Bound states of three and four resonantly interacting particles

We present an exact diagrammatic approach for the problem of dimer-dimer scattering in 3D for dimers being a resonance bound state of two fermions in a spin-singlet state, with corresponding scattering length a _F . Applying this approach to the calculation of the dimmer-dimer scattering length a _B , we recover exactly the already known result a _B = 0.6 a _F . We use the developed approach to obtain new results in 2D for fermions and bosons. Namely, we calculate bound state energies for three bbb and four bbbb resonantly interacting bosons in 2D. For the case of resonance interaction between fermions and bosons, we exactly calculate bound state energies of the following complexes: two bosons plus one fermion bbf, two bosons plus two fermions bf↑bf↓, and three bosons plus one fermion bbbf.     

The possible angular momenta of a system of fermions or bosons with spinj

Simple recurrence relations for the multiplicities of angular momenta are presented for a system of fermions or bosons with spinj. Tables are given for fermions withj=13/2 up to 19/2 and for bosons withj=2, 3, 4, 5 and 20 particles at most.     

Partial virial theorems for atomic-molecular systems

New virial relations for three-and four-particle atomic-molecular systems are proposed. Using operators of extension or squeezing of interparticle distances, it is shown that, for all pairs of j and k particles in S states of these systems, the following partial virial relations are valid: 〈2T _jk 〉+〈 V _jk 〉=0, where 〈V _jk 〉 is the average Coulomb interaction energy for a pair of particles and 〈T _jk 〉 is a part of the average kinetic energy of the system. There are three and six such relations for three-and four-particle systems, respectively. The conventional virial theorem (〈 2T〉+〈V〉=0) for the average total kinetic and potential energies of the system (〈 T〉 and 〈V〉, respectively) corresponds to the summation of partial virial relations over all pairs of particles. It is shown by an example of variational calculations of the helium atom ⁴He²⁺ e ^? e ^? and the helium muon-electron mesoatom ⁴He²⁺μ^? e ^? that partial virial relations are a highly sensitive indicator of the accuracy of wave functions.     

Magnetization and Static Magnetic Susceptibility of Fine-Crystalline High-Temperature YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript><Emphasis Type="Italic">y</Emphasis></Subscript> Superconductors Synthesized by the Sol–Gel Method

A comparative study of the magnetization and static magnetic susceptibility of high-temperature superconductors (HTSC) YBa₂Cu₃O_y synthesized by two variants of the sol–gel method with different average sizes of crystallites 〈 D〉 ranging 0.4–2 μm has been performed in constant magnetic fields (Н ≤ 6 kOe). It has been shown that the different annealing temperatures and times, at which their crystal structure is formed, change both the average sizes of crystallites 〈D〉 and the sizes of the structural homogeneity regions 〈l〉 and, at the same time, the magnetic field penetration depth (λ) and the coherence length (ξ). As a result, such parameters as 〈D〉 ~ λ and 〈l〉 ~ ξ become comparable, leading to a change in the physical characteristics of HTSCs. It has also been shown that the superconducting transition temperature T_c determined from the measurements of magnetic characteristics in constant magnetic fields remains within values optimal for superconductivity (T_c ≈ 92 K) in the case of an optimal number (y) of oxygen atoms, which determine the levels of charge doping for a given compound.     

Higher-order corrections to Higgs boson decays in the MSSM with complex parameters

We discuss Higgs boson decays in the CP-violating MSSM, and examine their phenomenological impact using cross section limits from the LEP Higgs searches. This includes a discussion of the full 1-loop results for the partial decay widths of neutral Higgs bosons into lighter neutral Higgs bosons (h _a →h _b h _c ) and of neutral Higgs bosons into fermions (\(h_{a} \to f \bar{f}\)). In calculating the genuine vertex corrections, we take into account the full spectrum of supersymmetric particles and all complex phases of the supersymmetric parameters. These genuine vertex corrections are supplemented with Higgs propagator corrections incorporating the full 1-loop and the dominant 2-loop contributions, and we illustrate a method of consistently treating diagrams involving mixing with Goldstone and Z bosons. In particular, the genuine vertex corrections to the process h _a →h _b h _c are found to be very large and, where this process is kinematically allowed, can have a significant effect on the regions of the CPX benchmark scenario which can be excluded by the results of the Higgs searches at LEP. However, there remains an unexcluded region of CPX parameter space at a lightest neutral Higgs boson mass of ～45 GeV. In the analysis, we pay particular attention to the conversion between parameters defined in different renormalisation schemes and are therefore able to make a comparison to the results found using renormalisation group improved/effective potential calculations.     

Dependence of the Daily <Emphasis Type="Italic">N</Emphasis><Subscript><Emphasis Type="Italic">m</Emphasis></Subscript>F2 Values over Mid-Latitude Stations on the Solar and Geomagnetic Activity

The results of studies of the dependence of the daily electron concentration at maximum of the F2 ionospheric layer in January 2008–2015 on the solar and geomagnetic activity are presented. The solar radio emission flux density indices F_10.7 and geomagnetic activity indices A _p were averaged over 27 days, and 〈F_10.7〉₂₇ and 〈A _p 〉₂₇, respectively, were obtained. Based on the data of three stations, 27-day median (with the middle of January 15) daily N _m F2 variations were obtained for 2008–2015. Based on these data, the following paradox was discovered: in January 2014, when the values of the solar activity index F_10.7 were larger than in 2015, the dailyN _m F2 values were smaller. Averaging over four hours of local daytime (10:00–14:00 LT) gave the daily average January 〈N _m F2〉 values for each selected station for each year. To solve this paradox, a double linear regression of 〈N _m F2〉 on 〈F_10.7〉₂₇ and 〈A _p 〉₂₇ was constructed. Due to this, it was concluded that the contribution of geomagnetic activity to daily January 〈N _m F2〉 values is positive. A comparison of the mean square errors of the linear and double linear regressions for 〈F_10.7〉₂₇ and 〈F_10.7〉₈₁ showed that the use of 〈F_10.7〉₂₇ led to smaller errors than the use of 〈F_10.7〉₈₁.     

Dark matter from the SU(4) model

The left-right symmetric Pati-Salam model of the unification of quarks and leptons is based on the SU(4) and SU(2)×SU(2) symmetry groups. These groups are naturally extended to include the classification of families of quarks and leptons. We assume that the family group (the group which unites the families) is also the SU(4) group. The properties of the fourth generation of fermions are the same as those of the ordinary-matter fermions in the first three generations except for the family charge of the SU(4)_F group: F=(1/3, 1/3, 1/3, ?1), where F=1/3 for fermions of ordinary matter and F=?1 for the fourth-generation fermions. The difference in F does not allow mixing between ordinary and fourth-generation fermions. Because of the conservation of the Fcharge, the creation of baryons and leptons in the process of electroweak baryogenesis must be accompanied by the creation of fermions of the fourth generation. As a result, the excess n _B of baryons over antibaryons leads to the excess n_4ν=N?N? of neutrinos over antineutrinos in the fourth generation with n_4ν=n _B . This massive neutrino may form nonbaryonic dark matter. In principle, the mass density of the fourth neutrino n_4νm _N in the Universe can make the main contribution to dark matter, since the lower bound on the neutrino mass m _N from the data on decay of the Z bosons is m _N <m _Z /2. The straightforward prediction of this model leads to the amount of cold dark matter relative to baryons, which is an order of magnitude higher than allowed by observations. This inconsistency may be avoided by nonconservation of the F charge.     

New type of exact solutions to the generalized Ashkin-Teller model and anisotropic Ising model with spin 3/2

The generalized Ashkin-Teller model involving both biquadratic and bilinear interactions between the Ising subsystems (α and s) and equivalent to the anisotropic Ising model with spin 3/2 is considered. For a certain magnitude of the opposite-sign bilinear interactions along the horizontal and vertical axes of a square lattice, the exact analytic solution is obtained that describes the phase transition between the disordered (〈α 〉=〈s〉=〈αs〉=0) and the correlated ordered (〈s〉 ≠0 and 〈α〉=〈s〉=0) states.     

Low-temperature plasticity and lattice dynamics of solid parahydrogen with an isotopic impurity

The low-temperature plasticity of solid polycrystalline parahydrogen doped with an isotopic impurity (deuterium) is studied. The dependences of the rate of steady-state creep in p-H₂ on the impurity concentration and stress are obtained. The deformation of p-H₂ is described with inclusion of the zero-point mean-square displacements 〈x²〉 of particles making up a crystal. The calculated and experimental values of 〈x²〉 are compared for two possible isotope molecules (HD and D₂) at three stress levels. A correlation between the 〈x²〉 values and an increase in the force constants of a p-H₂ crystal doped with the isotopic impurity is established. An increase in the mean-square displacements of p-H₂ with the tensile load is discussed. Deformation-induced purification of a p-H₂ crystal from the isotopic impurity is suggested to occur.     

Short-wavelength atomic-displacement modulation preceding the <Emphasis Type="Italic">B</Emphasis>2 → <Emphasis Type="Italic">B</Emphasis>19′ martensitic transformation in a TiNi-based alloy

Neutron diffraction studies of the fine structure of a Ti₄₉Ni₅₁ single crystal are performed before the onset of the B2 → B19′ martensitic transformation (temperature of the onset of the transformation M _s =200 K). Upon cooling below 460 K, extra reflections are found to form; their positions in the B2-phase reciprocal lattice correspond to the full non-Lifshitz star of the wave vector q=0.225〈112〉. At temperatures below 430 K, 0.45〈110〉 extra reflections appear, corresponding to second-order diffraction effects. In the temperature range 300–460 K, reversible and nonhysteretic changes in the intensities and positions of both types of extra reflections are observed. Analysis of the intensities and spatial distribution of the extra reflections in the B2-phase reciprocal lattice indicates that a displacive superstructure dominated by longitudinally polarized atomic-displacement waves with q=0.225〈112〉 arises in the single crystal in the pretransition temperature range.     

One-phonon Raman spectra of carbon in composite films prepared by modification of amorphous hydrogenated carbon by copper and cobalt

One-phonon visible-range Raman spectra of a-C: H〈Cu〉 and a-C: H〈Co〉 composite films with comparable metal and carbon contents were studied in the frequency region 1200–1700 cm^?1 including the carbon sp²-bond vibrations. Broad bands G and D characteristic of unmodified a-C: H films, as well as some additional features, are observed experimentally in the spectra. By unfolding the spectra into Gaussian components, it was possible to follow the variation of Raman shifts and of contributions of individual components to the spectrum as a function of metal content and thermal annealing. The data obtained, complemented by available information on carbon sp²-coordinated systems, show that incorporation of Cu or Co favors growth and ordering of graphite-like nanoclusters in a-C: H, the effect being substantially stronger in the case of Co. It is shown that the process of metal-stimulated graphitization includes carbon bond breaking with the formation of short chainlike fragments and their linkage with the formation of aromatic-ring nanoclusters. A qualitatively similar sp²-structure rearrangement takes place under thermal annealing. For the Cu and Co concentrations studied, the linear dimensions L _a of graphite-like clusters are estimated to vary from ～0.8 nm in unannealed a-C: H to ～1.0 and ～1.2 nm in annealed a-C: H〈Cu〉 and a-C: H〈Co〉, respectively. The number of aromatic rings in these clusters is approximately estimated to increase from 12 to 16 (for Cu) and 20 (for Co).     

Stealth multiboson signals

We introduce the ‘stealth bosons’ S, light boosted particles with a decay \(S \rightarrow AA \rightarrow q \bar{q} q \bar{q}\) into two daughter bosons A, which subsequently decay into four quarks that are reconstructed as a single fat jet. Variables that measure the two-pronged structure of fat jets, which are used for diboson resonance searches in hadronic or semi-leptonic final states, classify the jets produced in stealth boson decays as QCD-like – actually, for these variables they may seem more background-like than the QCD background itself. The number of tracks in those jets can also be, on average, much higher than for the fat jets arising from the hadronic decay of boosted W and Z bosons. Therefore, these elusive particles are hard to spot in standard searches. Heavy resonances decaying into two such stealth bosons, or one plus a W / Z boson, could offer an explanation for the recurrent small excesses found in hadronic diboson resonance searches near an invariant mass of 2 TeV.     

Structure and phase composition of thin a-C:H films modified by Ag and Ti

The structure and phase composition of thin a-C:H and a-C:H〈M〉 films (M = Ag, Ti, or Ag + Ti) have been studied by Raman and X-ray photoelectron spectroscopy. The a-C:H〈M〉 films were prepared by ion-plasma magnetron sputtering of a combined target of graphite and metal in an Ar–CH₄ gas mixture. The Raman spectra of these films indicate that their structure is amorphous. The a-C:H〈Ag + Ti〉 films have a more graphitized structure in comparison with pure a-C:H films and films containing only one metal. It is established that carbon in the a-C:H〈Ag + Ti〉 films is in the sp ², sp ³, and C=O states, which are characteristic of the a-C:H, a-C:H〈Ag〉, and a-C:H〈Ti〉 films. In addition, there are also ether (–C–O–C–) or epoxy (?C?O–) carbon groups in the a-C:H〈Ag + Ti〉 films. It has been revealed that silver atoms in the a-C:H〈Ag〉 and a-C:H〈Ag + Ti〉 films form no chemical bonds with carbon, oxygen, and titanium. Titanium in the a-C:H〈Ti〉 and a-C:H〈Ag + Ti〉 films exists in the form of titanium IV oxide (TiO₂).     

Model-independent analysis of <Emphasis Type="Italic">CP</Emphasis> violation effects in decays of the Higgs boson into a Pair of the <Emphasis Type="Italic">W</Emphasis> and <Emphasis Type="Italic">Z</Emphasis> bosons

Effects of CP and T invariance violation are studied in the most general interaction of the Higgs boson with the intermediate vector W ^± and Z bosons. Various angular distributions of the cascade decay Φ → W ⁺ W ^?/ZZ → 4 of fermions in the transversity and helicity systems are calculated, and asymmetries are constructed and evaluated. It is shown that studying the azimuthal angle distribution of the process Φ → ZZ → (e ^? e ⁺)(μ^?μ⁺) in the transversity system is effective for measuring the spatial parity of the Higgs boson.     

Nonlinear generation of vorticity in thin smectic films

The energy levels of the fermions bound to the vortex are considered for vortices in the superfluid/superconducting systems that contain the symmetry protected plane of zeroes in the gap function in bulk. The Caroli–de Gennes–Matricon branches with different approach zero energy level at p_z → 0. The density of states of the bound fermions diverges at zero energy giving rise to the \(\sqrt \Omega \) dependence of the density of states in the polar phase of superfluid ³He rotating with the angular velocity Ω and to the \(\sqrt B \) dependence of the density of states for superconductors in the (d_xz + id_yz)-wave pairing state.     

The <Emphasis Type="Italic">A</Emphasis><Emphasis Type="Italic">d</Emphasis><Emphasis Type="Italic">S</Emphasis><Subscript>5</Subscript> Warp of Spatially Hyperbolic Universes,Spinless Modes and Spectra and the Corresponding Wheeler–DeWitt Schrödinger-Like Equation

In this paper, we consider an A d S ₅ bulk with k=?1? FRW branes, together with bosons test particles, evolving in the 5D hyperspace. In the first part, we compute the wave function of the scalar fields in the bulk and the allowed mass spectrum for physically relevant cases. Also, an important quantization law, connecting the mass spectrum of the bosons on the brane and the bulk mass parameter is written down. In the second part, in oder to develop a quantization model, we use the Wheeler-DeWitt equation and solve its Schrödinger-like form, obtaining the wave function of the Universe. The solutions describe a universe emerging out of nothing, without tunneling. Lastly, using a mixture of states, we emphasize a smooth universe, with neither Bangs nor Crunches.     

Properties of proton clusters in inelastic CC interactions accompanied by the production of Λ and <Emphasis Type="Italic">K</Emphasis><Superscript>0</Superscript> particles at <Emphasis Type="Italic">p</Emphasis> = 4.2 GeV/<Emphasis Type="Italic">c</Emphasis> per nucleon

Within a new relativistically invariant approach, the properties of proton clusters that are formed together with Λ and K⁰ particles in inelastic CC interactions at p=4.2 GeV/c per nucleon are investigated in the space of relative 4-velocities. The observed proton clusters are shown to be characterized by high values of the mean kinetic energy of the protons in the cluster rest frame: 〈T _p 〉=100±2 MeV.     

Positions of the magnetoroton minima in the fractional quantum Hall effect

The multitude of excitations of the fractional quantum Hall state are very accurately understood, microscopically, as excitations of composite fermions across their Landau-like Λ levels. In particular, the dispersion of the composite fermion exciton, which is the lowest energy spin conserving neutral excitation, displays filling-factor-specific minima called “magnetoroton” minima. Simon and Halperin employed the Chern-Simons field theory of composite fermions [Phys. Rev. B 48, 17368 (1993)] to predict the magnetoroton minima positions. Recently, Golkar et al. [Phys. Rev. Lett. 117, 216403 (2016)] have modeled the neutral excitations as deformations of the composite fermion Fermi sea, which results in a prediction for the positions of the magnetoroton minima. Using methods of the microscopic composite fermion theory we calculate the positions of the roton minima for filling factors up to 5/11 along the sequence s/ (2s + 1) and find them to be in reasonably good agreement with both the Chern-Simons field theory of composite fermions and Golkar et al.’s theory. We also find that the positions of the roton minima are insensitive to the microscopic interaction in agreement with Golkar et al.’s theory. As a byproduct of our calculations, we obtain the charge and neutral gaps for the fully spin polarized states along the sequence s/ (2s ± 1) in the lowest Landau level and the n = 1 Landau level of graphene.     

Majorana neutrinos, <Emphasis Type="Italic">CP</Emphasis> violation,neutrinoless double beta and tritium beta decays

If the present or upcoming searches for neutrinoless double beta ((ββ)_0ν) decay give a positive result, the Majorana nature of massive neutrinos will be established. From the determination of the value of the (ββ)_0ν-decay effective Majorana mass parameter (|〈m〉|), it would be possible to obtain information on the type of neutrino mass spectrum. Assuming 3-ν mixing and massive Majorana neutrinos, we discuss the information that a measurement of, or an upper bound on, |〈m〉| can provide on the value of the lightest neutrino mass m₁. With additional data on the neutrino masses obtained in ³H β-decay experiments, it might be possible to establish whether the CP symmetry is violated in the lepton sector. This would require very high precision measurements. If CP invariance holds, the allowed patterns of the relative CP parities of the massive Majorana neutrinos would be determined.     

The nonlocal chiral quark model and the muon <Emphasis Type="Italic">g</Emphasis> – 2 problem

In the first part of the review we discuss the effective nonlocal approach in the quantum field theory. It concerns primary the historical retrospective of this approach, and than we concentrate on the interaction of matter particles (fermions and bosons) with the (abelian and nonabelian) gauge fields. In the second part of the review we consider the hadronic corrections (vacuum polarization) to the anomalous magnetic moment of the muon g - 2 factor discussed within the SU_f(2) nonlocal chiral quark model. This is considered in the leading and, partially, in the next-to-leading orders (the effect of the fermion propagator dressing due to pion field) of expansion in small parameter 1/N_c (N_c is the number of colors in QCD).