Higher <Emphasis Type="Italic">η</Emphasis><Subscript>c</Subscript>(<Emphasis Type="Italic">nS</Emphasis>) and <Emphasis Type="Italic">η</Emphasis><Subscript>b</Subscript>(<Emphasis Type="Italic">nS</Emphasis>) mesons

The hyperfine splittings in heavy quarkonia are studied in a model-independent way using experimental data on dielectron widths. Relativistic correlations are taken into account together with the smearing of spin-spin interaction. The radius of smearing is fixed by known G/ψ−η _c(1S), ψ(2S)−η _c′(2S) splittings, which appears to be small, r _ss ≅ 0.06 fm. Nevertheless, even with such a small radius, substantial suppression of hyperfine splittings (∼50%) is observed in bottomonium. For nS b states (n = 1, 2, ..., 6), our predicted splittings (in MeV) are 28, 12, 10, 5, 6, 3. For the 3S and 4S charmonium states, the splittings 16(2) and 12(4) MeV are obtained. The text was submitted by the authors in English.     

Two-photon decays of pseudotensor mesons <Emphasis Type="Italic">π</Emphasis><Subscript>2</Subscript>(1670), <Emphasis Type="Italic">π</Emphasis><Subscript>2</Subscript>(2250), and <Emphasis Type="Italic">π</Emphasis><Subscript>2</Subscript>(2510)

In terms of relativistic and gauge-invariant spectral-integral technique, we calculate amplitude for the π ₂ → γγ decay as a three-step transition π ₂ → q $ \bar q $ \bar q (2⁻⁺) → γ + q $ \bar q $ \bar q (1⁻⁻) → γγ. Using wave functions of the q $ \bar q $ \bar q components of photon (hep-ph/0406320) and those of pseudotensor mesons π ₂(1670), π ₂(2000), π ₂(2250), and π ₂(2510) (hep-ph/0511109), we obtain the following values for partial widths: Γ _{π2(1670)→γγ} = 0.072 ± 0.007 keV, Γ _{π2(2000)→γγ} = 0.037 ± 0.004 keV, Γ _{π2(2250)→γγ} = 0.027 ± 0.003 keV, and Γ _{π2(2510)→γγ} = 0.022 ± 0.002 keV. In the calculations, we use the momentum operator expansion, and, in this connection, discuss the problem of nilpotent operators inherent in the considered amplitude. It should be emphasized that measurement of two-photon decays of the π ₂ states can give valuable information about the long-range quark-antiquark forces which, as one may guess, are related to the quark confinement.     

Spectral-luminescent properties of AgLa<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Eu<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>(MoO<Subscript>4</Subscript>)<Subscript>2</Subscript> solid solutions

The luminescent properties of AgLa_{1 − x} Eu _x (MoO₄)₂ (x = 0.1, 0.2, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0) under laser excitation (λ = 337.1 nm) are studied. It is shown that, upon substitution of Eu³⁺ for La³⁺, the symmetry of luminescence centers does not vary. According to the X-ray diffraction data, all samples have scheelite-like structure; the pattern of variation in volumes of their unit cells counts in favor of the presence of a continuous series of solid solutions. It is found that an increase in the europium concentration in AgLa_{1 − x} Eu _x (MoO₄)₂ leads to an increase in the luminescence intensity with a maximum at x = 0.9.     

Thin <Emphasis Type="Italic">W</Emphasis>′ and <Emphasis Type="Italic">W</Emphasis> domain walls in ferroelastic Pb<Subscript>3</Subscript>(PO<Subscript>4</Subscript>)<Subscript>2</Subscript>

A model of ferroelastic domain walls consisting of matching interlayers of crystal lattices is proposed. The dependences of the parameters of the interlayers and of the parameters of the equations for W′ and W domain walls on the crystal lattice parameters of the ferroelastic phase in Pb₃(PO₄)₂ are determined. The problem concerning the number of possible orientational states and their interaction in a polydomain crystal is considered.     

Spectral-luminescent properties of LiRbLa<Subscript>2 − <Emphasis Type="Italic">x</Emphasis></Subscript>Eu<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>(MoO<Subscript>4</Subscript>)<Subscript>4</Subscript> solid solutions

The luminescent properties of LiRbLa_{2 − x} Eu _x (MoO₄)₄ (x = 0.002, 0.02, 0.1, 0.2, 0.5, 1.0, 1.5, 2.0) solid solutions are investigated under laser excitation {λ_ex = 337.1 nm). It is established that the composition containing 50 at % Eu³⁺ is the brightest of the considered set of phosphors and has the highest quantum yield.     

Large Deviations for Zeros of <Emphasis Type="Italic">P</Emphasis>(<Emphasis Type="Italic">ϕ</Emphasis>)<Subscript>2</Subscript> Random Polynomials

We extend the results of (Zeitouni and Zelditch in Int. Math. Res. Not. 2010(20):3939–3992, 2010) on LDPs (large deviations principles) for the empirical measures

$Z_s: = \frac{1}{N} \sum_{\zeta: s(\zeta) = 0} \delta_{\zeta}, \quad (N: = \# \{\zeta: s(\zeta) = 0\})$

of zeros of Gaussian random polynomials s in one variable to P(?)₂ random polynomials. The speed and rate function are the same as in the associated Gaussian case. It follows that the expected distribution of zeros in the P(?)₂ ensembles tends to the same equilibrium measure as in the Gaussian case.

     

On the <Emphasis Type="Italic">Λ</Emphasis>CDM Universe in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">G</Emphasis>) gravity

In the context of the so-called Gauss–Bonnet gravity, where the gravitational action includes function of the Gauss–Bonnet invariant, we study cosmological solutions, especially the well-known ΛCDM model. It is shown that the dark energy contribution and even the inflationary epoch can be explained in the frame of this kind of theories with no need of any other kind of component. Other cosmological solutions are constructed and the rich properties that this kind of theories provide are explored.     

The role of the intermediate resonance <Emphasis Type="Italic">a</Emphasis><Subscript>0</Subscript>(980) in the decay <Emphasis Type="Italic">η</Emphasis> → <Emphasis Type="Italic">πγγ</Emphasis>

It is shown that if the a₀(980) boson is the scalar chiral partner of a π meson, its contribution to the transition η → πγγ has a value comparable to that originated by vector meson exchange. Together, these two mechanisms give the decay probability consistent with the experimental observation.     

Crystal structure and magnetic susceptibility of (CuInSe<Subscript>2</Subscript>)<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>(2MnSe)<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>

The crystal structure of samples in the (CuInSe₂)_{1 ? x} (2MnSe) _x system at room temperature and their magnetic susceptibility in the temperature range 77–1000 K are investigated. It is established that compositions with concentrations 0≤ x ≤ 0.2 form solid solutions with a tetragonal structure, space group I \(\bar 4\)2d (122). The specific magnetic susceptibility χ of samples with 0.1 ≤ x ≤ 0.4 at 77 K lies in the range 9 × 10^?4?1.6 × 10^t-3cm³/g. The temperature dependence of the inverse magnetic susceptibility of the sample with x = 0.4 suggests the presence of a component with antiferromagnetic ordering and a reliably measured Néel temperature that is characteristic of MnSe. The dependences χ = f(T) of the compositions with x = 0.1, 0.2, 0.3, and 0.4 indicate the occurrence of magnetic phase transitions with a change in the spin state.     

On a Ströbel-Inspired <Emphasis Type="Italic">k</Emphasis>(<Emphasis Type="Italic">t</Emphasis>) FLRW Ansatz in a Class of Metric <Emphasis Type="Italic">F</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) Models

Assuming a D≥4 dimensional FLRW (Friedmann–Lemaître–Robertson–Walker) inspired ansatz with spatial curvature being a non-trivial function of time k(t) in a class of metric and Jordan frame F(R) gravity models, non-existence theorems for several types of sources are derived in a simple manner (using specific form of the modified gravity Einstein tensor components).     

Cosmology in modified <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>)-gravity

In the present paper we propose a further modification of f(R, T)-gravity (where T is trace of the energy-momentum tensor) by introducing higher derivatives matter fields. We discuss stability conditions in the proposed theory and find restrictions for the parameters to prevent appearance of main type of instabilities, such as ghost-like and tachyon-like instabilities. We derive cosmological equations for a few representations of the theory and discuss main differences with conventional f(R, T)-gravity without higher derivatives. It is demonstrated that in the theory presented inflationary scenarios appear quite naturally even in the dust-filled Universe without any additional matter sources. Finally, we construct an inflationary model in one of the simplest representation of the theory, calculate the main inflationary parameters and find that it may be in quite good agreement with observations.     

Anisotropic quark stars in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) gravity

The aim of this paper is to analyze the nature of anisotropic spherically symmetric relativistic star models in the framework of f(R, T) gravity. To discuss the features of compact stars, we consider that in the interior of the stellar system, the fluid distribution is influenced by MIT bag model equation of state. We construct the field equations by employing Krori–Barua solutions and obtain the values of unknown constants with the help of observational data of Her X-1, SAX J 1808.4-3658, RXJ 1856-37 and 4U1820-30 star models. For a viable f(R, T) model, we study the behavior of energy density, transverse as well as radial pressure and anisotropic factor in the interior of these stars for a specific value of the bag constant. We check the physical viability of our proposed model and stability of stellar structure through energy conditions, causality condition and adiabatic index. It is concluded that our model satisfies the stability criteria as well as other physical requirements, and the value of bag constant is in well agreement with the experimental value which highlights the viability of our considered model.     

Structure of β-decay Strength Function <Emphasis Type="Italic">S</Emphasis><Subscript>β</Subscript>(<Emphasis Type="Italic">E</Emphasis>) in Halo Nuclei

It is shown that when the parent nucleus has nn Borromean halo structure, then after Gamow–Teller (GT) β^–-decay of parent state or after M1 γ-decay of Isobar Analogue Resonance (IAR) the states with np tango halo structure or mixed np tango + nn Borromean halo structure can be populated. Resonances in the GT β-decay strength function S_β(E) of halo nuclei, may have np tango halo structure or mixed np tango + nn Borromean halo structure. Correct interpretation of halo structure is important in experiments on β-decay study, interpretation of M1 γ-decay of IAR, and charge-exchange nuclear reactions analysis.     

Vector tetraquark state candidates: <Emphasis Type="Italic">Y</Emphasis>(4260 / 4220), <Emphasis Type="Italic">Y</Emphasis>(4360 / 4320), <Emphasis Type="Italic">Y</Emphasis>(4390) and <Emphasis Type="Italic">Y</Emphasis>(4660 / 4630)

In this article, we construct the \(C \otimes \gamma _\mu C\) and \(C\gamma _5 \otimes \gamma _5\gamma _\mu C\) type currents to interpolate the vector tetraquark states, then carry out the operator product expansion up to the vacuum condensates of dimension-10 in a consistent way, and obtain four QCD sum rules. In calculations, we use the formula \(\mu =\sqrt{M^2_{Y}-(2{\mathbb {M}}_c)^2}\) to determine the optimal energy scales of the QCD spectral densities, moreover, we take the experimental values of the masses of the Y(4260 / 4220), Y(4360 / 4320), Y(4390) and Y(4660 / 4630) as input parameters and fit the pole residues to reproduce the correlation functions at the QCD side. The numerical results support assigning the Y(4660 / 4630) to be the \(C \otimes \gamma _\mu C\) type vector tetraquark state \(c\bar{c}s\bar{s}\), assigning the Y(4360 / 4320) to be \(C\gamma _5 \otimes \gamma _5\gamma _\mu C\) type vector tetraquark state \(c\bar{c}q\bar{q}\), and disfavor assigning the Y(4260 / 4220) and Y(4390) to be the pure vector tetraquark states.     

Study of the f<Subscript>2</Subscript>(1270) , f<Subscript>2</Subscript>′(1525) , f<Subscript>0</Subscript>(1370) and f<Subscript>0</Subscript>(1710) in the J/<Emphasis Type="Italic">ψ</Emphasis> radiative decays

In this paper we present an approach to study the radiative decay modes of the J/ψ into a photon and one of the tensor mesons f ₂(1270) , f′ ₂(1525) , as well as the scalar ones f ₀(1370) and f ₀(1710) . Especially, we compare predictions that emerge from a scheme where the states appear dynamically in the solution of vector meson-vector meson scattering amplitudes to those from a (admittedly naive) quark model. We provide evidence that it might be possible to distinguish amongst the two scenarios, once improved data are available.     

The anisotropic cosmological models in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) gravity with <Emphasis Type="Italic">Λ(T)</Emphasis>

The rare decay \(B\rightarrow {K^{*}}\ell ^+\ell ^-\) is a very significant mode to search for physics beyond the Standard Model (SM). The mode provides a very rich spectrum of observables obtained from the angular distribution of its decay products. The recent LHCb measured values of these observables are used to conclude an evidence of right-handed currents at the kinematic endpoint of this decay mode. As the conclusion is drawn at the maximum dilepton invariant mass square (\(q^2\)) kinematic endpoint, it relies only on heavy quark symmetries where it is valid without significant corrections.