<Emphasis Type="Italic">V</Emphasis>-<Emphasis Type="Italic">A</Emphasis> sum rules with <Emphasis Type="Italic">D</Emphasis> = 10 operators

The difference of vector and axial-vector charged current correlators is analyzed by means of QCD sum rules. The contribution of 10-dimensional 4-quark condensates is calculated and its value is estimated within the framework of the factorization hypothesis. It is compared to the result obtained from an operator fit of Borel sum rules in the complex q ²-plane, calculated from experimental data on hadronic -decays. This fit gives accurate values of the light quark condensate and the quark-gluon mixed condensate. The size of the high-order operators and the convergence of the operator series are discussed.Received: 10 May 2004, Revised: 7 September 2004, Published online: 18 November 2004     

Complete one-loop calculation of the <Emphasis Type="Italic">T</Emphasis>-violating <Emphasis Type="Italic">D</Emphasis>-parameter in neutron decay in the MSSM

We investigate the violation of time reversal invariance in the decay of the free neutron in the framework of the minimal supersymmetric standard model (MSSM). The coefficient of the triple product of the neutron spin and the momenta of electron and neutrino, the so-called D parameter, is computed at one-loop order including all diagrams. We find that D is mainly sensitive to the trilinear A coupling in the squark sector and to the phase of the coefficient which mixes the two Higgs superfields. The maximal MSSM contribution using parameters still allowed by experiment is however at , while QED final state interactions give a value of . Explicit expressions for all relevant diagrams are given in an appendix.Received: 3 March 2003, Revised: 16 May 2003, Published online: 3 July 2003     

Spherical Symmetric Perfect Fluid Collapse in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) Gravity

This paper contains the study of spherically symmetric perfect fluid collapse in the frame work of f(R, T) modified theory of gravity. We proceed our work by considering the non-static spherically symmetric background in the interior and static spherically symmetric background in the exterior regions of the star. The junction conditions between exterior and interior regions are presented by matching the exterior and interior regions. The field equations are solved by taking the assumptions that the Ricci scalar as well as the trace of energy-momentum tensor are to be constant, for a particular f(R, T) model. By inserting the solution of the field equations in junction conditions, we evaluate the gravitational mass of the collapsing system. Also, we discuss the apparent horizons and their time formation for different possible cases. It is concluded that the term f(R ₀, T ₀) behaves as a source of repulsive force and that’s why it slowdowns the collapse of the matter.     

Accelerating universe from <Emphasis Type="Italic">F</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) gravity

It is shown that the acceleration of the universe can be understood by considering a F(T) gravity models. For these F(T) gravity models, a variant of the accelerating cosmology reconstruction program is developed. Some explicit examples of F(T) are reconstructed from the background FRW expansion history.     

New types of <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) gravity

Recently f(T) theories based on modifications of teleparallel gravity, where torsion is the geometric object describing gravity instead of curvature, have been proposed to explain the present cosmic accelerating expansion. The field equations are always second order, remarkably simpler than f(R) theories. In analogy to the f(R) theory, we consider here three types of f(T) gravity, and find that all of them can give rise to cosmic acceleration with interesting features, respectively.     

Multiple two-variable <Emphasis Type="Italic">p</Emphasis>-adic <Emphasis Type="Italic">q-L</Emphasis>-function and its behavior at <Emphasis Type="Italic">s</Emphasis> = 0

The objective of this paper is to construct a multiple p-adic q-L-function of two variables which interpolates multiple generalized q-Bernoulli polynomials. By using this function, we solve a question of Kim and Cho. We also define a multiple partial q-zeta function which is related to the multiple q-L-function of two variables. Finally, we give a finite-sum representation of the multiple p-adic q-L-function of two variables and prove a multiple q-extension of the generalized formula of Diamond and Ferrero-Greenberg.     

Reconstruction of some cosmological models in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>,<Emphasis Type="Italic">T</Emphasis>) cosmology

In this paper, we reconstruct cosmological models in the framework of f(R,T) gravity, where R is the Ricci scalar and T is the trace of the stress-energy tensor. We show that the dust fluid reproduces ΛCDM, phantom–non-phantom era and phantom cosmology. Further, we reconstruct different cosmological models, including the Chaplygin gas, and scalar field with some specific forms of f(R,T). Our numerical simulation for the Hubble parameter shows good agreement with the BAO observational data for low redshifts, z<2.     

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.     

Static anisotropic solutions in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) theory

In previous work, we undertook to study static and anisotropic content in f(T) theory and obtained new spherically symmetric solutions considering a constant torsion and some particular conditions for the pressure. In this paper, still in the framework of f(T) theory, new spherically symmetric solutions are obtained, first considering the general case of an isotropic fluid and later the anisotropic content case in which the generalized conditions for the matter content are considered such that the energy density, the radial and tangential pressures depend on the algebraic f(T) and its derivative f _T (T). Moreover, we obtain the algebraic function f(T) through the reconstruction method for two cases and also study a polytropic model for the stellar structure.     

New static solutions in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) theory

We consider the equations of motion of an anisotropic space-time in f(T) theory, where T is the torsion. New spherically symmetric solutions of black holes and wormholes are obtained with a constant torsion and for the cases for which the radial pressure is proportional to a real constant, to some algebraic functions f(T) and their derivatives f _T (T), or vanishes identically.     

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.     

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.     

Friedmann Cosmology with Matter Creation in Modified <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) Gravity

The theoretical and observational consequences of thermodynamics of open systems which allow matter creation, are investigated in modified f(R, T) (R is the Ricci scalar and T is the trace of energy-momentum tensor) theory of gravity within the framework of a flat Friedmann-Robertson-Walker line element. The simplest model f(R, T)=R+2f(T) with “gamma-law” equation of state p = (γ?1)ρ is assumed to obtain the exact solution. A power-law expansion model is proposed by considering the natural phenomenological particle creation rate ψ = 3β n H, where β is a pure number of the order of unity, n the particle number density and H is the Hubble parameter. A Big Rip singularity is observed for γ<0 describing phantom cosmology. The accelerated expansion of the Universe is driven by the particle creation. The density parameter shows the negative curvature of the Universe due to particle creation. The entropy increases with the evolution of the Universe. Some kinematics tests such as lookback time, luminosity distance, proper distance, angular diameter versus redshift are discussed in detail to observe the role of particle creation in early and late time evolution of the Universe.     

<Emphasis Type="Italic">P</Emphasis>-and <Emphasis Type="Italic">T</Emphasis>-violating Schiff moment of the mercury nucleus

The Schiff moment of the ¹⁹⁹Hg nucleus was calculated using finite-range P-and T-violating weak nucleon-nucleon interaction. Effects of the core polarization were considered in the framework of RPA with effective residual forces.     

Summary on high <Emphasis Type="Italic">p</Emphasis><Subscript><Emphasis Type="Italic">T</Emphasis></Subscript> probes

Results on high-p _T probes shown at the Hard Probes 2008 Conference are summarized, with an appreciation of the improvements in precision of the measurements and experimental techniques since the beginning of RHIC operation. Particular attention is given to the latest measurements of the nuclear modification factor of identified particles, photon-hadron correlation measurements, and full jet reconstruction.     

<Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) models with phantom divide line crossing

In this paper, we propose two new models in f(T) gravity to realize the crossing of the phantom divide line for the effective equation of state, and we then study the observational constraints on the model parameters. The best fit results suggest that the observations favor a crossing of the phantom divide line.     

High-pressure magnetic properties and <Emphasis Type="Italic">P-T</Emphasis> phase diagram of iron borate

The high-pressure magnetic states of iron borate ⁵⁷FeBO₃ single-crystal and powder samples have been investigated in diamond anvil cells by nuclear forward scattering (NFS) of synchrotron radiation at different temperatures. In the low-pressure (0 < P < 46 GPa) antiferromagnetic phase, an increase of the Neél temperature from 350 to 595 K induced by pressure was found. At pressures 46–49 GPa, a transition from the antiferromagnetic to a new magnetic state with a weak magnetic moment (magnetic collapse) was discovered. It is attributed to the electronic transition in Fe³⁺ ions from the high-spin 3d⁵ (S = 5/2, ⁶A_1g) to the low-spin (S = 1/2, ²T_2g) state (spin crossover) due to the insulator-semiconductor-type transition with extensive suppression of strong d-d electron correlations. At low temperatures, NFS spectra of the high-pressure phase indicate magnetic correlations in the low-spin system with a magnetic ordering temperature of about 50 K. A tentative magnetic P-T phase diagram of FeBO₃ is proposed. An important feature of this diagram is the presence of two triple points where magnetic and paramagnetic phases of the high-spin and low-spin states coexist.     

Relationship between <Emphasis Type="Italic">T</Emphasis>-invariance and formation mechanisms for <Emphasis Type="Italic">T</Emphasis>-odd and <Emphasis Type="Italic">T</Emphasis>-even asymmetries in the angular distributions of fission fragments of oriented nuclei

The T-invariance condition was analyzed for the amplitude T _b,a of multiparticle multistep elastic or inelastic a → b nuclear reactions. This condition leads to the equality of the amplitude T _b,a to the amplitude \({\tilde T_{\bar a,\bar b}}\) of \(\bar b \to \bar a\) time-reversed reaction, for which the reaction operator \(\tilde T\) coincides with the inverse-reaction (b → a) operator. It is shown that, in the case where the original, inverse, and time-reversed reactions are governed by a common T-invariant mechanism, the coefficients D of asymmetries appearing in the differential cross sections for these reactions can be represented in the form of a unified scalar (pseudoscalar) function of arguments equal to the momentum and spin vectors of particles of the initial and final channels of the reactions under analysis. It is also shown that the use of the T-invariance condition for the coefficients D of asymmetries in the differential cross section for the original nuclear reaction that are different in P- and T-parity makes it possible to separate mechanisms leading to nonzero coefficients D for a number of the asymmetries under analysis from the remaining mechanisms leading to zero coefficients D of these asymmetries. It is proven that there exist such asymmetries in the differential cross section for the original reaction whose coefficients vanish for all possible T-invariant mechanisms of their appearance, so that, upon proving experimentally the appearance of nonzero coefficients of these asymmetries in the differential cross section for the original reaction, this fact can be used to assess features of T-noninvariant interactions in nuclear systems.