μ–τ symmetry in Zee–Babu model

We study the Zee–Babu two-loop neutrino mass generation model and look for a possible flavor symmetry behind the tri-bimaximal neutrino mixing. We find that there probably exists the μ–τ   symmetry in the case of the normal neutrino mass hierarchy, whereas there may not be in the inverted hierarchy case. We also propose a specific model based on a Froggatt–Nielsen-like Z₅$Z_5$ symmetry to naturally accomplish the μ–τ symmetry on the neutrino mass matrix for the normal hierarchy case.     

Measurement of the branching ratios for the decays J/ψ → ϱπ and J/ψ → γη′

Decays of the J/ψ (3.1) resonance into final states with two charged hadrons and two photons are investigated. Branching ratios for the decays J/ψ → ?π and J/ψ → γη′ are determined to be

$\text{Г(J/ψ → pφ)}\text{Г(J/ψ → all)}\text{= (1.0± 0.2) ·10}{}^{\mathrm{?2}}\text{,}\text{Г(J/ψ → γη′)}\text{ГJ/ψ → all)}\text{= (2.0± 0.7) ·}{}^{\mathrm{?3}}$

Upper limits for the same decay modes of ψ′ (3.7) are also determined.     

Photonic band structure and effect of ε and μ on the reflectivity of one-dimensional magnetic photonic crystal structure

In this paper, we study the photonic band structure and reflection properties in one-dimensional magnetic photonic crystals (MPCs). Investigation of dispersion characteristics shows that in the case of MPCs, photonic band gaps arise due to the contrast in the wave impedance, not due to the contrast in the refractive index, while contrast in the refractive index of the two layers decides the position and number of the band gaps. We also study the effect of permittivity and permeability on reflection bands, which shows that the structure that has larger values of magnetic permeability (μ) than dielectric permittivity (ε) have wider TM-reflection bands, whereas the structure for which ε is greater than μ has wider TE-reflection bands. But the gap to mid-gap frequency ratio for TM-reflection bands is larger than TE-reflection bands. Thus, magnetic permeability has greater impact on the reflectivity of MPCs than dielectric permittivity. Finally, the analysis of the omni-reflectance in MPCs has also been studied.     

Application of the vector ε and ρ extrapolation methods in the acceleration of the Richardson-Lucy algorithm

The vector ε and ρ extrapolation methods are applied in accelerating the convergence of the Richardson-Lucy (R-L) algorithm and its damped version. The theory and implementation are discussed in detail, and relevant numerical results are given, including the cases of noise-free images and images corrupted by the Poisson noise. The results show that the vector ε and ρ extrapolations of 9 orders can speed the convergence quite efficiently, and the ρ(9) method is more powerful than the ε(9) method for noisy degraded images. The extra computation burden due to the extrapolation is limited, and is well paid back by the accelerated convergence. The performances of these two methods are compared with the famous automatic acceleration method. For noise-free degraded images, the vector ε(9) and ρ(9) methods are more stable than the automatic method. For noisy degraded images, the damped R-L algorithm accelerated by vector ρ(9) or automatic methods is more powerful, and the instability of the automatic method is restrained by the damping strategy. We explain the instability of the method in accelerating the normal R-L algorithm by the numerical noise due to its frequent applications in the run.     

A deformed relativity with the quantum ℏ

Quantum relativity as a generalized, or rather deformed, version of Einstein relativity may offer a new framework to think about the structure of space–time at the true microscopic/quantum level. The approach typically gives some picture of a noncommutative (quantum) space–time. We propose a formulation with two deformations implemented on the Poincaré symmetry, using the independent Planck mass and Planck length as the invariant constraints. Together, they give the quantum ?  . The scheme leads to SO(2,4)$\mathit{SO}(2,4)$ as the relativity symmetry. We present a linear realization on a classical six-geometry beyond the familiar setting of space–time. Two extra coordinates to be considered as neither space nor time are needed. The last deformation step implementing the Planck length invariant constraines the six-geometry, as an extension of 4D space–time, giving it the structure of a AdS hypersurface. The resulted quantum world hence does not admit coordinate translation symmetries, which terminates further extension to an unstable symmetry. The quantum world is shown to be parallel to the “conformal universe”, but not scale invariant.     

Wideband wavelength conversion using double-pass cascaded χ:χ interaction in lossy waveguides

We report the wavelength conversion based on double-pass cascaded nonlinear interaction (χ⁽²⁾:χ⁽²⁾) of sum and difference frequency generation in quasi-phase matched lithium niobate waveguides and compare it with double-pass cascaded second harmonic generation and difference frequency generation with and without waveguide loss. It is shown that the efficiency decreases considerably even for the low-loss waveguide compared to the lossless one especially for long waveguides and to achieve the higher efficiency for the same length, the amount of the extra power to compensate the loss increases. Also, an increased detuning of pump wavelength is proposed to flatten the response with a small efficiency penalty. The detuning- and loss-compensating pump powers can be found using the design diagrams in which the criteria for the design of waveguide length and the assignment of pumps power to obtain the desired efficiency, ripple and bandwidth are presented assuming a 75-nm pump wavelength difference.     

Relative merit of χ and χ SHG by charged water microdroplets - Implications for LIDAR

We investigated second harmonic generation (SHG) from neutral and electrically charged water microdroplets of uniform size. We found that angular distribution, polarization, and conversion efficiency of the SHG emission did not change within applied surface charge densities from 0 to 7.2 × 10⁻⁵ C/m². The latter is consistent with previously observed charge sensitive SHG efficiency on water interfaces if one considers particular experimental conditions. A brief discussion of the applicability of SHG for optical detection of charges in atmospheric clouds is given.     

The property of κ-deformed statistics for a relativistic gas in an electromagnetic field: κ parameter and κ-distribution

We investigate the physical property of the κ parameter and the κ-distribution in the κ-deformed statistics, based on Kaniadakis entropy, for a relativistic gas in an electromagnetic field. We derive two relations for the relativistic gas in the framework of κ-deformed statistics, which describe the physical situation represented by the relativistic κ-distribution function, provide a reasonable connection between the parameter κ  , the temperature four-gradient and the four-vector potential gradient, and thus present for the case κ≠0$\kappa \ne 0$ one clearly physical meaning. It is shown that such a physical situation is a meta-equilibrium state of the system, but has a new physical characteristic.     

The hydrogen atom in D = 3 − 2ϵ dimensions

The nonrelativistic hydrogen atom in $D=3?2?$ dimensions is the reference system for perturbative schemes used in dimensionally regularized nonrelativistic effective field theories to describe hydrogen-like atoms. Solutions to the D-dimensional Schrödinger–Coulomb equation are given in the form of a double power series. Energies and normalization integrals are obtained numerically and also perturbatively in terms of ?. The utility of the series expansion is demonstrated by the calculation of the divergent expectation value $〈{(V^{\prime })}^2〉$.     

Duality in random matrix ensembles for all β

Gaussian and Chiral β  -Ensembles, which generalise well-known orthogonal (β=1$\beta =1$), unitary (β=2$\beta =2$), and symplectic (β=4$\beta =4$) ensembles of random Hermitian matrices, are considered. Averages are shown to satisfy duality relations like {β,N,n}⇔{4/β,n,N}$\{\beta ,N,n\}\iff \{4/\beta ,n,N\}$ for all β>0$\beta >0$, where N and n respectively denote the number of eigenvalues and products of characteristic polynomials. At the edge of the spectrum, matrix integrals of the Airy (Kontsevich) type are obtained. Consequences on the integral representation of the multiple orthogonal polynomials and the partition function of the formal one-matrix model are also discussed. Proofs rely on the theory of multivariate symmetric polynomials, especially Jack polynomials.     

QED distributions for hard photon emission in e+e− → μ+μ−γ

The hard photon emission in e⁺e^? → μ⁺μ^?γ is investigated to order α³. Formulas for a number of distributions are obtained, when neglecting terms of order (m_e/?)² and (m_μ/?)². Both charge-even and charge-odd contributions are calculated. The total contribution to the charge asymmetry parameter

$\text{? =}\text{[}\text{d}\text{σ(θ)}\text{d}\text{O}{}_{\mathrm{\mu }}{}^{\mathrm{+}}\text{?}\text{d}\text{Oσ(π?θ)}\text{d}\text{O}{}_{\mathrm{\mu }}{}^{\mathrm{+}}\text{]}\text{[}\text{d}\text{σ(θ)}\text{d}\text{O}{}_{\mathrm{\mu }}{}^{\mathrm{+}}\text{+}\text{d}\text{σ(π ? σ)}\text{d}\text{O}{}_{\mathrm{\mu }}{}^{\mathrm{+}}\text{]}$

does not exceed 5% for the c.m.s. energy 2? = 3 GeV.     

Inflationary predictions at small γ

This Letter explores single field inflation models with a constant, but arbitrary speed of sound cs$c_s$, obtained by deforming the kinetic energy terms to a Dirac–Born–Infeld form. Allowing cs<1$c_s<1$ provides a simple parametrization of non-Gaussianity. The dependence of inflationary observables on the parameter cs$c_s$ is considered in the leading order slow roll approximation. The results show that in most cases the dependence is actually rather weak for the range of cs$c_s$ allowed by existing bounds on non-Gaussianity.     

A correlation between the two ratios γ/χ(0) and |Jm|/TK in Kondo system

Using the approach based on molecular field calculations for resonant level model; a close relationship between the two ratios γ/χ(0) and |J_m|/T_K is obtained. Where γ represents the electronic contribution in the specific heat, χ(0) is the susceptibility at zero temperature, J_m is the molecular field parameter and T_K is the Kondo temperature.     

χ measurement and optical limiting studies of urea picrate

The molecular charge complex urea picrate (UP) was synthesized and its third order nonlinear optical properties have been investigated using a single beam Z-scan technique with nanosecond laser pulses at 532 nm. Open aperture data of the compound indicates two photon absorption at this wavelength. The nonlinear refractive index n₂, nonlinear absorption coefficient β, magnitude of effective third order susceptibility χ⁽³⁾, the second order hyperpolarizability γ_h and the coupling factor ρ have been estimated. The experimentally determined values of β, n₂, Re χ⁽³⁾ and Im χ⁽³⁾, γ_h and ρ of the compound UP are 2.146 cm/GW, −1.258×10⁻¹¹ esu, −1.347×10⁻¹³ esu, 0.377×10⁻¹³ esu, 0.69×10⁻³² esu and 0.28, respectively. The compound exhibits good optical limiting at 532 nm with the limiting threshold of 80 μJ/pulse. Our studies suggest that compound UP is a potential candidate for optical device applications such as optical limiters.     

Line mixing in the ν6Q branches of self- and nitrogen-broadened methyl bromide

Line-mixing effects are studied in the ν₆^RQ_K and ^PQ_K (K=0-6) branches of methyl bromide (CH₃Br) perturbed by nitrogen (N₂). Laboratory Fourier transform spectra have been obtained at room temperature, and for a large range of pressure values of atmospheric interest. In order to accurately model these spectra, a theoretical approach accounting for line-mixing effects is proposed. This model is based on the use of the state-to-state rotational cross-sections calculated by a statistical modified exponential-gap fitting law depending on a few empirical parameters. These parameters are deduced by adjusting the calculated diagonal elements of the relaxation matrix to the N₂-broadening coefficients, known from accurate previous measurements. Comparisons between experimental and calculated profiles for various Q branches and under various pressure conditions (0.2-1 atm) demonstrate the adequacy and consistency of the proposed model. To allow accurate laboratory measurements, line-mixing effects are also modeled in the case of self-perturbed CH₃Br.