Production of $ \Delta$(1232) -resonances on oxygen nuclei in 16O + p collisions at a momentum of 3.25 GeV/c per nucleon

The production of D⁺⁺ \Delta^{{++}}_{} and D⁰ \Delta^{0}_{} resonances on oxygen nuclei in ¹⁶O + p interactions at 3.25A GeV/c was investigated with 4p \pi acceptance. The masses and widths of the resonances were obtained from an analysis of the experimental and background invariant-mass distributions of pp^± \pi^{{\pm}}_{} pairs. The fractions of charged pions coming from D⁺⁺ \Delta^{{++}}_{} and D⁰ \Delta^{0}_{} decay were estimated. The momentum, kinetic energy, and emission angle distributions of D⁺⁺ \Delta^{{++}}_{} and D⁰ \Delta^{0}_{} resonances were reconstructed in the oxygen nucleus rest frame. The slope parameters, T₀ , of the reconstructed spectra of invariant cross-sections of D⁺⁺ \Delta^{{++}}_{} and D⁰ \Delta^{0}_{} resonances, produced on oxygen nuclei in ¹⁶O + p interactions at 3.25A GeV/c , were determined.     

Stability of One-Electron Molecules in the Brown–Ravenhall Model

In appropriate units, the Brown-Ravenhall Hamiltonian for a system of 1 electron relativistic molecules with K fixed nuclei having charge and position Zk, R_k, k=1,2, ?,Kk=1,2, \ldots,K, is of the form \bB_1,K = L₊ ( D₀ + aV_c) L₊ \bB_{1,K}= \Lambda_+ \bigl( D_0 + \alpha V_c\bigr) \Lambda_+ , where v₊ is the projection onto the positive spectral subspace of the free Dirac operator D₀ and V_c = - ?_k=1^K \fracaZ_k\lmod \bx-R_k \rmod + ?_{k < l,  k,l=1}^K \fracaZ_k Z_l\lmod R_k-R_l \rmod V_c= - \sum_{k=1}^K \frac{\alpha Z_k}{\lmod \bx-R_k \rmod} + \sum_{kZ_k ￡ aZ_c = \frac2p/2 + 2/ p\alpha Z_k \leq \alpha Z_c = \frac{2}{\pi /2 + 2/ \pi}, k=1,2, ?,Kk=1,2, \ldots,K, and a ￡ \frac2 p(p²+4)(2+?{1+ p/2})\alpha \leq \frac{2 \pi}{(\pi^2+4)(2+\sqrt{1+ \pi /2})}, \ \bB_1,K 3 \operatornameconst \cdotp K\bB_{1,K} \geq \operatorname{const} \cdotp K.     

Analysis of the <Emphasis Type="Italic">Y</Emphasis>(4140) with QCD sum rules

In this article, we assume that there exists a scalar D_s^*[`(D)]<sub>s</sub><sup>*</sup>D_{s}^{\ast}{\bar{D}}_{s}^{\ast} molecular state in the J/ψ φ invariant mass distribution, and we study its mass using the QCD sum rules. The predictions depend heavily on the two criteria (pole dominance and convergence of the operator product expansion) of the QCD sum rules. The value of the mass is about M<sub>Ds<sup>*</sup>[`(D)]s^*</sub>=(4.43±0.16)M_{D_{s}^{\ast}{\bar{D}}_{s}^{\ast}}=(4.43\pm0.16)  GeV, which is inconsistent with the experimental data. The D_s^*[`(D)]_s^*D_{s}^{\ast}{\bar{D}}_{s}^{\ast} is probably a virtual state and is not related to the meson Y(4140). Another possibility, such as a hybrid charmonium, is not excluded.     

Defect structures in nematic liquid crystals around charged particles

We numerically study the orientation deformations in nematic liquid crystals around charged particles. We set up a Ginzburg-Landau theory with inhomogeneous electric field. If the dielectric anisotropy e₁ \varepsilon_{1}^{} is positive, Saturn-ring defects are formed around the particles. For e₁ \varepsilon_{1}^{} < 0 , novel “ansa” defects appear, which are disclination lines with their ends on the particle surface. We find unique defect structures around two charged particles. To lower the free energy, oppositely charged particle pairs tend to be aligned in the parallel direction for e₁ \varepsilon_{1}^{} > 0 and in the perpendicular plane for e₁ \varepsilon_{1}^{} < 0 with respect to the background director. For identically charged pairs the preferred directions for e₁ \varepsilon_{1}^{} > 0 and e₁ \varepsilon_{1}^{} < 0 are exchanged. We also examine competition between the charge-induced anchoring and the short-range anchoring. If the short-range anchoring is sufficiently strong, it can be effective in the vicinity of the surface, while the director orientation is governed by the long-range electrostatic interaction far from the surface.     

Analysis of the <Emphasis Type="Italic">Y</Emphasis>(4140) and related molecular states with QCD sum rules

In this article, we assume that there exist scalar D^*[`(D)]<sup>*</sup>{D}^{\ast}{\bar {D}}^{\ast}, D<sub>s</sub><sup>*</sup>[`(D)]_s^*{D}_{s}^{\ast}{\bar{D}}_{s}^{\ast}, B^*[`(B)]<sup>*</sup>{B}^{\ast}{\bar {B}}^{\ast} and B<sub>s</sub><sup>*</sup>[`(B)]_s^*{B}_{s}^{\ast}{\bar{B}}_{s}^{\ast} molecular states, and study their masses using the QCD sum rules. The numerical results indicate that the masses are about (250–500) MeV above the corresponding D ^*–[`(D)]<sup>*</sup>{\bar{D}}^{\ast}, D <sub>s</sub> <sup>*</sup>–[`(D)]_s^*{\bar {D}}_{s}^{\ast}, B ^*–[`(B)]<sup>*</sup>{\bar{B}}^{\ast} and B <sub>s</sub> <sup>*</sup>–[`(B)]_s^*{\bar {B}}_{s}^{\ast} thresholds, the Y(4140) is unlikely a scalar D_s^*[`(D)]<sub>s</sub><sup>*</sup>{D}_{s}^{\ast}{\bar{D}}_{s}^{\ast} molecular state. The scalar D<sup>*</sup>[`(D)]^*D^{\ast}{\bar{D}}^{\ast}, D_s^*[`(D)]<sub>s</sub><sup>*</sup>D_{s}^{\ast}{\bar{D}}_{s}^{\ast}, B<sup>*</sup>[`(B)]^*B^{\ast}{\bar{B}}^{\ast} and B_s^*[`(B)]<sub>s</sub><sup>*</sup>B_{s}^{\ast}{\bar{B}}_{s}^{\ast} molecular states maybe not exist, while the scalar D￠<sup>*</sup>[`(D)]^￠*{D'}^{\ast}{\bar{D}}^{\prime\ast}, D_s^￠*[`(D)]<sub>s</sub><sup>￠*</sup>{D}_{s}^{\prime\ast}{\bar{D}}_{s}^{\prime\ast}, B<sup>￠*</sup>[`(B)]^￠*{B}^{\prime\ast}{\bar{B}}^{\prime\ast} and B_s^￠*[`(B)]_s^￠*{B}_{s}^{\prime\ast}{\bar{B}}_{s}^{\prime\ast} molecular states maybe exist.     

From crystal to amorphous: A novel route to unjamming in soft disk packings

Numerical studies on the unjamming packing fraction of bi- and polydisperse disk packings, which are generated through compression of a monodisperse crystal, are presented. In bidisperse systems, a fraction f ₊ = 0.400 up to 0.800 of the total number of particles has their radii increased by D \Delta R , while the rest has their radii decreased by the same amount. Polydisperse packings are prepared by changing all particle radii according to a uniform distribution in the range [- D \Delta R,D \Delta R] . The results indicate that the critical packing fraction is never larger than the value for the initial monodisperse crystal, f₀ \phi_{0}^{} = p \pi/?{12} \sqrt{{12}} , and that the lowest value achieved is approximately the one for random close packing. These results are seen as a consequence of the interplay between the increase in small-small particle contacts and the local crystalline order provided by the large-large particle contacts.     

Radiative corrections to neutral pion-pair production

We calculate the one-photon loop radiative corrections to the neutral pion-pair photoproduction process p^-g ?p^-p⁰p⁰\pi^-\gamma \ensuremath \rightarrow\pi^-\pi^0\pi^0 . At leading order this reaction is governed by the chiral pion-pion interaction. Since the chiral p⁺ \pi^{+}_{} p^- \pi^{-}_{} ? \rightarrow p⁰ \pi^{0}_{} p⁰ \pi^{0}_{} contact vertex depends only on the final-state invariant mass it factors out of all photon loop diagrams. We give analytical expressions for the multiplicative correction factor R ~ a/2p\ensuremath R\sim \alpha/2\pi arising from eight classes of contributing one-photon loop diagrams. An electromagnetic counterterm has to be included in order to cancel the ultraviolet divergences generated by the photon loops. Infrared finiteness of the virtual radiative corrections is achieved (in the standard way) by including soft photon radiation below an energy cut-off l \lambda . The radiative corrections to the total cross-section vary between +2% and -2% for center-of-mass energies from threshold up to 7m_p\ensuremath 7m_{\pi} . We study also the radiative corrections to the p⁰p⁰\ensuremath \pi^0\pi^0 mass spectrum.     

The mixing of scalar mesons and the baryon-baryon interaction

By introducing the mixing of scalar mesons in the chiral SU(3) quark model, we dynamically investigate the baryon-baryon interaction. The hyperon-nucleon and nucleon-nucleon interactions are studied by solving the resonating group method (RGM) equation in a coupled-channel calculation. In our present work, the experimental lightest pseudoscalar p \pi, K,h \eta,h^￠ \eta^{{\prime}}_{} mesons correspond exactly to the chiral nonet pseudoscalar fields p \pi, K,h \eta,h^￠ \eta^{{\prime}}_{} in the chiral SU(3) quark model. The h \eta,h^￠ \eta^{{\prime}}_{} mesons are considered as the mixing of singlet and octet mesons, and the mixing angle q_ps \theta_{{ps}}^{} is taken to be -23^° . For scalar nonet mesons, we suppose that there exists a correspondence between the experimental lightest scalar f ₀(600) , k \kappa , a ₀(980) , f ₀(980) mesons and the theoretical scalar nonet s \sigma , k \kappa , s^￠ \sigma^{{\prime}}_{} , e \epsilon fields in the chiral SU(3) quark model. For scalar mesons, we consider two different mixing cases: one is the ideal mixing and another is the q_s \theta_{s}^{} = 19^° mixing. The masses of the s^￠ \sigma^{{\prime}}_{} and e \epsilon mesons are taken to be 980MeV, which are just the masses of the experimental a ₀(980) , f ₀(980) mesons. The mass of the s \sigma meson is an adjustable parameter and is decided by fitting the binding energy of the deuteron, the masses of 560MeV and 644MeV are obtained for the ideal mixing and the q_s \theta_{s}^{} = 19^° mixing, respectively. We find that, in order to reasonably describe the YN interactions, the mass of the k \kappa meson is near 780MeV for the ideal mixing. However, we must enhance the mass of the k \kappa meson for the q_s \theta_{s}^{} = 19^° mixing, the 1050MeV is favorably used in the present work. The experimental s \sigma and k \kappa scalar mesons are very strange, both have larger widths. Hence, no matter what kind of mixing is considered, all the masses of scalar mesons we used in the present work seem to be consistent with the present PDG information.     

Temperature dependence of yields from multi-foil SPES target

The temperature dependence of neutron-rich isotope yields was studied within the framework of the HRIBF-SPES Radioactive Ion Beams (RIB) project. On-line release measurements of fission fragments from a uranium carbide target at $\ensuremath 1600 {}^{\circ}\mathrm{C}$\ensuremath 1600 {}^{\circ}\mathrm{C} , 1800 ^°C\ensuremath 1800 {}^{\circ}\mathrm{C} and 2000 ^°C\ensuremath 2000 {}^{\circ}\mathrm{C} were performed at ORNL (USA). The fission reactions were induced by a 40MeV proton beam accelerated into a uranium carbide target coupled to a plasma ion source. The experiments allowed for tests of performance of the SPES multi-foil target prototype loaded with seven UC₂/graphite discs (ratio C/U = 4 with density about 4g/cm³.     

Production of the P-wave excited Bc-states through the Z0 boson decays

In Deng et al. (Eur. Phys. J. C 70:113, 2010), we have dealt with the production of the two color-singlet S-wave (c[`(b)])(c\bar{b})-quarkonium states B<sub>c</sub>(|(c[`(b)])₁[¹S₀]?)B_{c}(|(c\bar {b})_{\mathbf{1}}[^{1}S_{0}]\rangle) and B^*_c(|(c[`(b)])<sub>1</sub>[<sup>3</sup>S<sub>1</sub>]?)B^{*}_{c}(|(c\bar{b})_{\mathbf{1}}[^{3}S_{1}]\rangle) through the Z <sup>0</sup> boson decays. As an important sequential work, we make a further discussion on the production of the more complicated P-wave excited (c[`(b)])(c\bar{b})-quarkonium states, i.e. |(c[`(b)])<sub>1</sub>[<sup>1</sup>P<sub>1</sub>]?|(c\bar{b})_{\mathbf{1}}[^{1}P_{1}]\rangle and |(c[`(b)])₁[³P_J]?|(c\bar{b})_{\mathbf{1}}[^{3}P_{J}]\rangle (with J=(1,2,3)). More over, we also calculate the channel with the two color-octet quarkonium states |(c[`(b)])<sub>8</sub>[<sup>1</sup>S<sub>0</sub>]g?|(c\bar{b})_{\mathbf{8}}[^{1}S_{0}]g\rangle and |(c[`(b)])₈[³S₁]g?|(c\bar{b})_{\mathbf{8}}[^{3}S_{1}]g\rangle, whose contributions to the decay width maybe at the same order of magnitude as that of the color-singlet P-wave states according to the naive nonrelativistic quantum chromodynamics scaling rules. The P-wave states shall provide sizable contributions to the B _c production, whose decay width is about 20% of the total decay width \varGamma _{Z⁰? Bc}\varGamma _{Z^{0}\to B_{c}}. After summing up all the mentioned (c[`(b)])(c\bar {b})-quarkonium states’ contributions, we obtain \varGamma _{Z⁰? Bc}=235.9^+352.8_-122.0\varGamma _{Z^{0}\to B_{c}}=235.9^{+352.8}_{-122.0} KeV, where the errors are caused by the main sources of uncertainty.     

Global Solutions to the 3-D Incompressible Anisotropic Navier-Stokes System in the Critical Spaces

In this paper, we consider the global wellposedness of the 3-D incompressible anisotropic Navier-Stokes equations with initial data in the critical Besov-Sobolev type spaces B{\mathcal{B}} and B^{-\frac12,\frac12}₄{\mathcal{B}^{-\frac12,\frac12}_4} (see Definitions 1.1 and 1.2 below). In particular, we proved that there exists a positive constant C such that (ANS _ν ) has a unique global solution with initial data u₀ = (u₀^h, u₀³){u_0 = (u_0^h, u_0^3)} which satisfies ||u₀^h||_B exp(\fracCn⁴ ||u₀³||_B⁴) ￡ c₀n{\|u_0^h\|_{\mathcal{B}} \exp\bigl(\frac{C}{\nu^4} \|u_0^3\|_{\mathcal{B}}^4\bigr) \leq c_0\nu} or ||u₀^h||_{B^{-\frac12,\frac12}4} exp(\fracCn⁴ ||u₀³||_{B^{-\frac12,\frac12}4}⁴) ￡ c₀n{\|u_0^h\|_{\mathcal{B}^{-\frac12,\frac12}_{4}} \exp \bigl(\frac{C}{\nu^4} \|u_0^3\|_{\mathcal{B}^{-\frac12,\frac12}_{4}}^4\bigr)\leq c_0\nu} for some c ₀ sufficiently small. To overcome the difficulty that Gronwall’s inequality can not be applied in the framework of Chemin-Lerner type spaces, [(L^p_t)\tilde](B){\widetilde{L^p_t}(\mathcal{B})}, we introduced here sort of weighted Chemin-Lerner type spaces, [(L²_{t, f})\tilde](B){\widetilde{L^2_{t, f}}(\mathcal{B})} for some apropriate L ¹ function f(t).     

On a possible interpretation of the X(3872) as a 1<Superscript>1</Superscript>D<Subscript>2</Subscript> state in a constituent-quark model based on a generalized Fermi-Breit equation

A recent experimental analysis suggested to represent the X(3872) -resonance as a c [`(c)] \bar{{c}} 1¹ D ₂ state but this attribution is being hotly debated. We calculate the mass values for that state by means of a previously studied constituent-quark model. The different contributions of the model Hamiltonian to the total mass are also explicitly shown.     

Solar System planetary tests of $${\dot c/c}$$

Analytical and numerical calculations show that a putative temporal variation of the speed of light c, with the meaning of space-time structure constant c _ST, assumed to be linear over timescales of about one century, would induce a secular precession of the longitude of the pericenter v{\varpi} of a test particle orbiting a spherically symmetric body. By comparing such a predicted effect to the corrections D[(v)\dot]{\Delta\dot\varpi} to the usual Newtonian/Einsteinian perihelion precessions of the inner planets of the Solar System, recently estimated by E.V. Pitjeva by fitting about one century of modern astronomical observations with the standard classical/relativistic dynamical force models of the EPM epehemerides, we obtained [(c)\dot]/c = (0.5±2)×10^-7 yr^-1{\dot c/c =(0.5\pm 2)\times 10^{-7} {\rm yr}^{-1}} . Moreover, the possibility that [(c)\dot]/c 1 0{\dot c/c\neq 0} over the last century is ruled out at 3−12σ level by taking the ratios of the perihelia for different pairs of planets. Our results are independent of any measurement of the variations of other fundamental constants which may be explained by a variation of c itself (with the meaning of electromagnetic constant c _EM). It will be important to repeat such tests if and when other teams of astronomers will estimate their own corrections to the standard Newtonian/Einsteinian planetary perihelion precessions with different ephemerides.     

D?→Dπ and D?→Dγ decays: axial coupling and magnetic moment of D? meson

The axial coupling and the magnetic moment of D ^∗-meson or, more specifically, the couplings g_D^*Dpg_{D^{\ast}D\pi} and g_D^*Dgg_{D^{\ast}D\gamma }, encode the non-perturbative QCD effects describing the decays D ^∗→Dπ and D ^∗→Dγ. We compute these quantities by means of lattice QCD with N _f=2 dynamical quarks, by employing the Wilson (“clover”) action. On our finer lattice (a≈0.065 fm) we obtain g_D^*Dp⁺=20±2g_{D^{\ast}D\pi^{+}}=20\pm2, and g_{D^*0 D⁰g}=2.0±0.6 GeV^-1g_{D^{\ast0} D^{0}\gamma}=2.0\pm 0.6~{\rm GeV}^{-1}. This is the first determination of g_{D^*0 D⁰g}g_{D^{\ast0} D^{0}\gamma} on the lattice. We also provide a short phenomenological discussion and the comparison of our result with experiment and with the results quoted in the literature.     

Analysis of the ΛQ baryons in the nuclear matter with the QCD sum rules

In this article, we study the Λ c and Λ b baryons in the nuclear matter using the QCD sum rules, and obtain the in-medium masses M\varLambda c*=2.335 GeVM_{\varLambda _{c}}^{*}=2.335~\mathrm{GeV}, M\varLambda b*=5.678 GeVM_{\varLambda _{b}}^{*}=5.678~\mathrm{GeV}, the in-medium vector self-energies \varSigma \varLambda cv=34 MeV\varSigma ^{\varLambda _{c}}_{v}=34~\mathrm{MeV}, \varSigma \varLambda bv=32 MeV\varSigma ^{\varLambda _{b}}_{v}=32~\mathrm {MeV}, and the in-medium pole residues l\varLambda c*=0.021 GeV3\lambda_{\varLambda _{c}}^{*}=0.021~\mathrm{GeV}^{3}, l\varLambda b*=0.026 GeV3\lambda_{\varLambda _{b}}^{*}=0.026~\mathrm{GeV}^{3}. The mass-shifts are M\varLambda c*-M\varLambda c=51 MeVM_{\varLambda _{c}}^{*}-M_{\varLambda _{c}}=51~\mathrm{MeV} and M\varLambda b*-M\varLambda b=60 MeVM_{\varLambda _{b}}^{*}-M_{\varLambda _{b}}=60~\mathrm{MeV}, respectively.     

Isospin breaking in pion Compton scattering

Using chiral perturbation theory we calculate for pion Compton scattering the isospin-breaking effects induced by the difference between the charged and neutral pion mass. At one-loop order this correction is directly proportional to mp±2-mp02\ensuremath{m_{\pi^\pm}^2-m_{\pi^0}^2} and free of (electromagnetic) counterterm contributions. The differential cross-section for charged pion Compton scattering p-g? p-g\ensuremath{\pi^-\gamma \rightarrow \pi^-\gamma} gets affected (in backward directions) at the level of a few permille. At the same time the isospin-breaking correction leads to a small shift of the pion polarizabilities by d(ap- bp) @ 1.3 ·10-5\ensuremath{\delta(\alpha_\pi- \beta_\pi) \simeq 1.3 \cdot 10^{-5}} fm^3. In case of the low-energy gg? p0p0\ensuremath{\gamma\gamma \rightarrow \pi^0\pi^0} reaction isospin breaking manifests itself through a cusp effect at the p+p-\ensuremath{\pi^+\pi^-} threshold. We give an improved estimate for it based on the empirical p \pi p \pi -scattering length difference a0-a2\ensuremath{a_0-a_2} .     

Entangled Fourier Transformation and its Application in Weyl-Wigner Operator Ordering and Fractional Squeezing

In order to entangle the functions to be transformed, we proposed the entangled. Fourier integration transformation (EFIT) which has the property of keeping modulus-invariant for its inverse transformation. Then we then studied Wigner operator’s EFIT and found that a function’s EFIT is just related to its Weyl-corresponding operator’s matrix element, in so doing we also derived new operator re-ordering formulas \( \delta \left(x-P\right)\left(y-Q\right)=\frac{1}{\pi }{\displaystyle \begin{array}{c}:\\ {}:\end{array}}{e}^{-2i\left(P-x\right)\left(Q-y\right)}\ {\displaystyle \begin{array}{c}:\\ {}:\end{array}} \);\( \delta \left(y-Q\right)\left(x-P\right)=\frac{1}{\pi }{\displaystyle \begin{array}{c}:\\ {}:\end{array}}{e}^{2i\left(P-x\right)\left(Q-y\right)}\ {\displaystyle \begin{array}{c}:\\ {}:\end{array}} \), where P, Q are momentum and coordinate operator respectively, the symbol \( {\displaystyle \begin{array}{c}:\\ {}:\end{array}}\ {\displaystyle \begin{array}{c}:\\ {}:\end{array}} \) denotes Weyl ordering. By virtue of EFIT we also found the operator which can generate fractional squeezing transformation.

     

Quenching of the E1 strength in <Superscript>149</Superscript>Nd

Lifetime measurements of excited states in ¹⁴⁹Nd have been performed using the advanced time-delayed b \beta g \gamma g \gamma(t) method. Half-lives of 14 excited states in ¹⁴⁹Nd have been determined for the first time or measured with higher precision. Twelve new g \gamma -lines and 5 new levels have been introduced into the decay scheme of ¹⁴⁹Pr based on results of the g \gamma g \gamma coincidence measurements. Reduced transition probabilities have been determined for 40 g \gamma -transitions in ¹⁴⁹Nd . Configuration assignments for 6 rotational bands in ¹⁴⁹Nd are proposed. Enhanced E1 transitions indicate that the ground-state band and the band built on the 332.9keV level constitute a pair of the K^p = 5/2^±\ensuremath K^{\pi} = 5/2^{\pm} parity doublet bands. Potential energy surfaces on the (b₂,b₃)\ensuremath (\beta_{2},\beta_{3}) -plane have been calculated for the lowest single quasi-particle configurations in ¹⁴⁹Nd using the Strutinski method and the axially deformed Woods-Saxon potential. The predicted occurrence of the octupole-deformed K = 5/2 configuration is in agreement with experiment. Unexpectedly low |D₀|\ensuremath \vert D_0\vert values obtained for the K^p = 5/2^±\ensuremath K^{\pi} = 5/2^{\pm} parity doublet bands may result from cancellation between the proton and neutron shell correction contributions to |D₀|\ensuremath \vert D_0\vert .