Vanishing β-function for Grosse–Wulkenhaar model in a magnetic field

We prove that the β-function of the Grosse–Wulkenhaar model including a magnetic field vanishes at all order of perturbations. We compute the renormalization group flow of the relevant dynamic parameters and find a non-Gaussian infrared fixed point. Some consequences of these results are discussed.     

Zero-energy states bound to a magnetic π-flux vortex in a two-dimensional topological insulator

We show that the existence of a pair of zero-energy modes bound to a vortex carrying a π-flux is a generic feature of the topologically non-trivial phase of the M–B model, which was introduced to describe the topological band insulator in HgTe quantum wells. We explicitly find the form of the zero-energy states of the corresponding Dirac equation, which contains a novel momentum-dependent mass term and describes a generic topological transition in a band insulator. The obtained modes are exponentially localized in the vortex-core, with the dependence of characteristic length on the parameters of the model matching the dependence extracted from a lattice version of the model. We consider in full generality the short-distance regularization of the vector potential of the vortex, and show that a particular choice yields the modes localized and simultaneously regular at the origin. Finally, we also discuss a realization of two-dimensional spin-charge separation through the vortex zero-modes.     

η-Photoproduction in a gauge-invariant chiral unitary framework

We analyze photoproduction of η mesons off the proton in a gauge-invariant chiral unitary framework. The interaction kernel for meson-baryon scattering is derived from the leading order chiral effective Lagrangian and iterated in a Bethe-Salpeter equation. The recent precise threshold data from the Crystal Ball at MAMI can be described rather well and the complex pole corresponding to the S₁₁(1535) is extracted. An extension of the kernel is also discussed.     

Spin-polarized transport in a δ-doped magnetic-barrier nanostructure

We theoretically investigate the electron spin transport properties through a δ-doped magnetic-barrier nanostructure, which can be realized experimentally by depositing two identical ferromagnetic stripes with the opposite in-plane magnetization on the top of a semiconductor heterostructure in parallel configuration and by using atomic layer doping technique. The δ-doping dependent transmission, conductance and spin polarization are calculated exactly by analytically solving Schrödinger equation of the spin electron. It is found that the electronic spin-polarized behavior in this device can be manipulated by changing the weight and/or the position of the δ-doping. Therefore, such a device can be used as a controllable spin filter, which may be helpful for spintronics applications.     

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.     

The QCD β-function from global solutions to Dyson-Schwinger equations

We study quantum chromodynamics from the viewpoint of untruncated Dyson-Schwinger equations turned to an ordinary differential equation for the gluon anomalous dimension. This non-linear equation is parameterized by a function P(x) which is unknown beyond perturbation theory. Still, very mild assumptions on P(x) lead to stringent restrictions for possible solutions to Dyson-Schwinger equations.We establish that the theory must have asymptotic freedom beyond perturbation theory and also investigate the low energy regime and the possibility for a mass gap in the asymptotically free theory.     

β delayed emission of a proton by a one-neutron halo nucleus

Some one-neutron halo nuclei can emit a proton in a β decay of the halo neutron. The branching ratio towards this rare decay mode is calculated within a two-body potential model of the initial core + neutron bound state and final core + proton scattering states. The decay probability per second is evaluated for the ¹¹Be, ¹⁹C and ³¹Ne one-neutron halo nuclei. It is very sensitive to the neutron separation energy.     

Three loop QCD MOM β-functions

We present the full expressions for the QCD β  -function in the MOMggg, MOMq and MOMh renormalization schemes at three loops for an arbitrary colour group in the Landau gauge. The results for all three schemes are in very good agreement with the SU(3)$\mathit{SU}(3)$ numerical estimates provided by Chetyrkin and Seidensticker.     

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.     

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.     

A resummable β-function for massless QED

Within the set of schemes defined by generalized, manifestly gauge invariant exact renormalization groups for QED, it is argued that the β-function in the four-dimensional massless theory cannot possess any nonperturbative power corrections. Consequently, the perturbative expression for the β-function must be resummable. This argument cannot be extended to flows of the other couplings or to the anomalous dimension of the fermions and so perturbation theory does not define a unique trajectory in the critical surface of the Gaussian fixed point. Thus, resummability of the β-function is not inconsistent with the expectation that a non-trivial fixed point does not exist.     

Local variation of the dielectric properties of poly(vinylidene fluoride) during the α- to β-phase transformation

The phase transformation from the non-polar α-phase to the polar electroactive β-phase of polyvinylidene fluoride (PVDF) has been investigated using the fluorescence from Nile red. Films of α-PVDF doped with Nile red were stretched at controlled rates at a temperature of 80 °C to produce the α- to β-phase transition. The thermo/mechanical dependent changes in the crystalline structure are related to the physical rotation of the polar (CH₂-CF₂) group, which can be monitored by steady state fluorescence techniques. The degree of phase transformation is related to variation in the fluorescence, which in turn is linked to local dielectric constant of the polymer. The variation of the refractive index is more associated to the alignment of the polymeric chains than to the phase transformation. Thus, fluorescence is a suitable technique to monitor phase transitions coupled to a variation in the polarity of the dielectric medium.     

Spin-dependent electron transport in a magnetic nanostructure with the δ-doping

We report on a theoretical study of spin-dependent electron transport in a magnetic nanostructure with the δ-doping. It is revealed that the transmission probability, the electron conductance and the spin-polarization obviously depend on the weight of the δ-doping. It is also revealed that the transmission probability and the spin-polarization (PT) both show a periodic profile with the increase of the length L₂. These interesting phenomena will be more helpful for understanding the experimental physical phenomena in δ-doping and for making new types of devices.     

Resummed corrections to the ρ parameter in the complex mass scheme

We present all order results for the heavy top corrections to the ρ parameter in the complex mass scheme. We derive translation formulas between the complex mass and the on-shell scheme and show that they are ultimately equivalent. We show that a naive treatment with a fixed width for the top quark cannot give even approximately correct results.     

High-resolution study of the ν1/ν5 and 2ν1/ν1+ν5 P-H stretching bands of PH2D

The P-H stretching bands ν₁/ν₅ and 2ν₁/ν₁+ν₅ were recorded using a Bruker 120 HR interferometer with a resolution of 0.0042 and 0.0088 cm⁻¹, respectively, and analyzed. From the fits 33 and 50, respectively, vibrational, rotational, centrifugal distortion, and resonance interaction parameters were obtained. These reproduce 668 and 497 rovibrational energies of the pairs of states ν₁/ν₅ and 2ν₁/ν₁+ν₅ with experimental accuracies, rms=0.00016 and , respectively. “Local mode” behavior of the PH₂ fragment is established and discussed in detail.