LRS Bianchi Type II Massive String Cosmological Model for Stiff Fluid Distribution with Decaying Vacuum Energy (Λ)

An LRS Bianchi Type II model formed by massive strings with decaying vacuum energy (Λ) for stiff fluid distribution is studied in the context of general relativity. To get the deterministic model, we have assumed that $\frac{\sigma}{\theta} =\mathrm{constant}$ where σ is shear and θ the expansion in the model and decaying vacuum energy (Λ) is proportional to H ² (H is Hubble parameter) as used in Arbab (Gen. Relativ. Gravit. 29:51, 1997). We find that the model represents decelerating and accelerating phases of universe. The decaying vacuum energy (Λ) is proportional to $\frac{1}{\tau^{2}}$ as obtained by Bertolami (Nuovo Cimento B 93:36, 1986) and Hubble parameter is proportional to $\frac{1}{\tau}$ which matches with the observation. The model in general represents anisotropic space-time. However, in special case, it isotropizes. The particle density (ρ _p ) and string tenson (λ) are initially large but decrease due to lapse of time. The model also admits particle horizon and entropy is inversely proportional absolute temperature. Thus the model is in good agreement with present age of universe.     

Structure of some FeII − III hydroxysalt green rusts (carbonate, oxalate, methanoate) from Mössbauer spectroscopy

The abundances of Fe^II and Fe^III environments within green rusts one, GR1s, that intercalate carbonate, oxalate and methanoate (formate) anions are found from Mössbauer spectra for compositions corresponding to [Fe $^{\rm II}_{6}$ Fe $^{\rm III}_{2}$ (OH)₁₆]^2?+??[CO $_{3}^{2-}$ ?5H₂O]^2???, [Fe $^{\rm II}_{4}$ Fe $^{\rm III}_{2}$ (OH)₁₂]^2?+??[CO $_{3}^{2-}$ ?3H₂O]^2???, [Fe $^{\rm II}_{6}$ Fe $^{\rm III}_{2}$ (OH)₁₆]^2?+??[C₂O $_{4}^{2-}$ ?4H₂O]^2??? and [Fe $^{\rm II}_{5}$ Fe $^{\rm III}_{2}$ (OH)₁₄]^2?+??[2HCOO^????3H₂O]^2???. These formulae correspond to orders α, β and γ where cation distances are (2 × a ₀), ( $\surd 3$ × a ₀) or a mixture of both leading to (7 × a ₀), where ratio x = {[Fe^III]/[Fe_total]} = 1/4, 1/3 and 2/7, respectively. Anion distributions within interlayers are also devised and long-range orders determined accordingly.     

On the Stability and Thermodynamics of the Dark Energy Based on Generalized Uncertainty Principle

The new agegraphic Dark Energy (NADE) model (based on generalized uncertainty principle) interacting with Dark Matter (DM) is considered in this study via power-law form of the scale factor a(t). The equation of state (EoS) parameter ω _G is observed to have a phantom-like behaviour. The stability of this model is investigated through the squared speed of sound $v_{s}^{2}$ . It is found that $v_{s}^{2}$ always stays at negative level. This indicates instability of the considered model. Moreover, validity of the generalized second law of thermodynamics has been investigated assuming that the apparent horizon is the enveloping horizon. It has been observed that the generalized second law is valid throughout the evolution of the universe.     

Galaxy cluster number count data constraints on cosmological parameters

We use data on massive galaxy clusters (M _cluster>8×10¹⁴ h ^?1 M _?? within a comoving radius of R _cluster=1.5h ^?1?Mpc) in the redshift range 0.05?z?0.83 to place constraints, simultaneously, on the nonrelativistic matter density parameter ?? _m , on the amplitude of mass fluctuations ?? ₈, on the index n of the power-law spectrum of the density perturbations, and on the Hubble constant H ₀, as well as on the equation-of-state parameters (w ₀,w _a ) of a smooth dark energy component. For the first time, we properly take into account the dependence on redshift and cosmology of the quantities related to cluster physics: the critical density contrast, the growth factor, the mass conversion factor, the virial overdensity, the virial radius and, most importantly, the cluster number count derived from the observational temperature data. We show that, contrary to previous analyses, cluster data alone prefer low values of the amplitude of mass fluctuations, ?? ₈??0.69 (1?? C.L.), and large amounts of nonrelativistic matter, ?? _m ??0.38 (1?? C.L.), in slight tension with the ??CDM concordance cosmological model, though the results are compatible with ??CDM at 2??. In addition, we derive a ?? ₈ normalization relation, $\sigma_{8} \varOmega_{m}^{1/3} = 0.49 \pm 0.06$ (2?? C.L.). Combining cluster data with ?? ₈-independent baryon acoustic oscillation observations, cosmic microwave background data, Hubble constant measurements, Hubble parameter determination from passively evolving red galaxies, and magnitude?Credshift data of type Ia supernovae, we find $\varOmega_{m} = 0.28^{+0.03}_{-0.02}$ and $\sigma_{8} = 0.73^{+0.03}_{-0.03}$ , the former in agreement and the latter being slightly lower than the corresponding values in the concordance cosmological model. We also find $H_{0} = 69.1^{+1.3}_{-1.5}~\mbox {km}/\mbox {s}/\mbox {Mpc}$ , the fit to the data being almost independent on n in the adopted range [0.90,1.05]. Concerning the dark energy equation-of-state parameters, we show that the present data on massive clusters weakly constrain (w ₀,w _a ) around the values corresponding to a cosmological constant, i.e. (w ₀,w _a )=(?1,0). The global analysis gives $w_{0} = -1.14^{+0.14}_{-0.16}$ and $w_{a} = 0.85^{+0.42}_{-0.60}$ (1?? C.L. errors). Very similar results are found in the case of time-evolving dark energy with a constant equation-of-state parameter w=const (the XCDM parametrization). Finally, we show that the impact of bounds on (w ₀,w _a ) is to favor top-down phantom models of evolving dark energy.     

Delocalization and Diffusion Profile for Random Band Matrices

We consider Hermitian and symmetric random band matrices H = (h _xy ) in ${d\,\geqslant\,1}$ d ? 1 dimensions. The matrix entries h _xy , indexed by ${x,y \in (\mathbb{Z}/L\mathbb{Z})^d}$ x , y ∈ ( Z / L Z ) d , are independent, centred random variables with variances ${s_{xy} = \mathbb{E} |h_{xy}|^2}$ s x y = E | h x y | 2 . We assume that s _xy is negligible if |x ? y| exceeds the band width W. In one dimension we prove that the eigenvectors of H are delocalized if ${W\gg L^{4/5}}$ W ? L 4 / 5 . We also show that the magnitude of the matrix entries ${|{G_{xy}}|^2}$ | G x y | 2 of the resolvent ${G=G(z)=(H-z)^{-1}}$ G = G ( z ) = ( H - z ) - 1 is self-averaging and we compute ${\mathbb{E} |{G_{xy}}|^2}$ E | G x y | 2 . We show that, as ${L\to\infty}$ L → ∞ and ${W\gg L^{4/5}}$ W ? L 4 / 5 , the behaviour of ${\mathbb{E} |G_{xy}|^2}$ E | G x y | 2 is governed by a diffusion operator whose diffusion constant we compute. Similar results are obtained in higher dimensions.     

Statistics of directed self-avoiding walks on percolation clusters at the percolation threshold

We here study directed self-avoiding walks on site diluted square lattice at the percolation threshold by two parameter real space renormalization group method. We found \(v_\parallel ^{p_c } = 1.00\) and \(v_ \bot ^{p_c } = 0.4348\) from cell-to-cell transformation method. This \(v_ \bot ^{p_c } \) value is then compared with the modified Alexander-Orbach formula that \(v_ \bot ^{p_c } = {{d_S } \mathord{\left/ {\vphantom {{d_S } {2d_L }}} \right. \kern-0em} {2d_L }}\) whered _s is the fracton dimension andd _L is the spreading dimension of the infinite directed percolation cluster.     

Rules of thumb for theZ line shape

In this paper the theoretical parameters of theZ line shape, such asM _Z andΓ _Z, and the one photon exchange diagram are related to a set of parameters characterizing the experimental line shape. The latter are the peak height σ_max, peak position \(\sqrt {s_{\max } } \) and half peak positions \(\sqrt {s_ \pm } \) . The rules of thumb are accurate within 10 MeV. As a result we obtain approximate formulae which expressM _Z and Γ_Z in the measured \(\sqrt {s_{\max } } \) and \(\sqrt {s_ + } - \sqrt {s_ - } \) .     

Annihilation-type charmless radiative decays of B meson in non-universal Z′ model

We study charmless pure annihilation type radiative B decays within the QCD factorization approach. After adding the vertex corrections to the naive factorization approach, we find that the branching ratios of $\overline{B}^{0}_{d}\to\phi\gamma$ , $\overline{B}^{0}_{s}\to\rho^{0}\gamma$ and $\overline{B}^{0}_{s}\to\omega\gamma$ within the standard model are at the order of $\mathcal{O}(10^{-12})$ , $\mathcal{O}(10^{-10})$ and $\mathcal{O}(10^{-11})$ , respectively. The smallness of these decays in the standard model makes them sensitive probes of flavor physics beyond the standard model. To explore their physics potential, we have estimated the contribution of Z′ boson in the decays. Within the allowed parameter space, the branching ratios of these decay modes can be enhanced remarkably in the non-universal Z′ model: The branching ratios can reach to $\mathcal{O}(10^{-8})$ for $\overline{B}_{s}^{0}\to \rho^{0}(\omega)\gamma$ and $\mathcal{O}(10^{-10})$ for the $\overline{B}_{d}^{0}\to \phi \gamma$ , which are large enough for LHC-b and/or Super B-factories to detect those channels in near future. Moreover, we also predict large CP asymmetries in suitable parameter space. The observation of these modes could in turn help us to constrain the Z′ mass within the model.     

Truncated Connectivities in a Highly Supercritical Anisotropic Percolation Model

We consider an anisotropic bond percolation model on $\mathbb{Z}^{2}$ , with p=(p _h ,p _v )∈[0,1]², p _v >p _h , and declare each horizontal (respectively vertical) edge of $\mathbb{Z}^{2}$ to be open with probability p _h (respectively p _v ), and otherwise closed, independently of all other edges. Let $x=(x_{1},x_{2}) \in\mathbb{Z}^{2}$ with 0<x ₁<x ₂, and $x'=(x_{2},x_{1})\in\mathbb{Z}^{2}$ . It is natural to ask how the two point connectivity function $\mathbb{P}_{\mathbf{p}}(\{0\leftrightarrow x\})$ behaves, and whether anisotropy in percolation probabilities implies the strict inequality $\mathbb{P}_{\mathbf{p}}(\{0\leftrightarrow x\})>\mathbb{P}_{\mathbf {p}}(\{0\leftrightarrow x'\})$ . In this note we give an affirmative answer in the highly supercritical regime.     

Alternative technique for Standard Model estimation of the rare kaon decay branchings \left. {BR(K \to \pi \nu \bar \nu )} \right|_{SM}

We estimate $BR(K \to \pi \nu \bar \nu )$ in the context of the Standard Model by fitting for λ _t≡V _tdV _ts ^* of the “kaon unitarity triangle” relation. To find the vertex of this triangle, we fit data from |? _K|, the CP-violating parameter describing K mixing, and a _ψ,K , the CP-violating asymmetry in B _d ⁰ → J/ψK ⁰ decays, and obtain the values $\left. {BR(K \to \pi \nu \bar \nu )} \right|_{SM} = (7.07 \pm 1.03) \times 10^{ - 11} $ and $\left. {BR(K_L^0 \to \pi ^0 \nu \bar \nu )} \right|_{SM} = (2.60 \pm 0.52) \times 10^{ - 11} $ . Our estimate is independent of the CKM matrix element V _cb and of the ratio of B-mixing frequencies ${{\Delta m_{B_s } } \mathord{\left/ {\vphantom {{\Delta m_{B_s } } {\Delta m_{B_d } }}} \right. \kern-0em} {\Delta m_{B_d } }}$ . We also use the constraint estimation of λ _t with additional data from $\Delta m_{B_d } $ and |V _ub|. This combined analysis slightly increases the precision of the rate estimation of $K^ + \to \pi ^ + \nu \bar \nu $ and $K_L^0 \to \pi ^0 \nu \bar \nu $ (by ?10 and ?20%, respectively). The measured value of $BR(K^ + \to \pi ^ + \nu \bar \nu )$ can be compared both to this estimate and to predictions made from ${{\Delta m_{B_s } } \mathord{\left/ {\vphantom {{\Delta m_{B_s } } {\Delta m_{B_d } }}} \right. \kern-0em} {\Delta m_{B_d } }}$ .     

On the Second Mixed Moment of the Characteristic Polynomials of 1D Band Matrices

We consider the asymptotic behavior of the second mixed moment of the characteristic polynomials of 1D Gaussian band matrices, i.e., of the Hermitian N × N matrices H _N with independent Gaussian entries such that 〈H _ij H _lk 〉 = δ _ik δ _jl J _ij , where ${J=(-W^2\triangle+1)^{-1}}$ . Assuming that ${W^2=N^{1+\theta}}$ , ${0 < \theta \leq 1}$ , we show that the moment’s asymptotic behavior (as ${N\to\infty}$ ) in the bulk of the spectrum coincides with that for the Gaussian Unitary Ensemble.     

Dynamical Localization for the Random Dimer Schrödinger Operator

We study the one-dimensional random dimer model, with Hamiltonian H _ω =Δ+V _ω , where for all x∈ $\mathbb{Z}$ , V _ω(2x)=V _ω(2x+1) and where the V _ω(2x) are i.i.d. Bernoulli random variables taking the values ±V, V>0. We show that, for all values of Vand with probability one in ω, the spectrum of His pure point. If V≤1 and V≠1/ $\sqrt 2$ , the Lyapunov exponent vanishes only at the two critical energies given by E=±V. For the particular value V=1/ $\sqrt 2$ , respectively, V= $\sqrt 2$ , we show the existence of new additional critical energies at E=±3/ $\sqrt 2$ , respectively, E=0. On any compact interval Inot containing the critical energies, the eigenfunctions are then shown to be semi-uniformly exponentially localized, and this implies dynamical localization: for all q>0 and for all ψ∈ $\ell$ ²( $\mathbb{Z}$ ) with sufficiently rapid decrease $${\mathop {\sup }\limits_t} r_{\psi ,I}^{\left( q \right)} {\kern 1pt} \left( t \right): = {\mathop {\sup }\limits_t} \left\langle {P_I \left( {H\omega } \right)\psi _t ,\left| X \right|^q P_I \left( {H\omega } \right)\psi _t } \right\rangle < \infty $$ Here $\psi _t = e^{- iH_{\omega ^t}} \psi$ , and P _I(H _ω) is the spectral projector of H _ωonto the interval I. In particular, if V>1 and V≠ $\sqrt 2$ , these results hold on the entire spectrum [so that one can take I=σ(H _ω)].     

Exotic Mesons with Hidden Bottom Near Thresholds

We discuss exotic meson spectroscopy near open bottom thresholds. Assuming the exotic mesons as ${B^{(\ast)}\bar{B}^{(\ast)}}$ molecular states, we study the interaction among two heavy mesons in terms of the one boson exchange potential model. It is shown that masses of Z _b (10610) and Z _b (10650) are reproduced as ${B^{(\ast)}\bar{B}^{(\ast)}}$ bound and resonance states. Besides, we also show that ${B^{(\ast)}\bar{B}^{(\ast)}}$ molecular states having various exotic quantum numbers can exist around the thresholds. By contrast, there are no ${D^{(\ast)}\bar{D}^{(\ast)}}$ molecular states having exotic quantum numbers.     

A remark on the definition of superselection rules in terms of unbounded operators

The mathematical definition of superselection rules in the case when observables are described by unbounded operators in a fixed Hilbert space (for instance, in the frame of Wightman's axioms) is examined. The additional condition \(P_{H_q } D \subset D\) (whereD is the common domain of definition of the operators,H _q is theqth sector, and \(P_{H_q } \) is the projection onH _q ) is found to be sufficient in order to preserve-as in the case of bounded observables—the one-to-one correspondence between reducing subspacesH _q and projections \(P_{H_q } \) from the commutantA′ of the algebraA of observables. This additional condition is equivalent to the physical requirement that every physical vector state can be uniquely represented as a linear combination of physical states, each belonging to some sector.     

35Cl NQR spectra of group 1 and silver dichloromethanesulfonates

The dichloromethanesulfonates of silver and other +1-charged cations, M ^?+?(Cl₂CHSO $_{3}^{-})$ (M = Ag, Tl, Li, Na, K, Rb, Cs) were synthesized and studied by ³⁵Cl NQR. Dichloromethanesulfonic acid was prepared by the methanolysis of dichloromethanesulfonyl chloride, and was then neutralized with the carbonates of the +1-charged cations to produce the corresponding dichloromethanesulfonate salt. This NQR study completed the investigation of the chloroacetates and chloromethanesulfonates of silver, Ag^?+?(Cl _x CH_3???x SO $_{3}^{-})$ and Ag^?+?(Cl _x CH_3???x CO $_{2}^{-})$ , and suggests (1) that the ability of organochlorine atoms to coordinate to silver decreases as the number of electron-withdrawing groups (Cl, SO $_{3}^{-}$ , CO $_{2}^{-})$ attached to the carbon atom increases; (2) that the unusually large NQR spectral width found among M ^?+?(Cl₂CHCO $_{2}^{-})$ salts is not present among M ^?+?(Cl₂CHSO $_{3}^{-})$ salts, and therefore is not generally characteristic of the dichloromethyl group in salts.     

Analysis of the {1\over2}^{\pm} flavor antitriplet heavy baryon states with QCD sum rules

In this article, we study the masses and pole residues of the ${1\over2}^{\pm}$ flavor antitriplet heavy baryon states ( $\varLambda _{c}^{+}$ , $\varXi _{c}^{+},\varXi _{c}^{0})$ and ( $\varLambda _{b}^{0}$ , $\varXi _{b}^{0},\varXi _{b}^{-})$ by subtracting the contributions from the corresponding ${1\over2}^{\mp}$ heavy baryon states with the QCD sum rules, and observe that the masses are in good agreement with the experimental data and make reasonable predictions for the unobserved ${1\over2}^{-}$ bottom baryon states. Once reasonable values of the pole residues λ _Λ and λ _Ξ are obtained, we can take them as basic parameters to study the relevant hadronic processes with the QCD sum rules.     

K S 0 , Λ and ≡ production at intermediate to high pT from Au+Au collisions at \sqrt {s_{NN} } = 39, 11.5 and 7.7 GeV

We report on the p _T dependence of nuclear modification factors (R _CP) for K _S ⁰ , ??, ?? and the $\bar NK_S^0 $ ratios at mid-rapidity from Au+Au collisions at $\sqrt {s_{NN} } $ = 39, 11.5 and 7.7 GeV. At $\sqrt {s_{NN} } $ = 39 GeV, the R _CP data show a baryon/meson separation at intermediate p _T and a suppression for K _S ⁰ for p _T up to 4.5 GeV/c; the $\bar \Lambda K_S^0 $ shows baryon enhancement in the most central collisions. However, at $\sqrt {s_{NN} } $ = 11.5 and 7.7 GeV, R _CP shows less baryon/meson separation and $\bar NK_S^0 $ shows almost no baryon enhancement. These observations indicate that the matter created in Au+Au collisions at $\sqrt {s_{NN} } $ = 11.5 or 7.7 GeV might be distinct from that created at $\sqrt {s_{NN} } $ = 39 GeV.     

Radiative and semileptonic B decays involving higher K-resonances in the final states

We study the radiative and semileptonic B decays involving a spin-J resonant $K_{J}^{(*)}$ with parity (?1) ^J for $K_{J}^{*}$ and (?1) ^J+1 for K _J in the final state. Using large energy effective theory (LEET) techniques, we formulate $B\to K_{J}^{(*)}$ transition form factors in the large recoil region in terms of two independent LEET functions $\zeta_{\perp}^{K_{J}^{(*)}}$ and $\zeta_{\parallel}^{K_{J}^{(*)}}$ , the values of which at zero momentum transfer are estimated in the BSW model. According to the QCD counting rules, $\zeta_{\perp,\parallel}^{K_{J}^{(*)}}$ exhibit a dipole dependence in q ². We predict the decay rates for $B\to K_{J}^{(*)}\gamma$ , $B\to K_{J}^{(*)}\ell^{+}\ell^{-}$ and $B\to K_{J}^{(*)}\nu \bar{\nu}$ . The branching fractions for these decays with higher K-resonances in the final state are suppressed due to the smaller phase spaces and the smaller values of $\zeta^{K_{J}^{(*)}}_{\perp,\parallel}$ . Furthermore, if the spin of $K_{J}^{(*)}$ becomes larger, the branching fractions will be further suppressed due to the smaller Clebsch–Gordan coefficients defined by the polarization tensors of the $K_{J}^{(*)}$ . We also calculate the forward–backward asymmetry of the $B\to K_{J}^{(*)}\ell^{+}\ell^{-}$ decay, for which the zero is highly insensitive to the K-resonances in the LEET parametrization.     

Study of f 0(980) and f 0(1500) from B s →f 0(980)π,f 0(1500)π decays

In this paper, we analyze the scalar mesons f ₀(980) and f ₀(1500) from the decays $\bar{B}^{0}_{s}\to f_{0}(980)\pi^{0},\allowbreak f_{0}(1500)\pi^{0}$ within Perturbative QCD approach. From the leading-order calculations, we find that (a) in the allowed mixing angle ranges, the branching ratio of $\bar{B}^{0}_{s}\to f_{0}(980)\pi^{0}$ is about (1.0～1.6)×10^?7, which is smaller than that of $\bar{B}^{0}_{s}\to f_{0}(980)K^{0}$ (the difference is a few times even one order); (b) the decay $\bar{B}^{0}_{s}\to f_{0}(1500)\pi^{0}$ is better to distinguish between the lowest lying state or the first excited state for f ₀(1500), because the branching ratios for two scenarios have about one-order difference in most of the mixing angle ranges; and (c) the direct CP asymmetries of $\bar{B}^{0}_{s}\to f_{0}(1500)\pi^{0}$ for two scenarios also exists great difference. In scenario II, the variation range of the value ${\mathcal{A}}^{\mathrm{dir}}_{CP}(\bar{B}^{0}_{s}\to f_{0}(1500)\pi^{0})$ according to the mixing angle in scenario II is very small, except for the values for mixing angles near 90° or 270°, while the variation range of ${\mathcal{A}}^{\mathrm{dir}}_{CP}(\bar{B}^{0}_{s}\to f_{0}(1500)\pi^{0})$ in scenario I is very large. Compared with the future data for the decay $\bar{B}^{0}_{s}\to f_{0}(1500)\pi^{0}$ , it is easy to determine the nature of the scalar meson f ₀(1500).