<Emphasis Type="Italic">SU</Emphasis><Subscript><Emphasis Type="Italic">L</Emphasis></Subscript>(4)×<Emphasis Type="Italic">U</Emphasis>(1) model for electroweak unification and sterile neutrinos

Some of the basic problems in neutrino physics, such as new energy scales, the enormous gap between the neutrino masses and the lightest charged fermion mass, and the possible existence of sterile neutrinos in the eV mass range are studied in the local gauge group SU _L (4)×U(1) for electroweak unification, which does not contain fermions with exotic electric charges. It is shown that the neutrino mass spectrum can be decoupled from that of the other fermions. The further normal seesaw mechanism for neutrinos, with right-handed neutrino Majorana masses of order M≫M _weak as well a new eV-scale can be accommodated. The eV-scale seesaw may manifest itself in experiments like the Liquid Scintillation Neutrino Detector (LSND) and MiniBooNE (MB) experimental results and future neutrino experiments.     

The challenge of correlations in hadronic production of <Emphasis Type="Italic">V</Emphasis><Superscript>0</Superscript><Emphasis Type="Italic">V</Emphasis><Superscript>0</Superscript> pairs

The paper concerns the determination of the role of the γ-phase particles on the microstructure and properties of Co-Ni-Ga alloys. The studies cover the alloys of chemical composition which show two types of microstructure: single phase martensite BCT( Body Centred Tetragonal) lattice with c/a > 1(a), BCT + γ(b). The particle analysis was performed to determine the amount of the γ-phase in the studied alloys. The compression test on prism samples proved that the increase of the γ-phase volume fraction significantly improves the strength and plasticity of the alloys. Thus the presence of the γ-phase precipitates cause the decrease of the brittleness observed in the single phase martensitic alloys. TEM observations were performed for specimens before and after deformation to reveal the mechanism of the γ-phase deformation.     

Passive Advection and the Degenerate Elliptic Operators <Emphasis Type="Italic">M</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

 We prove estimates for the stationary state n-point functions at zero molecular diffusivity in the Kraichnan model [13]. This is done by proving upper bounds for the heat kernels and Green's functions of the degenerate elliptic operators M _n that occur in the Hopf equations for the n-point functions. Received: 25 August 2001 / Accepted: 30 September 2002 Published online: 20 January 2003 Communicated by A. Kupiainen     

GaSe<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript><Emphasis Type="Italic">S</Emphasis><Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> solid solutions

The most probable parameters of the pure, doped, and mixed GaSe_1−xS_x (x ≤ 0.4) crystals (solid solutions) are presented together with the results of investigations of their crystal structure and defects, optical and mechanical properties, and damage thresholds. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 35–40, June, 2007.     

<Emphasis Type="Italic">Λ</Emphasis>N scattering length from the reaction <Emphasis Type="Italic">γ</Emphasis>d→K<Superscript>+</Superscript><Emphasis Type="Italic">Λ</Emphasis>n

The prospects of utilizing the strangeness production reaction γd→K ⁺ Λn for the determination of the Λn low-energy scattering parameters are investigated. The spin observables that need to be measured in order to isolate the Λn singlet (¹ S ₀) and triplet (³ S ₁) states are identified. Possible kinematical regions where the extraction of the Λn scattering lengths might be feasible are discussed.     

2γ and 3γ annihilation as calibration processes for high energy <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> colliders

Born differential cross sections and the lowest-order radiative correction to them are obtained in the kinematics of large-angle final photon emissions in high-energy electron-positron annihilation processes. Taking into account the possible emission of real soft and hard photons in collinear kinematics, we show the validity of the Drell-Yan form of the differential cross section with the nonsinglet structure functions of the initial leptons. The leading and next-to-leading contribution to the cross sections is obtained. The relevant numerical estimations are presented. The text was submitted by the authors in English.     

Super <Emphasis Type="Italic">D</Emphasis>-Differentiation for <Emphasis Type="Italic">R</Emphasis><Superscript> ∞ </Superscript>-Supermanifolds

The concept of ‘D-Differentiation’, which, in the context of smooth manifolds, generalises Lie and covariant differentiation, is extended to R ^∞-supermanifolds under the name of ‘Super D-Differentiation’. This is done by defining new (non-linear) mappings, called ‘μ-mappings’ and by relating their non-linearity to the Leibniz rule that a derivation must satisfy when it acts on a tensor product. The resulting axiomatics, which is basis-independent and coordinate-free, is then expressed in a general basis (not necessarily holonomic). Super Lie and Super covariant differentiation are, amongst others, special cases of Super D-Differentiation. In particular, the transformation rules for the connection coefficients and the commutation coefficients of non-holonomic bases are obtained. These special cases are found to be in agreement with the DeWitt Super covariant and Super Lie derivatives.      

Tests of the final-state radiation model at DAFNE near <Emphasis Type="Italic">π</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">π</Emphasis><Superscript>-</Superscript> threshold

Effects due to the non-pointlike behaviour of pions in the process e ⁺ e ^-→π ⁺ π ^- γ can arise for hard photons in the final state. By means of a Monte Carlo event generator, which also includes the contribution of the direct decay φ→π ⁺ π ^- γ, we estimate these effects in the framework of the resonance perturbation theory. We consider angular cuts used in the KLOE analysis of the pion form factor at threshold. A method to reveal the effects of the non-pointlike behaviour of pions in a model-independent way is proposed.     

On the value of an element of Sobolev space <Emphasis Type="Italic">W˚</Emphasis><Stack><Subscript>2</Subscript><Superscript>1</Superscript></Stack>(<Emphasis Type="Italic">X</Emphasis>) at a point of domain <Emphasis Type="Italic">X</Emphasis>

A concept of cosheaf of Sobolev spaces is introduced; the value of an element of Sobolev space at a point is defined. Some theorems relating the convergence in norm with pointwise convergence are presented.     

The determination of <Emphasis Type="Italic">α</Emphasis><Subscript><Emphasis Type="Italic">S</Emphasis></Subscript> from <Emphasis Type="Italic">τ</Emphasis> decays revisited

We revisit the determination of α _S (m _τ ²) using a fit to inclusive τ hadronic spectral moments in light of (1) the recent calculation of the fourth-order perturbative coefficient K ₄ in the expansion of the Adler function, (2) new precision measurements from BABAR of e⁺e⁻ annihilation cross sections, which decrease the uncertainty in the separation of vector and axial-vector spectral functions, and (3) improved results from BABAR and Belle on τ branching fractions involving kaons. We estimate that the fourth-order perturbative prediction reduces the theoretical uncertainty, introduced by the truncation of the series, by 20% with respect to earlier determinations. We discuss to some detail the perturbative prediction of two different methods: fixed-order perturbation theory (FOPT) and contour-improved perturbative theory (CIPT). The corresponding theoretical uncertainties are studied at the τ and Z mass scales. The CIPT method is found to be more stable with respect to the missing higher order contributions and to renormalization scale variations. It is also shown that FOPT suffers from convergence problems along the complex integration contour. Nonperturbative contributions extracted from the most inclusive fit are small, in agreement with earlier determinations. Systematic effects from quark-hadron duality violation are estimated with simple models and found to be within the quoted systematic errors. The fit based on CIPT gives α _S (m _τ ²)=0.344±0.005±0.007, where the first error is experimental and the second theoretical. After evolution to M _Z we obtain α _S (M _Z ²)=0.1212±0.0005±0.0008±0.0005, where the errors are respectively experimental, theoretical and due to the evolution. The result is in agreement with the corresponding N³LO value derived from essentially the Z width in the global electroweak fit. The α _S (M _Z ²) determination from τ decays is the most precise one to date.     

Poincaré Duality and <Emphasis Type="Italic">G</Emphasis><Superscript>+++</Superscript> Algebras

Theories with General Relativity as a sub-sector exhibit enhanced symmetries upon dimensional reduction, which is suggestive of “exotic dualities”. Upon inclusion of time-like directions in the reductions one can dualize to theories in different space-time signatures. We clarify the nature of these dualities and show that they are well captured by the properties of infinite-dimensional symmetry algebras (G ⁺⁺⁺- algebras), but only after taking into account that the realization of Poincaré duality leads to restrictions on the denominator subalgebra appearing in the non-linear realization. The correct realization of Poincaré duality can be encoded in a simple algebraic constraint, that is invariant under the Weyl-group of the G ⁺⁺⁺-algebra, and therefore independent of the detailed realization of the theory under consideration. We also construct other Weyl-invariant quantities that can be used to extract information from the G ⁺⁺⁺-algebra without fixing a level decomposition. Post-doctoraal onderzoeker van het Fonds voor Wetenschappelijk Onderzoek, Vlaanderen.     

Once more about gauge invariance in <Emphasis Type="Italic">ϕ</Emphasis> → <Emphasis Type="Italic">γπ</Emphasis><Superscript>0</Superscript><Emphasis Type="Italic">π</Emphasis><Superscript>0</Superscript>

It is argued that the realization of gauge invariance condition as a consequent of cancellation between the ϕ → γf ₀ → γπ ⁰ π ⁰ resonance contribution and the ϕ → γπ ⁰ π ⁰ background one, suggested by A.V. Anisovich et al., Yad. Fiz. 68, 1614 (2005), is misleading. The text was submitted by the author in English.     

The <Emphasis Type="Italic">Φ</Emphasis>→K<Superscript>0</Superscript>¯<Emphasis Type="Italic">γ</Emphasis> decay

The scalar contributions to the radiative decay φ→K ⁰ˉ⁰ γ are studied within the framework of the Linear Sigma Model (LσM). Theoretical predictions for the associated subprocesses φ→f ₀ γ and φ→a ₀ γ as well as the ratio φ→f ₀ γ/a ₀ γ are also given.     

Dimension and Dynamical Entropy for Metrized <Emphasis Type="Italic">C</Emphasis><Superscript><Emphasis Type="Italic">*</Emphasis></Superscript>-Algebras

 We introduce notions of dimension and dynamical entropy for unital C ^* -algebras ``metrized' by means of , which are complex-scalar versions of the Lip-norms constitutive of Rieffel's compact quantum metric spaces. Our examples involve the UHF algebras and noncommutative tori. In particular we show that the entropy of a noncommutative toral automorphism with respect to the canonical coincides with the topological entropy of its commutative analogue. Received: 13 February 2002 / Accepted: 20 August 2002 Published online: 22 November 2002     

Disappearing cosmological constant in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

For higher-derivative f(R) gravity, where R is the Ricci scalar, a class of models is proposed, which produce viable cosmology different from the ACDM at recent times and satisfy cosmological, Solar System, and laboratory tests. These models have both flat and de Sitter spacetimes as particular solutions in the absence of matter. Thus, a cosmological constant is zero in a flat spacetime, but appears effectively in a curved one for sufficiently large R. A “smoking gun” for these models would be a small discrepancy in the values of the slope of the primordial perturbation power spectrum determined from galaxy surveys and CMB fluctuations. On the other hand, a new problem for dark energy models based on f(R) gravity is pointed out, which is connected with the possible overproduction of new massive scalar particles (scalarons) arising in this theory in the very early Universe. The text was submitted by the author in English.     

Resummed pQCD for <Emphasis Type="Italic">W</Emphasis><Superscript><Emphasis Type="Italic">±</Emphasis></Superscript> and <Emphasis Type="Italic">Z</Emphasis><Superscript>0</Superscript> transverse momentum spectra at RHIC and LHC

The transverse momentum distributions of W_± and Z₀ are predicted at RHIC and LHC. A resummation formalism with power corrections to the renormalization group equations is used. Shadowing effects are discussed and found to be unimportant at RHIC, but important for LHC. We study the enhancement of power corrections due to multiple scattering in nuclear collisions and numerically illustrate the weak effects of the dependence on the nuclear mass.     

Electronic structure and stability of Mg<Subscript>6</Subscript>Ti<Emphasis Type="Italic">M</Emphasis> (<Emphasis Type="Italic">M</Emphasis> = Mg,Al, Zn) and their hydrides

The influence of Al and Zn atoms on the stability of the Mg₇Ti compound and its hydride Mg₇TiH₁₆ has been studied theoretically. The calculations have been carried out in terms of the full-potential linearized augmented plane wave method. It has been demonstrated that the partial substitution of Al or Zn atoms for magnesium atoms leads to a decrease in the stability of the hydride and to an increase in the stability of the intermetallic compound.     

Identifying new physics contributions in the Higgs sector at linear <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> colliders

Loop-driven decay modes of the Higgs are sensitive to new physics contributions because of new particles in the loops. To highlight this we look at the dilepton-dijet signal in the dominant Higgs production channel at a linear e ⁺ e ⁻ collider. We show that by taking a simple ratio between cross-sections of two different final states such contributions can be very easily identified.