Asymmetries of various <Emphasis Type="Italic">P</Emphasis>- and <Emphasis Type="Italic">T</Emphasis>-parities in angular distributions of products of cold-polarized-neutron-induced binary and ternary fission of oriented nuclei and <Emphasis Type="Italic">T</Emphasis>-invariance

It is shown that a quantum system whose Hamiltonian is independent of time is T -invariant if this Hamiltonian contains only those terms that do not change sign upon time reversal. It is also shown that the coincidence of the amplitudes for multistep direct and statistical nuclear reactions with the timereversed amplitudes for the reactions being studied is a condition that ensures the T -invariance of the amplitudes in question, the transition from the original amplitudes to their time-reversed counterparts being accomplished, first, upon introducing the inverse-reactionmatrices T instead of the original-reaction matrix T and, second, upon replacing the wave functions for the initial, final, and intermediate states of the system by the respective time-reversed functions. It is found that the T -even (T -odd) asymmetries in cross sections for nuclear reactions stem from the interference between the amplitudes characterizing these reactions and having identical (opposite) T -parities. It is shown that the T -invariance condition for the above T -even (T -odd) asymmetries is related to the conservation of (change in) the sign of these asymmetries upon going over from original to inverse nuclear reactions. Mechanisms underlying the appearance of possible T -even and T-odd asymmetries in the cross sections for the cold-polarizedneutron- induced binary and ternary fission of oriented target nuclei are analyzed for the case of employing T -invariant Hamiltonians for the systems under study. It is also shown that the asymmetries in question satisfy the T -invariance condition if the reactions being considered have a sequential multistep statistical character. It is concluded that T -invariance is violated in the limiting case where, in ternary nuclear fission, the emission of a light third particle froma fissile compound nucleus formed upon incident-neutron capture by a target nucleus and its separation to two fission fragments are simultaneous events.     

Application of <Emphasis Type="Italic">T</Emphasis>-Invariance Conditions in Selecting Mechanisms of Nuclear Reactions,Decays, and Fission

T-invariance conditions for the differential cross sections of multiparticle multistep nuclear reactions are found with allowance for spin orientations of particles in the initial channels of such reactions. It is shown that the asymmetry coefficients for different T-parities in the differential cross sections for original and time-reversed reactions are expressed in terms of unified scalar (pseudoscalar) functions that depend of the 3-momenta and spins of particles involved in the initial and final channels of the reactions under analysis. It is also shown that knowledge of the aforementioned functions for the asymmetries under analysis in the original reaction makes it possible to reconstruct the respective functions for the analogous asymmetries in the time-reversed reaction without studying it experimentally. By considering the example of T-even and T-odd asymmetries in reactions where oriented nuclei undergo binary and ternary fission induced by cold polarized neutrons, it is demonstrated that the T-invariance conditions in question can be used to select mechanisms behind the appearance of the above asymmetries—in particular, mechanisms associated with the presence of T-noninvariant interactions.     

Cosmic acceleration in non-flat <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) cosmology

We study f(T) cosmological models inserting a non-vanishing spatial curvature and discuss its consequences on cosmological dynamics. To figure this out, a polynomial f(T) model and a double torsion model are considered. We first analyze those models with cosmic data, employing the recent surveys of Union 2.1, baryonic acoustic oscillation and cosmic microwave background measurements. We then emphasize that the two popular f(T) models enable the crossing of the phantom divide line due to dark torsion. Afterwards, we compute numerical bounds up to 3-\(\sigma \) confidence level, emphasizing the fact that \(\Omega _{k0}\) turns out to be non-compatible with zero at least at 1\(\sigma \). Moreover, we underline that, even increasing the accuracy, one cannot remove the degeneracy between our models and the \(\Lambda \)CDM paradigm. So that, we show that our treatments contain the concordance paradigm and we analyze the equation of state behaviors at different redshift domains. We also take into account gamma ray bursts and we describe the evolution of both the f(T) models with high redshift data. We calibrate the gamma ray burst measurements through small redshift surveys of data and we thus compare the main differences between non-flat and flat f(T) cosmology at different redshift ranges. We finally match the corresponding outcomes with small redshift bounds provided by cosmography. To do so, we analyze the deceleration parameters and their variations, proportional to the jerk term. Even though the two models well fit late-time data, we notice that the polynomial f(T) approach provides an effective de-Sitter phase, whereas the second f(T) framework shows analogous results compared with the \(\Lambda \)CDM predictions.     

Model-independent reconstruction of <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) teleparallel cosmology

We propose a model-independent formalism to numerically solve the modified Friedmann equations in the framework of f(T) teleparallel cosmology. Our strategy is to expand the Hubble parameter around the redshift \(z=0\) up to a given order and to adopt cosmographic bounds as initial settings to determine the corresponding \(f(z)\equiv f(T(H(z)))\) function. In this perspective, we distinguish two cases: the first expansion is up to the jerk parameter, the second expansion is up to the snap parameter. We show that inside the observed redshift domain \(z\le 1\), only the net strength of f(z) is modified passing from jerk to snap, whereas its functional behavior and shape turn out to be identical. As first step, we set the cosmographic parameters by means of the most recent observations. Afterwards, we calibrate our numerical solutions with the concordance \(\Lambda \)CDM model. In both cases, there is a good agreement with the cosmological standard model around \(z\le 1\), with severe discrepancies outer of this limit. We demonstrate that the effective dark energy term evolves following the test-function: \(f(z)={\mathcal {A}}+{\mathcal {B}}{z}^2e^{{\mathcal {C}}{z}}\). Bounds over the set \(\left\{ {\mathcal {A}}, {\mathcal {B}}, {\mathcal {C}}\right\} \) are also fixed by statistical considerations, comparing discrepancies between f(z) with data. The approach opens the possibility to get a wide class of test-functions able to frame the dynamics of f(T) without postulating any model a priori. We thus re-obtain the f(T) function through a back-scattering procedure once f(z) is known. We figure out the properties of our f(T) function at the level of background cosmology, to check the goodness of our numerical results. Finally, a comparison with previous cosmographic approaches is carried out giving results compatible with theoretical expectations.     

Violation of causality in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) gravity

In the standard formulation, the f(T) field equations are not invariant under local Lorentz transformations, and thus the theory does not inherit the causal structure of special relativity. Actually, even locally violation of causality can occur in this formulation of f(T) gravity. A locally Lorentz covariant f(T) gravity theory has been devised recently, and this local causality problem seems to have been overcome. The non-locality question, however, is left open. If gravitation is to be described by this covariant f(T) gravity theory there are a number of issues that ought to be examined in its context, including the question as to whether its field equations allow homogeneous Gödel-type solutions, which necessarily leads to violation of causality on non-local scale. Here, to look into the potentialities and difficulties of the covariant f(T) theories, we examine whether they admit Gödel-type solutions. We take a combination of a perfect fluid with electromagnetic plus a scalar field as source, and determine a general Gödel-type solution, which contains special solutions in which the essential parameter of Gödel-type geometries, \(m^2\), defines any class of homogeneous Gödel-type geometries. We show that solutions of the trigonometric and linear classes (\(m^2 < 0\) and \(m=0\)) are permitted only for the combined matter sources with an electromagnetic field matter component. We extended to the context of covariant f(T) gravity a theorem which ensures that any perfect-fluid homogeneous Gödel-type solution defines the same set of Gödel tetrads \(h_A^{~\mu }\) up to a Lorentz transformation. We also showed that the single massless scalar field generates Gödel-type solution with no closed time-like curves. Even though the covariant f(T) gravity restores Lorentz covariance of the field equations and the local validity of the causality principle, the bare existence of the Gödel-type solutions makes apparent that the covariant formulation of f(T) gravity does not preclude non-local violation of causality in the form of closed time-like curves.     

Top-quark <Emphasis Type="Italic">p</Emphasis><Subscript><Emphasis Type="Italic">T</Emphasis></Subscript>-spectra at CMS and flavor independence of <Emphasis Type="Italic">z</Emphasis>-scaling

We present new results of analysis of top-quark differential cross sections obtained by the CMS Collaboration in pp collisions in the framework of the z-scaling approach. The spectra are measured over a wide range of collision energy \(\sqrt s = 7,8,13TeV\) and transverse momentum p _T = 30?500 GeV/c of top-quark using leptonic and jet decay modes. Flavor independence of the scaling function ψ(z) is verified in the new kinematic range. The results of analysis of the top-quark spectra obtained at the LHC are compared with similar spectra measured in \(\overline p p\) collisions at the Tevatron energy \(\sqrt s = 1.96TeV\). A tendency to saturation of ψ(z) for the process at low z and a power-law behavior of ψ(z) at high z is observed. The measurements of high-p _T is observed. The measurements of highspectra of the top-quark production at highest LHC energy is of interest for verification of self-similarity of particle production, understanding flavor origin and search for new physics symmetries with top-quark probe.     

Decay Behaviors of the <Emphasis Type="Italic">P</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript> Hadronic Molecules

In this proceeding, we present our recent work on decay behaviors of the P_c hadronic molecules, which can help to disentangle the nature of the two P_c pentaquark-like structures. The results turn out that the relative ratio of the decays of P _c ⁺ (4380) to \({\bar D *}{\Lambda _c}\) and J/ψp is very different for P_c being a \({\bar D *}{\Sigma _c}\) or \(\bar D\Sigma _c *\) bound state with \({J^P} = \frac{{{3 - }}}{2}\) And from the total decay width, we find that P_c(4380) being a \(\bar D\Sigma _c *\) molecule state with \({J^P} = \frac{{{3 - }}}{2}\) and P_c(4450) being a \({\bar D *}{\Sigma _c}\) molecule state with \({J^P} = \frac{{{5 + }}}{2}\) is more favorable to the experimental data.     

Why <Emphasis Type="Italic">X</Emphasis>(3872) is not a molecule

We discuss the scenario where the X(3872) resonance is the \(c\bar c\) = χ_c1(2P) charmonium which “sits on” the D*⁰\({\bar D^0}\) threshold. We explain the shift of the mass of the X(3872) resonance with respect to the prediction of a potential model for the mass of the χ_c1(2P) charmonium by the contribution of the virtual D*\(\bar D\) + c.c. intermediate states into the self energy of the X(3872) resonance. This allows us to estimate the coupling constant of the X(3872) resonance with the D*⁰\({\bar D^0}\) channel, the branching ratio of the X(3872) → D*⁰\({\bar D^0}\) + c.c. decay, and the branching ratio of the X(3872) decay into all non-D*⁰\({\bar D^0}\) + c.c. states. We predict a significant number of unknown decays of X(3872) via two gluon: X(3872) → gluongluon → hadrons. We suggest a physically clear program of experimental researches for verification of our assumption.     

The strong decays of <Emphasis Type="Italic">X</Emphasis>(3940) and <Emphasis Type="Italic">X</Emphasis>(4160)

The new mesons X(3940) and X(4160) have been found by Belle Collaboration in the processes \(e^+e^-\rightarrow J/\psi D^{(*)}{\bar{D}}^{(*)}\). Considering X(3940) and X(4160) as \(\eta _c(3S)\) and \(\eta _c(4S)\) states, the two-body open charm OZI-allowed strong decay of \(\eta _c(3S)\) and \(\eta _c(4S)\) are studied by the improved Bethe–Salpeter method combined with the \(^3P_0\) model. The strong decay width of \(\eta _c(3S)\) is \(\Gamma _{\eta _c(3S)}=(33.5^{+18.4}_{-15.3})\) MeV, which is close to the result of X(3940); therefore, \(\eta _c(3S)\) is a good candidate of X(3940). The strong decay width of \(\eta _c(4S)\) is \(\Gamma _{\eta _c(4S)}=(69.9^{+22.4}_{-21.1})\) MeV, considering the errors of the results, it is close to the lower limit of X(4160). But the ratio of the decay width \(\frac{\Gamma (D{\bar{D}}^*)}{\Gamma (D^*{\bar{D}}^*)}\) of \(\eta _c(4S)\) is larger than the experimental data of X(4160). According to the above analysis, \(\eta _c(4S)\) is not the candidate of X(4160), and more investigations of X(4160) is needed.     

Current status of research on <Emphasis Type="Italic">T</Emphasis> invariance in neutron-nuclear reactions

In this work, the current state of research on T invariance in neutron-nuclear reactions is considered. The promising character of investigations in this field related to possible enhancement of T-invariance violation in compound states of medium and heavy nuclei is underlined. Progress in preparation of experimental tests of T invariance using three-and five-vector correlations in cross sections of interaction of polarized neutrons with aligned nuclei is described in detail. T-invariance tests in reactions of radiative neutron capture and in coherent scattering of polarized neutrons on crystals are also considered.     

Quantum Fisher Information for <Emphasis Type="Italic">s</Emphasis><Emphasis Type="Italic">u</Emphasis>(2) Atomic Coherent States and <Emphasis Type="Italic">s</Emphasis><Emphasis Type="Italic">u</Emphasis>(1, 1) Coherent States

We investigate quantum Fisher information (QFI) for s u(2) atomic coherent states and s u(1, 1) coherent states. In this work, we find that for s u(2) atomic coherent states, the QFI with respect to \(\vartheta ~(\mathcal {F}_{\vartheta })\) is independent of φ, the QFI with respect to \(\varphi (\mathcal {F}_{\varphi })\) is governed by ??. Analogously, for s u(1,1) coherent states, \(\mathcal {F}_{\tau }\) is independent of φ, and \(\mathcal {F}_{\varphi }\) is determined by τ. Particularly, our results show that \(\mathcal {F}_{\varphi }\) is symmetric with respect to ?? = π/2 for s u(2) atomic coherent states. And for s u(1,1) coherent states, \(\mathcal {F}_{\varphi }\) also possesses symmetry with respect to τ = 0.     

Hadroproduction of heavy quarkonia at high energies within the <Emphasis Type="Italic">k</Emphasis><Subscript><Emphasis Type="Italic">T</Emphasis></Subscript>-factorization approach

On the basis of the k _T -factorization approach, heavy-quarkonium \((c\bar c,b\bar b)\) hadroproduction at high energies is considered within nonrelativistic QCD in the leading order in α _s and v. The p _T spectra of various S-and P-wave quarkonium states at the Tevatron collider energies (run I and run II) are fitted, and sets of octet nonperturbative matrix elements are obtained for three different versions of the noncollinear gluon distribution in the proton.     

Test of <Emphasis Type="Italic">T</Emphasis>-invariance in <Emphasis Type="Italic">pd</Emphasis> scattering with double polarization

A formalism of the invariant spin amplitudes of the pd-scattering process in the Madison frame of reference is developed. The condition for T invariance with conservation of P-parity is formulated in terms of these amplitudes, and the relationships between differential spin observables that follow from this condition, are derived. The relative efficiency of the method for testing T-invariance on the basis of these relationships is compared to the method based on recording a null-test signal in an experiment with a polarized proton beam and the deuteron target.     

Influence of an external electric field on the probabilities of two-photon transitions between 2<Emphasis Type="Italic">s</Emphasis>, 2<Emphasis Type="Italic">p</Emphasis> and 1<Emphasis Type="Italic">s</Emphasis> levels for hydrogen and antihydrogen atoms

The probabilities of two-photon decay for hydrogen (H) and antihydrogen (\(\bar H\)) atoms in the presence and absence of an external electric field are analytically calculated. In particular, the probabilities of the E1E2 and E1M1 transitions between the 2p and 1s levels are calculated for the case when emitted photons are characterized by polarization vectors and wavevectors. It is shown that, in an external electric field, the decay probabilities for 2s and 2p levels differ for H and \(\bar H\) atoms because of interference terms linear in field. Coulomb Green’s function method is used for summing over intermediate states.     

<Emphasis Type="Italic">U</Emphasis>(2) and minimal flavour violation in supersymmetry

Rather than sticking to the full U(3)³ approximate symmetry normally invoked in Minimal Flavour Violation, we analyze the consequences on the current flavour data of a suitably broken U(2)³ symmetry acting on the first two generations of quarks and squarks. A definite correlation emerges between the ΔF=2 amplitudes \(\mathcal{M}( K^{0} \to \bar{K}^{0} )\), \(\mathcal{M}( B_{d} \to \bar{B}_{d} )\) and \(\mathcal{M}( B_{s} \to \bar{B}_{s} )\), which can resolve the current tension between \(\mathcal{M}( K^{0} \to \bar{K}^{0} )\) and \(\mathcal{M}( B_{d} \to \bar{B}_{d} )\), while predicting \(\mathcal{M}( B_{s}\to \bar{B}_{s} )\). In particular, the CP violating asymmetry in B _s →ψφ is predicted to be positive S _ψφ =0.12±0.05 and above its Standard Model value (S _ψφ =0.041±0.002). The preferred region for the gluino and the left-handed sbottom masses is below about 1÷1.5 TeV. An existence proof of a dynamical model realizing the U(2)³ picture is outlined.     

Glueballs of the <Emphasis Type="Italic">f</Emphasis><Subscript>0</Subscript> and <Emphasis Type="Italic">f</Emphasis><Subscript>2</Subscript> families,observed in processes with Pseudoscalar mesons

Within the approach based on analyticity and unitarity, the experimental data on the isoscalar S and D waves of the ππ → ππ, K\(\bar K\), ηη, ηη′ processes have been jointly analyzed for studying the status and quantum chromodynamics nature of the f ₀ andf ₂ mesons. Assignment of scalar and tensor mesons to lower nonets is proposed. Two states (f ₀ (1500) and f ₂ (2000)) are interpreted as glueballs.     

Dark Energy Models in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) Theory with Variable Deceleration Parameter

In this communication we have investigated Bianchi type-II dark energy (DE) cosmological models with and without presence of magnetic field in modified f(R, T) gravity theory as proposed by Harko et al. (Phys. Rev. D, 84, 024020, 2011). The exact solution of the field equations is obtained by setting the deceleration parameter q as a time function along with suitable assumption the scale factor \(a(t)= [sinh(\alpha t)]^{\frac {1}{n}}\), α and n are positive constant. We have obtained a class of accelerating and decelerating DE cosmological models for different values of n and α. The present study believes that the mysterious dark energy is the main responsible force for accelerating expansion of the universe. For our constructed models the DE candidates cosmological constant (Λ) and the EoS parameter (ω) both are found to be time varying quantities. The cosmological constant Λ is very large at early time and approaches to a small positive value at late time whereas the EoS parameters is found small negative at present time. Physical and kinematical properties of the models are discussed with the help of pictorial representations of the parameters. We have observed that our constructed models are compatible with recent cosmological observations.     

Scattering of <Emphasis Type="Italic">W</Emphasis> and <Emphasis Type="Italic">Z</Emphasis> bosons at high-energy lepton colliders

We present a new study of quasi-elastic W and Z scattering processes in high-energy \(e^+e^-\) collisions, based on and extrapolating the low-energy effective theory which extends the standard model with a \(125\;\text {GeV}\) Higgs boson. We parameterize deviations in the low-energy range in terms of the dimension-eight operators that arise in the effective theory. Smoothly extending this to higher energy, we study a set of simplified models of new physics in W / Z scattering, (1) a structureless extrapolation of the effective theory, and (2) scalar and tensor resonance multiplets. The high-energy asymptotics of all models is regulated by a universal unitarization procedure. This enables us to provide benchmark scenarios which can be meaningfully evaluated off shell and in exclusive event samples, and to determine the sensitivity of an \(e^+e^-\) collider to the model parameters. We analyze the longitudinal vector-boson scattering modes, where we optimize the cuts for the fiducial cross section for different collider scenarios. Here, we choose energy stages of 1.0, 1.4 and 3 TeV, as motivated by the extendability of the ILC project and the staging scenario of the CLIC project.     

Hypersurface-homogeneous Universe filled with perfect fluid in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) theory of gravity

The exact solutions of the field equations with respect to hypersurface-homogeneous Universe filled with perfect fluid in the framework of f(R, T) theory of gravity (Harko et al, Phys. Rev. D 84, 024020 (2011)) is derived. The physical behaviour of the cosmological model is studied.     

Existence and Uniqueness of SRB Measure on <Emphasis Type="Italic">C</Emphasis><Superscript>1</Superscript> Generic Hyperbolic Attractors

Let M be a smooth Riemannian manifold. We show that for C ¹ generic \({f\in {\rm Diff}^1(M)}\), if f has a hyperbolic attractor Λ _f , then there exists a unique SRB measure supported on Λ _f . Moreover, the SRB measure happens to be the unique equilibrium state of potential function \({\psi_f\in C^0(\Lambda_f)}\) defined by \({\psi_f(x)=-\log|\det(Df|E^u_x)|, x\in \Lambda_f}\), where \({E^u_x}\) is the unstable space of T _x M.