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We give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of simultaneous rational interpolants with a bounded number of poles. The conditions are expressed in terms of intrinsic properties of the system of functions used to build the approximants. Exact rates of convergence for these denominators and the simultaneous rational approximants are provided., Comment: 27 pages

We consider row sequences of simultaneous rational approximations constructed in terms of Fourier expansions and prove a Montessus de Ballore type theorem., Comment: 16 pages

We give a Montessus de Ballore type theorem for row sequences of Hermite-Pad\'e approximations of vector valued analytic functions refining some results in this direction due to P.R. Graves-Morris and E.B. Saff. We do this introducing the notion of incomplete Pad\'e approximation which contains, in particular, simultaneous Pad\'e approximation and may be applied in the study of other systems of approximants as well., Comment: 20 pages

Lepton number violation (LNV) can be induced by Majorana neutrinos in four-body decays of the neutral B meson and the top quark. We study the effects of Majorana neutrinos in these |\Delta L|=2 decays in an scenario where a single heavy neutrino can enhance the amplitude via the resonant mechanism. Using current bounds on heavy neutrino mixings, the most optimistic branching ratios turn out to be at the level of 10^{-6} for \bar{B} -> D^+e^-e^-\pi^+ and t -> bl^+l^+W^- decays. Searches for these LNV decays at future facilities can provide complementary constraints on masses and mixings of Majorana neutrinos., Comment: 15 pages, 6 figures, "Added comments on sensitivities. Version accepted for publication"

Light tensor mesons (T = a_2, f_2 and K_2^*) can be produced in decays of tau leptons. In this paper we compute the branching ratios of tau --> T pi nu decays by assuming the dominance of intermediate virtual states to model the form factors involved in the relevant hadronic matrix element. The exclusive f_2(1270) pi^- decay mode turns out to have the largest branching ratio, of O(10^-4) . Our results indicate that the contributions of tensor meson intermediate states to the three-pseudoscalar channels of tau decays are rather small., Comment: 10 pages, 1 figure. Version accepted for publication in PRD, some typos are corrected and comments are added in section 4. Conclusions remain unchanged

K. Mahler introduced the concept of perfect systems in the theory of simultaneous Hermite-Pad\'{e} approximation of analytic functions. Recently, we proved that Nikishin systems, generated by measures with bounded support and non-intersecting consecutive supports contained on the real line, are perfect. Here, we prove that they are also perfect when the supports of the generating measures are unbounded or touch at one point. As an application, we give a version of Stieltjes' theorem in the context of simultaneous Hermite-Pad\'e approximation., Comment: 26 pages

We present kinematic data for 211 bright planetary nebulae in eleven Local Group galaxies: M31 (137 PNe), M32 (13), M33 (33), Fornax (1), Sagittarius (3), NGC 147 (2), NGC 185 (5), NGC 205 (9), NGC 6822 (5), Leo A (1), and Sextans A (1). The data were acquired at the Observatorio Astron\'omico Nacional in the Sierra de San Pedro M\'artir using the 2.1m telescope and the Manchester Echelle Spectrometer in the light of [\ion{O}{3}]$\lambda$5007 at a resolution of 11 km/s. A few objects were observed in H$\alpha$. The internal kinematics of bright planetary nebulae do not depend strongly upon the metallicity or age of their progenitor stellar populations, though small systematic differences exist. The nebular kinematics and H$\beta$ luminosity require that the nebular shells be accelerated during the early evolution of their central stars. Thus, kinematics provides an additional argument favoring similar stellar progenitors for bright planetary nebulae in all galaxies., Comment: Accepted for publication in the October 2010 issue of the Revista Mexicana de Astronom\'ia y Astrof\'isica

We describe some recent results on isospin breaking corrections which are of relevance for predictions of the leading order hadronic contribution to the muon anomalous magnetic moment (amuhadLO) when using tau lepton data. When these corrections are applied to the new combined data on the pi^+pi^0 spectral function, the prediction for amuhadLO based on tau lepton data gets closer to the one obtained using e^+e^- data., Comment: 6 pages, 3 figures, Proceedings of the PhiPsi09 Workshop, Oct. 13-16, 2009, Beijing, China. Some typos corrected, and the FSR correction used in a previous work is added to Table 1

K. Mahler introduced the concept of perfect systems in the general theory he developed for the simultaneous Hermite-Pade approximation of analytic functions. We prove that Nikishin systems are perfect providing, by far, the largest class of systems of functions for which this important property holds. As consequences, in the context of Nikishin systems, we obtain: an extension of Markov's theorem to simultaneous Hermite-Pade approximation, a general result on the convergence of simultaneous quadrature rules of Gauss-Jacobi type, the logarithmic asymptotics of general sequences of multiple orthogonal polynomials, and an extension of the Denisov-Rakhmanov theorem for the ratio asymptotics of mixed type multiple orthogonal polynomials., Comment: 39 pages

Observing charge-parity (CP) or time-reversal (T) violations in the leptonic sector will give useful information to elucidate the nature of neutrinos. CP-violating couplings in charged leptonic currents carry out the weak phases necessary to break these symmetries. Here we study the interference of $W^{\pm}$ and $H^{\pm}$ bosons mediated amplitudes as the origin of possible CP and T violation in semileptonic decays of $K^{\pm}$ mesons and $\tau^{\pm}$ leptons. We use the experimental bound on the T-odd transverse polarization asymmetry in $K^+_{\mu 3}$ decays to predict an upper limit on the CP violating effects in $\tau \to K \pi \nu$ decays. In the framework of this model with scalar-mediated interactions, we find that current limits on the former process indicate that the CP violating effects in the latter are much smaller than the limits reported so far., Comment: 9 pages, 2 figures

We revisit the procedure for comparing the pi pi spectral function measured in tau decays to that obtained in e+e- annihilation. We re-examine the isospin-breaking corrections using new experimental and theoretical input, and find improved agreement between the tau- --> pi- pi0 nu_tau branching fraction measurement and its prediction using the isospin-breaking-corrected e+e- --> pi+pi- spectral function, though not resolving all discrepancies. We recompute the lowest order hadronic contributions to the muon g-2 using e+e- and tau data with the new corrections, and find a reduced difference between the two evaluations. The new tau-based estimate of the muon magnetic anomaly is found to be 1.9 standard deviations lower than the direct measurement., Comment: 10 pages, 6 figures, submitted to Eur. Phys. J. C; (v2): Revised version with improved and uniform treatment of tau and e+e- data with HVPTools and a few minor bug fixes; (v3): Final version accepted for publication

We find formulas for the birational maps from a Kummer surface K and its dual K^* to their common minimal desingularization S. We show how the nodes of K blow up. Then we give a description of the group of linear automorphisms of S., Comment: 22 pages

We study the logarithmic and ratio asymptotic of linear forms constructed from a Nikishin system which satisfy orthogonality conditions with respect to a system of measures generated from another Nikishin system. This construction combines type I and type II multiple orthogonal polynomials. The logarithmic asymptotic of the linear forms is expressed in terms of the extremal solution of an associated vector valued equilibrium problem for the logarithmic potential. The ratio asymptotic is described by means of a conformal representation of an appropriate Riemann surface of genus zero onto the extended complex plane., Comment: 46 pages

Current predictions for the ratio of phi -> K^+K^-/K_LK_S decay rates exceed the corresponding experimental value in about five standard deviations. By far, the dominant sources of isospin breaking to this ratio are the phase-space (52%) and the electromagnetic radiative (4.3%, computed within scalar QED) corrections. Here we estimate the effects of the electromagnetic structure of kaons and other model-dependent contributions into the radiative corrections., Comment: 8 pages, Latex, 2 .eps figures

The \tau -> (\omega, \phi)P^-\nu decays, where P^-=\pi^-, K^-, are considered within a phenomenological model with dominance of meson intermediate states. We assume SU(3) flavor symmetry to fix some of the unknown strong interaction couplings. Our predictions for the \tau -> \phi (\pi^-, K^-)\nu branching fractions are in good agreement with recent measurements of the BABAR and BELLE Collaborations., Comment: 15 pages, 3 figures

We compute the rates of semileptonic B_A \to B_Bl^-l^- (l=e or \mu) hyperon transitions in a model where intermediate states involve loops of baryons and a Majorana neutrino. These rates turn out to be well below present experimental bounds and other theoretical estimates. From the experimental upper limit on the \Xi^- \to p\mu^-\mu^- decay, we derive the bound < 22 TeV for the effective Majorana mass of the muon neutrino. Also, an estimate of background contributions for these decays due to the allowed B_A \to B_Bl^-l^-\bar{\nu}\bar{\nu} decays are provided., Comment: 10 pages, 1 figure

We compute the difference in decay widths of charged and neutral \rho(770) vector mesons. The isospin breaking arising from mass differences of neutral and charged \pi and \rho mesons, radiative corrections to \rho -> \pi\pi, and the \rho -> \pi\pi\gamma decays are taken into account. It is found that the width difference \Delta \Gamma_rho is very sensitive ot the isospin breaking in the $\rho$ meson mass \Delta m_\rho. This result can be useful to test the correlations observed between the values of these parameters extracted from experimental data., Comment: 16 pages, 4 figures

Based on the description of unstable $K_{L,S}$ particles in quantum field theory (QFT), we compute the time-dependent probabilities for transitions between asymptotic states in $\tau^{\pm} \to [\pi^+\pi^-]_K\pi^{\pm}\nu$ decays, where the pair $[\pi^+\pi^-]_K$ is the product of (intermediate state) neutral kaon decays. Then we propose a definition of $\tau$ decays into $K_L$ and $K_S$ states, which reflects into the cancellation between their CP rate asymmetries, thus solving in a natural way the paradox pointed out previously in litterature. Since our definition of $K_{L,S}$ final states in $\tau$ decays is motivated on experimental grounds, our predictions for the integrated CP rate asymmetries can be tested in a dedicated experiment., Comment: 4 pages, 1 figure

The first binary neutron star merger has already been detected in gravitational waves. The signal was accompanied by an electromagnetic counterpart including a kilonova component powered by the decay of radioactive nuclei, as well as a short γ-ray burst. In order to understand the radioactively powered signal, it is necessary to simulate the outflows and their nucleosynthesis from the post-merger disk. Simulating the disk and predicting the composition of the outflows requires general relativistic magnetohydrodynamical (GRMHD) simulations that include a realistic, finite-temperature equation of state (EOS) and self-consistently calculating the impact of neutrinos. In this work, we detail the implementation of a finite-temperature EOS and the treatment of neutrinos in the GRMHD code HARM3D+NUC, based on HARM3D. We include formal tests of both the finite-temperature EOS and the neutrino-leakage scheme. We further test the code by showing that, given conditions similar to those of published remnant disks following neutron star mergers, it reproduces both recombination of free nucleons to a neutron-rich composition and excitation of a thermal wind.

We construct an approximate metric that represents the spacetime of spinning binary black holes (BBH) approaching merger. We build the metric as an analytical superposition of two Kerr metrics in harmonic coordinates, where we transform each black hole term with time-dependent boosts describing an inspiral trajectory. The velocities and trajectories of the boost are obtained by solving the post-Newtonian (PN) equations of motion at 3.5 PN order. We analyze the spacetime scalars of the new metric and we show that it is an accurate approximation of Einstein’s field equations in vacuum for a BBH system in the inspiral regime. Furthermore, to prove the effectiveness of our approach, we test the metric in the context of a 3D general relativistic magnetohydrodynamical (GRMHD) simulation of accreting minidisks around the black holes. We compare our results with a previous well-tested spacetime construction based on the asymptotic matching method. We conclude that our new spacetime is well-suited for long-term GRMHD simulations of spinning binary black holes on their way to the merger.

The long-distance electromagnetic radiative corrections to tau- -> pi- pi0 nu are re-evaluated. A meson dominance model is used to describe the emission of real photons in this decay. Results obtained for the hadronic spectrum and the decay rate in photon inclusive reactions are compared with previous calculations based on the chiral resonance theory. Independent tests in tau -> pi pi nu gamma that can help to validate the predictions of one of the two models are briefly discussed., Comment: 5 pages, 4 figures, talk given by GLC at the 9th International Workshop on Tau Lepton Physics, Pisa (Italy), september 2006

We propose some empirical formulae relating the masses of the heaviest particles in the standard model (the W,Z,H bosons and the t quark) to the charge of the positron $e$ and the Higgs condensate v. The relations for the masses of gauge bosons m_W = (1+e)v/4 and m_Z=sqrt{(1+e^2)/2}*(v/2) are in excellent agreement with experimental values. By requiring the electroweak standard model to be free from quadratic divergencies at the one-loop level, we find: m_t=v/sqrt{2} and m_H=v/sqrt{2e}, or the very simple ratio (m_t/m_H)^2=e., Comment: 6 pages

We evaluate the model-dependent piece of O(alpha) long-distance radiative corrections to tau^- \to \pi^- \pi^0\nu_{\tau} decays by using a meson dominance model. We find that these corrections to the di-pion invariant mass spectrum are smaller than in previous calculations based on chiral perturbation theory. The corresponding correction to the photon inclusive rate is tiny (-0.15%) but it can be of relevance when new measurements reach better precision., Comment: 4 pages, 2 figures. An estimate of the shift produced in the evaluation of the h.v.p. contribution to the muon anomalous magnetic moment is added. Version to appear in Phys. Rev. D

We compute the SUSY effective hamiltonian that describes the |\Delta S|=1 semileptonic decays of tau leptons. We provide analytical expressions for supersymmetric contribution to tau --> u bar{s} nu_{tau} transition in mass insertion approximation. We show that SUSY contributions may enhance the CP asymmetry of tau --> K pi nu_{tau} decays by several orders of magnitude than the standard model expectations. However, the resulting asymmetry is still well below the current experimental limits obtained by CLEO collaborations. We emphasize that measuring CP rate asymmetry in this decay larger than 10^{-6} would be a clear evidence of physics beyond the supersymmetric extensions of the standard model., Comment: 16 pages, 3 figures

We consider the bremsstrahlung and model-dependent contributions to the radiative decay $\tau^- \to \pi^-\pi^0\nu_{\tau}\gamma$ in the context of a meson dominance model. We focus on several observables related to this decay, including the branching ratio and the photon and di-pion spectra. Particular attention is paid to the sensitivity of different observables upon the effects of model-dependent contributions and of the magnetic dipole moment of the $\rho^-(770)$ vector meson. Important numerical differences are found with respect to results obtained in the framework of chiral perturbation theory., Comment: 14 pages, 8 figures, submitted for publication

The leading order contribution to the direct CP asymmetry in tau^{+/-} -> K^{+/-} pi^0 nu_{tau} decay rates is evaluated within the Standard Model. The weak phase required for CP violation is introduced through an interesting mechanism involving second order weak interactions, which is also responsible for tiny violations of the Delta S= Delta Q rule in K_{l3} decays. The calculated CP asymmetry turns out to be of order 10^{-12}, leaving a large window for studying effects of non-standard sources of CP violation in this observable., Comment: 5 pages, 3 figures, version published in Phys.Rev.D