits current neutrino oscillation data and correlates the octant of the atmospheric angle with the magnitude of the lightest neutrino mass, with maximal mixing excluded for any neutrino mass

U(2)-like flavor symmetries and approximate bimaximal neutrino mixing

Models involving a U(2) flavor symmetry, or any of a number of its non-Abelian discrete subgroups, can explain the observed hierarchy of charged fermion masses and CKM angles. It is known that a large neutrino mixing angle connecting second and third generation fields may arise via the seesaw mechanism in these models, without a fine tuning of parameters. Here we show that it is possible to obtain approximate bimaximal mixing in a class of models with U(2)-like Yukawa textures. We find a minimal form for Dirac and Majorana neutrino mass matrices that leads to two large mixing angles, and show that our result can quantitatively explain atmospheric neutrino oscillations while accommodating the favored, large angle MSW solution to the solar neutrino problem. We demonstrate that these textures can arise in models by presenting a number of explicit examples.

Non-diagonal charged lepton mass matrix and non-zero θ13

Abstract Assuming that the neutrino mass matrix is diagonalized by the tribimaximal mixing matrix, we explore the textures for the charged lepton mass matrix that render a U PMNS lepton mixing matrix consistent with data. In particular we are interested in finding the textures with the maximum number of zeros. We explore the cases of real matrices with three and four zeros and find that only ten matrices with three zeros provide solutions in agreement with data. We present the successful Yukawa textures including the relative sizes of their non-zero entries as well as some new and interesting relations among the entries of these textures in terms of the charged lepton masses. We also show that these relations can be obtained directly from a parametrization of the charged lepton mixing matrix U l .

Neutrino masses generation in a Z_4 model

We present a renormalizable flavor model with Z_4 as flavor symmetry in both the quark and lepton sectors. The model is constructed with a minimal approach and no-right handed neutrinos are introduced. In this approach a minimum number of two SU(2) Higgs doublets and one scalar singlet are required in order to obtain the Nearest Neighbor Interaction form for charged fermions and to generate neutrino masses radiatively. For the quark sector we follow the charge assignations made by Branco et. al. in reference [1]. All fermion masses and mixing angles in the model are in agreement with current experimental data and only the inverted hierarchy for the neutrino mass spectrum is allowed. Since neutrinos are Majorana the contribution to neutrinoless double beta decay is also analyzed.

Limits on a Light Leptophobic Gauge Boson

Abstract We consider the phenomenology of a naturally leptophobic Z -prime boson in the 1 to 10 GeV mass range. The Z -primes couplings to leptons arise only via a radiatively-generated kinetic mixing with the Z and photon, and hence are suppressed. We map out the allowed regions of the mass-coupling plane and show that such a Z -prime that couples to quarks with electromagnetic strength is not excluded by the current data. We then discuss possible signatures at bottom and charm factories.

A new method for the solution of the Schrödinger equation

We present a new method for the solution of the Schrodinger equation applicable to problems of a non-perturbative nature. The method works by identifying three different scales in the problem, which then are treated independently: an asymptotic scale, which depends uniquely on the form of the potential at large distances; an intermediate scale, still characterized by an exponential decay of the wavefunction; and, finally, a short distance scale, in which the wavefunction is sizable. The notion of optimized perturbation is then used in the last two regimes. We apply the method to the quantum anharmonic oscillator and find it suitable to treat both energy eigenvalues and wavefunctions, even for strong couplings.