Pion damping width from <Emphasis Type="Italic">SU</Emphasis>(2)×<Emphasis Type="Italic">SU</Emphasis>(2) NJL model

Within the framework of the NJL model, we investigate the modification of the pion damping width in a hot pion gas for temperatures ranging from 0 to 180 MeV. The pion is found to broaden noticeably at T > 60 MeV. Near the chiral phase transition T ～ 180 MeV, the pion width is saturated and amounts to 70 MeV. The main contribution to the width comes from pion-pion collisions. Other contributions are found to be negligibly small.     

On the <Emphasis Type="Italic">SU</Emphasis>(2)×<Emphasis Type="Italic">SU</Emphasis>(2) symmetry in the Hubbard model

We discuss the one-dimensional Hubbard model, on finite sites spin chain, in context of the action of the direct product of two unitary groups SU(2)×SU(2). The symmetry revealed by this group is applicable in the procedure of exact diagonalization of the Hubbard Hamiltonian. This result combined with the translational symmetry, given as the basis of wavelets of the appropriate Fourier transforms, provides, besides the energy, additional conserved quantities, which are presented in the case of a half-filled, four sites spin chain. Since we are dealing with four elementary excitations, two quasiparticles called “spinons”, which carry spin, and two other called “holon” and “antyholon”, which carry charge, the usual spin-SU(2) algebra for spinons and the so called pseudospin-SU(2) algebra for holons and antiholons, provide four additional quantum numbers.     

Twin-unified <Emphasis Type="Italic">SU</Emphasis>(5) × <Emphasis Type="Italic">SU</Emphasis>(5)′ GUT and phenomenology

In this article, after a short introduction, grand unified SU(5)×SU(5)^′ model augmented by D₂ parity has been discussed. The latter turns out to be important for phenomenology. Specific pattern of the GUT symmetry breaking causes new strong dynamics at low energies. Consequently, the Standard Model leptons, along with right-handed /sterile neutrinos, come out as composite states. Issues of the gauge coupling unification, generation of the charged fermion and neutrino masses will be presented. Also, various phenomenological implications and constraints will be discussed.     

Charged nontopological soliton of the <Emphasis Type="Italic">SU</Emphasis>(2) × <Emphasis Type="Italic">U</Emphasis>(1) gauge model

The SU(2) × U(1) gauge model that is the bosonic sector of the Standard Model of electroweak interactions is considered. The existence of electrically charged nontopological solitons is shown to be possible in this model. Some properties of a charged nontopological soliton are investigated. Asymptotic expressions are derived for the soliton radius, energy, and phase frequency in the thin-wall regime by the method of trial functions. Numerical solutions of the model field equations corresponding to electrically charged non-topological solitions have been obtained. The dependences of the soliton energy and charge on phase frequency are given for several model parameters. It follows from the data obtained that there exists a domain of parameters in which a charged nontopological soliton is stable to the transition to a plane-wave field configuration.     

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.     

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).     

Constraints on <Emphasis Type="Italic">SU</Emphasis>(2) ⊗ <Emphasis Type="Italic">SU</Emphasis>(2) invariant polynomials for a pair of entangled qubits

We discuss the entanglement properties of two qubits in terms of polynomial invariants of the adjoint action of SU(2) ⊕ SU(2) group on the space of density matrices \(\mathfrak{P}_ +\). Since elements of \(\mathfrak{P}_ +\) are Hermitian, non-negative fourth-order matrices with unit trace, the space of density matrices represents a semi-algebraic subset, \(\mathfrak{P}_ + \in \mathbb{R}^{15}\). We define \(\mathfrak{P}_ +\) explicitly with the aid of polynomial inequalities in the Casimir operators of the enveloping algebra of SU(4) group. Using this result the optimal integrity basis for polynomial SU(2) ⊕ SU(2) invariants is proposed and the well-known Peres-Horodecki separability criterion for 2-qubit density matrices is given in the form of polynomial inequalities in three SU(4) Casimir invariants and two SU(2) ⊕ SU(2) scalars; namely, determinants of the so-called correlation and the Schlienz-Mahler entanglement matrices.     

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.     

Dirac monopoles embedded in <Emphasis Type="Italic">SU</Emphasis>(<Emphasis Type="Italic">N</Emphasis>) gauge theory with the θ term

Dirac monopoles embedded in SU(N) gauge theory with the θ term are considered. For θ=4πM (where M is half-integer and integer for N=2 and N>2, respectively), these monopoles acquire an SU(N) charge due to the θ term and become dyons. They belong to various (but not any) irreducible representations of the SU(N) group. The admissible representations are listed. Their minimum dimension increases with N. The basic result of the study is the representation of the partition function of any SU(N) model involving the θ term and complemented by singular gauge fields corresponding to the indicated monopoles in the form of a vacuum average of the product of Wilson loops viewed along the world lines of the monopoles. This vacuum average must be calculated in the corresponding model without the θ term.     

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.     

On <Emphasis Type="Italic">osp</Emphasis>(<Emphasis Type="Italic">M</Emphasis>∣2<Emphasis Type="Italic">n</Emphasis>) Integrable Open Spin Chains

We consider open spin chains based on osp(M2n) Yangians and solve the reflection equations for some classes of reflection matrices, including the diagonal ones. Having then integrable open spin chains, we write the analytical Bethe Ansatz equations. More details and references can be found in D. Arnaudon et al.: Nucl. Phys B 668 (2003) 469 and 687 (2004) 257.     

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.     

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.     

Contribution of final-state interaction to the branching ratio of <Emphasis Type="Italic">B</Emphasis>→<Emphasis Type="Italic">J</Emphasis>/<Emphasis Type="Italic">ψ</Emphasis><Emphasis Type="Italic">D</Emphasis>

To test the validity of perturbative QCD (pQCD) and investigate its range of application, one should look for a suitable process. B→J/ψ D is a promising candidate. The linear momentum of the products is relatively small, so that there may exist a region where exchanged gluons are soft and the perturbative treatment may fail, so that the non-perturbative effect would be significant. We attribute such non-perturbative QCD effects to the long-distance final-state interaction (FSI) which is estimated in this work. We find that the contribution from the FSI to the branching ratio is indeed sizable and may span the rather wide range of 10⁻⁶∼10⁻⁵ and cover a region where the pQCD prediction is of the same order. A more accurate measurement of its branching ratio may provide important information about the application region of pQCD and help to clarify the picture of inelastic rescattering (i.e. FSI), which is generally believed to play an important role in B decays.     

On the nature of the phase transition in <Emphasis Type="Italic">SU</Emphasis>(<Emphasis Type="Italic">N</Emphasis>), <Emphasis Type="Italic">Sp</Emphasis>(2) and <Emphasis Type="Italic">E</Emphasis>(7) Yang–Mills theory

We study the nature of the confinement phase transition in d=3+1 dimensions in various non-abelian gauge theories with the approach put forward in Phys. Lett. B 684, 262 (2010). We compute an order-parameter potential associated with the Polyakov loop from the knowledge of full 2-point correlation functions. For SU(N) with N=3,…,12 and Sp(2) we find a first-order phase transition in agreement with general expectations. Moreover our study suggests that the phase transition in E(7) Yang–Mills theory also is of first order. We find that it is weaker than for SU(N). We show that this can be understood in terms of the eigenvalue distribution of the order parameter potential close to the phase transition.     

Late-time cosmological approach in mimetic <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) gravity

In this paper, we investigate the late-time cosmic acceleration in mimetic f(R, T) gravity with the Lagrange multiplier and potential in a Universe containing, besides radiation and dark energy, a self-interacting (collisional) matter. We obtain through the modified Friedmann equations the main equation that can describe the cosmological evolution. Then, with several models from \(\mathcal {Q}(z)\) and the well-known particular model f(R, T), we perform an analysis of the late-time evolution. We examine the behavior of the Hubble parameter, the dark energy equation of state and the total effective equation of state and in each case we compare the resulting picture with the non-collisional matter (assumed as dust) and also with the collisional matter in mimetic f(R, T) gravity. The results obtained are in good agreement with the observational data and show that in the presence of the collisional matter the dark energy oscillations in mimetic f(R, T) gravity can be damped.     

Exact solutions and conserved quantities in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) Gravity

This paper explores Noether and Noether gauge symmetries of anisotropic universe model in f(R, T) gravity. We consider two particular models of this gravity and evaluate their symmetry generators as well as associated conserved quantities. We also find exact solution by using cyclic variable and investigate its behavior via cosmological parameters. The behavior of cosmological parameters turns out to be consistent with recent observations which indicates accelerated expansion of the universe. Next we study Noether gauge symmetry and corresponding conserved quantities for both isotropic and anisotropic universe models. We conclude that symmetry generators and the associated conserved quantities appear in all cases.