Rare decay modes of the neutral pion

The slope of the form factor forπ ⁰→e ⁺ e ^-γ and the real part of the amplitude forπ ⁰→e ⁺ e ^- are calculated by means of the quark triangle mechanism. The correct sign for the form factor slope is reproduced. Theπ ⁰→e ⁺ e ^- rate obtained is slightly larger than the unitarity limit and smaller than the present experimental rate.     

Rare decay modes of fission fragments

The experimental data on rare modes of radioactive decay of fission fragments is reviewed. These decay modes are due to a large excess of neutrons and a high energy of β decay fragments. They appear in delayed emission of various particles after the β decay (several neutrons, α particles, or heavy clusters) and excitation of unusual states (giant multipole resonances and shape isomers). The β decay and internal conversion of γ radiation into bound states of the atomic electron shell and their influence on the probability of secondary particle emission are considered. The possibility is discussed of observing decays that have not yet been experimentally detected, but theoretically predicted, as well as information on the nuclear structure obtained by studying such decay modes.     

The lagrangian formulation of chiral scalars

The lagrangian proposed by Siegel describing left- or right-moving scalars in two dimensions is analysed. The existence of anomalies is pointed out and a modification of the lagrangian leading to the elimination of anomalies is proposed. The generalization for chiral scalars defined on an arbitrary Riemann surface is discussed.     

The tadpole in the chiral lagrangian of K decays

We prove that when the chiral lagrangian is expanded to first order in G_F and to any finite order in meson masses and momenta the tadpole can be completely rotated away, namely: the tadpole is not physically observable.     

Chiral lagrangian calculation of nucleon decay modes induced by d=5 supersymmetric operators

We consider the general baryon-number violating operators which are produced by dressing the supersymmetric dimension-five operators by gaugino exchanges. We then use chiral dynamics to calculate the widths for the decay modes $\text{p}\text{→}\text{K}{}^{\mathrm{+}}\text{ν}{}_{\mathrm{d}}\text{,}\text{K}{}^0\text{e}{}_{\mathrm{d}}{}^{\mathrm{+}}\text{,}\text{and n}\text{→}\text{k}{}^0\text{ν}{}_{\mathrm{d}}$. The resulting branching ratios are rather sensitive to the precise admixture of the various baryon-number violating operators involved. In particular the decay mode $\text{p}\text{→}\text{K}{}^{\mathrm{+}}\text{ν}{}_{\mathrm{d}}$ is generally dominant in qualitative agreement with previous quark model results.     

Electromagnetic interactions in a chiral effective lagrangian for nuclei

Electromagnetic (EM) interactions are incorporated in a recently proposed effective field theory of the nuclear many-body problem. Earlier work with this effective theory exhibited EM couplings that are correct only to lowest order in both the pion fields and the electric charge. The Lorentz-invariant effective field theory contains nucleons, pions, isoscalar scalar (σ) and vector (ω) fields, and isovector vector (ρ) fields. The theory exhibits a nonlinear realization of SU(2)_L × SU(2)_R chiral symmetry and has three desirable features: it uses the same degrees of freedom to describe the currents and the strong-interaction dynamics, it satisfies the symmetries of the underlying QCD, and its parameters can be calibrated using strong-interaction phenomena, like hadron scattering or the empirical properties of finite nuclei. It has been verified that for normal nuclear systems, the effective lagrangian can be expanded systematically in powers of the meson fields (and their derivatives) and can be truncated reliably after the first few orders. The complete EM lagrangian arising from minimal substitution is derived and shown to possess the residual chiral symmetry of massless, two-flavor QCD with EM interactions. The uniqueness of the minimal EM current is proved, and the properties of the isovector vector and axial-vector currents are discussed, generalizing earlier work. The residual chiral symmetry is maintained in additional (non-minimal) EM couplings expressed as a derivative expansion and in implementing vector meson dominance. The role of chiral anomalies in the EM lagrangian is briefly discussed.     

Effective lagrangian analysis of the chiral phase transition at finite density

Introducing a finite chemical potential μ for the quark number density ψ^°ψ, we study analytically the restoration of Π^° chiral symmetry as μ is varied. In the strong coupling limit, the effective lagrangian for SU(N) gauge theories coupled to fermion fields in d dimensions is derived for all N. In the case of SU(2) we predict a second order chiral symmetry restoration phase transition, whereas for all N?3 the transition is first order. Predictions are given for the critical values of the chemical potential μ.     

Radiative kaon decay in the chiral perturbation theory

We analyze the possibility of experimental investigation of new low-energy relations between the values of resonance masses in the meson form factors and the differential rate of radiative kaon decay K ⁺ → π⁺ e ⁺ e ⁻(μ⁺μ⁻) at the current level of the experimental precision. A set of arguments is listed in favor that these relations can be a consequence of weak static interactions in the Standard Model. The results were presented at the 5th NA48 Mini-Workshop on Kaon Physics, CERN, Dec. 12, 2006. The text was submitted by the authors in English.     

Viscoelastic modes in chiral liquid crystals

Viscoelastic properties of liquid crystals are very important for applications like display technology. However, there are not many direct techniques to study them. In this review, we describe our studies on the viscoelastic modes of some chiral liquid crystals using dynamic light scattering. We discuss viscoelastic modes corresponding to the C director fluctuations in the chiral smectic C phase and the behaviour of the Goldstone-mode near the chiral smectic C-smectic A phase transition. In cholesteric liquid crystals, we consider the director fluctuations in a wavevector range comparable to the inverse pitch of the cholesteric. Here, the study of the scattered light in the vicinity of the Bragg reflection using a novel geometry will be presented.     

Isospin and the tau hadronic decay modes

Isospin constraints onτ decay modes are revisited with a special interest for the low branching ratio channels. It is shown that dominance of the vector current in the channel is suggested by the present data and that some discrepancies exist betweenτ partial width ande ⁺ e ⁻ cross-section measurements in the 6π channel.     

Threedimensional dynamics of nuclear decay modes

We study nondissipative fission dynamics in a wide range of mass asymmetry, covering three groups of nuclear decay modes: cluster radioactivities; alpha-decay and cold fission. The WKB action integral is calculated by using the Werner-Wheeler inertia tensor and the deformation energy within Yukawa-plus-exponential model extended to binary systems with different charge densities. The optimum dynamical trajectory in a threedimensional deformation space (elongation, necking-in and mass-asymmetry) is determined by solving a nonlinear system of differential equations. This new method is illustrated for three decay modes of²³⁴U:α-decay, Mg-radioactivity and cold fission with¹⁰⁰Zr as a light fragment.     

Rare decay modes of the K mesons and KL-KS mass difference in an asymptotically free gauge theory

Rare decay modes of the K mesons are calculated for the Weinberg-Salam model of weak and electromagnetic interactions, assuming that the strong interactions are described by an asymptotically free gauge theory.     

Optical defect modes in chiral liquid crystals

An analytic approach to the theory of optical defect modes in chiral liquid crystals (CLCs) is developed. The analytic study is facilitated by the choice of the problem parameters. Specifically, an isotropic layer (with the dielectric susceptibility equal to the average CLC dielectric susceptibility) sandwiched between two CLC layers is studied. The chosen model allows eliminating the polarization mixing and reducing the corresponding equations to the equations for light of diffracting polarization only. The dispersion equation relating the defect mode (DM) frequency to the isotropic layer thickness and an analytic expression for the field distribution in the DM structure are obtained and the corresponding dependences are plotted for some values of the DM structure parameters. Analytic expressions for the transmission and reflection coefficients of the DM structure (CLC-defect layer-CLC) are presented and analyzed for nonabsorbing, absorbing, and amplifying CLCs. The anomalously strong light absorption effect at the DM frequency is revealed. The limit case of infinitely thick CLC layers is considered in detail. It is shown that for distributed feedback lasing in a defect structure, adjusting the lasing frequency to the DM frequency results in a significant decrease in the lasing threshold. The DM dispersion equations are solved numerically for typical values of the relevant parameters. Our approach helps clarify the physics of the optical DMs in CLCs and completely agrees with the corresponding results of the previous numerical investigations.     

Guided modes in the chiral negative refractive index fiber

The novel characteristics of guided modes in the chiral negative refractive index fiber are investigated theoretically in this letter.We derive the characteristic equation of guided modes.Based on two types of chiral metamaterial parameters,we present the dispersion curves,energy flux,and power of guided modes.Some abnormal features,such as the existence of surface mode and dispersion curves with different shapes,intersection of dispersion curves of different guided modes,negative energy flux in the achiral cladding,and zero power at some normalized frequencies,are found in the chiral negative refractive index fiber.     

Effective baryon-lepton coupling and the proton decay modes

We present a simple model for the phenomenology of baryon-number violating nucleon decays in which the basic process is taken to be a direct conversion of a baryon into a lepton or an antilepton. A large number of branching modes are found to be correlated, independently of any specific grand unification scheme.     

The pionic beta decay in chiral perturbation theory

Within the framework of chiral perturbation theory with virtual photons and leptons, we present an updated analysis of the pionic beta decay including all electromagnetic contributions of order e ² p ² . We discuss the extraction of the Cabibbo-Kobayashi-Maskawa matrix element |V _ud | from the experimental data. The method employed here is consistent with the analogous treatment of the decays and the determination of |V _us |. Received: 19 September 2002 / Published online: 24 January 2003     

Fluctuations of Goldstone modes and the chiral transition in QCD

We provide evidence for the influence of thermal fluctuations of Goldstone modes on the chiral condensate at finite temperature. We show that at fixed temperature, T<T_c, in the vicinity of the chiral transition temperature this leads to a characteristic dependence of the chiral condensate on the square root of the light quark mass (m_l), which is expected for 3-dimensional models with broken O(N) symmetry. As a consequence the chiral susceptibility shows a strong quark mass dependence for all temperatures below T<T_c and diverges like in the chiral limit.