Multiplicity moments in deep inelastic scattering at HERA

Multiplicity moments of charged particles in deep inelastic e⁺p scattering have been measured with the ZEUS detector at HERA using an integrated luminosity of 38.4 pb⁻¹. The moments for Q²>1000 GeV² were studied in the current region of the Breit frame. The evolution of the moments was investigated as a function of restricted regions in polar angle and, for the first time, both in the transverse momentum and in absolute momentum of final-state particles. Analytic perturbative QCD predictions in conjunction with the hypothesis of Local Parton–Hadron Duality (LPHD) reproduce the trends of the moments in polar-angle regions, although some discrepancies are observed. For the moments restricted either in transverse or absolute momentum, the analytic results combined with the LPHD hypothesis show considerable deviations from the measurements. The study indicates a large influence of the hadronisation stage on the multiplicity distributions in the restricted phase-space regions studied here, which is inconsistent with the expectations of the LPHD hypothesis.     

Fluctuations of multiplicities in rapidity windows in sulphur-sulphur collisions at 200A GeV

Multiplicity distributions and their second moments fornegatively charged particles produced in³²S-S central and minimum bias interactions at 200A GeV are studied in various rapidity intervals. Fritiof and Venus models mostly describe the dependence of second moments on rapidity intervals in minimum bias interactions, but not in central collisions. For central collisions the behaviour of second moments might indicate enhanced multiplicity fluctuations.     

Exciton level densities with spin and parity based on random matrix model

Level densities for fixedJ ^π and the exciton number are evaluated for closed shell nuclei⁴⁰Ca and²⁰⁸Pb. The single particle spectra and wave functions are generated by Woods-Saxon potentials. The effects of the residual interaction are taken into account statistically by the method of generating function and Grassmann integral. The matrix elements for the residual interaction are assumed to be random variables with Gaussian distributions whose second moments are calculated by using a zero range interaction. The second moments are evaluated for fixedJ ^π by ignoring the Pauli principle between active nucleons and the spectator. This approximation is shown numerically to be very good. The partial level densities are calculated using the second moments as well as independent particle model spectra. The resulting level densities spread over wider energy ranges, have a smoother energy dependence and are enhanced at low energies compared with the independent particle model densities, although the total level densities do not differ by much.     

Coherence and intensity moments of laser light

Taking the modal behaviours of the laser field into account, the coherence properties of laser light can be characterized by mode coherence functions (MCFs) and mode coherence coefficients (MCCs). Changes in laser light properties due to optical operations can be described by transformation laws for the MCFs and the MCCs. The transformation laws as well as transformation matrices for propagation in free space, phase transformations, spatial amplitude modulations and aperturizing are given. Furthermore, intensity distributions and intensity moments in the spatial and in the spatial frequency domains are expressed in terms of the MCCs. General expressions for the beam quality factors,M ²s, obtained using the intensity moments and some useful expressions for intensity moments of higher order are discussed.     

Magnetic ordering on Yb3+ in YbBa2Cu3O7−x

The high critical temperature superconductor YbBa₂Cu₃O_7−x has been studied over the range 0.05 to 95K using ¹⁷⁰Yb Mössbauer absorption spectroscopy. Magnetic ordering occurs within the Yb³⁺ sublattice at 0.35K. The saturated magnetic moments are 1.7μ_B. At all temperatures the hyperfine parameters show the presence of distributions attributed to some disordering of the oxygen vacancies.     

Electric quadrupole and magnetic octupole moments of the light decuplet baryons within light cone QCD sum rules

The electric quadrupole and magnetic octupole moments of the light decuplet baryons are calculated in the framework of the light cone QCD sum rules. The obtained non-vanishing values for the electric quadrupole and magnetic octupole moments of these baryons show nonspherical charge distribution. The sign of electric quadrupole moment is positive for Ω⁻, Ξ^*−, Σ^*− and negative for Σ^*+, which correspond to the prolate and oblate charge distributions, respectively. A comparison of the obtained results with the predictions of non-covariant quark model which shows a good consistency between two approaches is also presented. Comparison of the obtained results on the multipole moments of the decuplet baryons containing strange quark with those of Δ baryons shows a large SU(3) flavor symmetry breaking.     

尖晶石铁氧体TixNi1-xFe2O4中阳离子分布和Ti离子磁矩的实验研究

采用固相反应法制备了系列样品Ti_xNi_1-xFe₂O₄ (x=0.0, 0.1, 0.2, 0.3, 0.4). 室温下的X射线衍射谱表明样品全部为(A)[B]₂O₄型单相立方尖晶石结构, 属于空间群Fd3m. 样品的晶格常数随Ti掺杂量的增加而增大. 样品在10 K温度下的比饱和磁化强度σ_S随着Ti掺杂量x的增加逐渐减小. 研究发现, 当Ti掺杂量x≥ 0.2时, 磁化强度σ随温度T的变化曲线出现两个转变温度T_L和T_N. 当温度低于T_N时, 磁化强度明显减小; 当温度达到T_N时, dσ/dT具有最大值. σ-T曲线的这些特征表明, 由于Ti掺杂在样品中出现了附加的反铁磁结构. 这说明样品中的Ti离子不是无磁性的+4价离子, 而是以+2和+3价态存在, 其离子磁矩的方向与Fe和Ni离子的磁矩方向相反. 利用本课题组提出的量子力学方势垒模型拟合样品在10 K温度下的磁矩, 得到了Ti, Fe和Ni三种阳离子在(A)位和[B]位的分布情况, 并发现在所有掺杂样品中, 80%的Ti离子以+2价态占据尖晶石结构的[B]位.     

Generalized parton distributions from hadronic observables: non-zero skewness

We propose a physically motivated parameterization for the unpolarized generalized parton distributions, H and E, valid at both zero and non-zero values of the skewness variable, ζ. Our approach follows a previous detailed study of the ζ=0 case where H and E were determined using constraints from simultaneous fits of the experimental data on both the nucleon elastic form factors and the deep inelastic structure functions in the non-singlet sector. Additional constraints at ζ≠0 are provided by lattice calculations of the higher moments of generalized parton distributions. We illustrate a method for extracting generalized parton distributions from lattice moments based on a reconstruction using sets of orthogonal polynomials. The inclusion in our fit of data on Deeply Virtual Compton Scattering is also discussed. Our method provides a step towards an extraction of generalized distributions based on a global fit of the available data within the given set of constraints.     

Ligand polarization contributions to lanthanide 4f → 4f magnetic dipole transition moments and rotatory strengths

Radiation-induced (dynamic) polarizations of electronic charge distributions on ligands may contribute to both the electric- and magnetic-dipole moments of 4f → 4f transitions in lanthanide complexes. These ligand-polarization effects on magnetic-dipole transition moments are examined in the present study, and their possible influence on the rotatory strengths of 4f → 4f transitions in chiral lanthanide systems is given special attention. The ligand-polarization mechanism for magnetic-dipole transition moments is not likely to contribute significantly to the total dipole strengths of 4f → 4f transitions in noncentrosymmetric lanthanide systems. However, this mechanism may contribute significantly (or detectably) to the rotatory strengths of certain 4f → 4f transitions in chiral lanthanide systems. The relative importance of these contributions will be greatest for transitions with predominantly |ΔJ| ≥ 2 character and with relatively large U ^λ(λ = 2, 4, and 6) matrix elements.     

Asymptotic behaviour of the Boltzmann equation with infinite range forces

We have previously obtained existence results for the space-homogeneous, non-linear Boltzmann equation for a class of encounters with infinite range, including inversek ^th power molecules withk>3. In the present paper those solutions are proved to converge in weakL ¹-sense fork5 to Maxwellian distributions whent. Also the higher moments converge to those of the relevant Maxwellian. The method of proof relies on non-standard techniques.     

Current distribution on a three-dimensional,bond-diluted,random-resistor network at the percolation threshold

Current and logarithm-current distributions on a three-dimensional random-bond percolation cubic network were studied at the percolation threshold by computer simulations. Predictions of a hierarchical model that combine fractal structure and randomness agree with our numerical simulations. In the thermodynamic limit the logarithm-current distribution exhibits ann(ln(i))i ^1/3 dependence below some characteristic currenti _c. This distribution may scale with lni/lnL, but the data are insufficient to make this a definite conclusion. Due to the small range of lnL considered, a study of the moments does not reveal this behavior and a study of the distribution itself is required.     

Probing the QCD critical point by higher moments of net-proton multiplicity distributions at STAR

Higher moments (kurtosis (??), skewness (S) and variance (?? ²)) of multiplicity distributions are sensitive to the correlation length and can be used to search for the QCD critical point. The moment products ??? ² and S ?? of net-proton distributions, which are also related to volume independent baryon number susceptibility ratios, can be compared with Lattice QCD and Hadron Resonance Gas (HRG) model calculations. We discuss the recent progress in the higher moments analysis of net-protons multiplicity distributions.     

End-to-end distribution functions for polymers having a most probable molecular weight distribution

End-to-end chain distribution functions for a polymer with a most probable molecular weight distribution are obtained by assuming the end-to-end distribution for each molecular weight species is Gaussian and the degree of polymerization is large. The resulting radial distribution functions using the most probable number and weight species distributions are:

W_n (r,p) = k²re-^kr and W_w (r,p) = k³r²/2 e^?kr

respectively, where k is a function of the short-range effects and the extent of the reaction is p. The first and second moments of these functions are identical with those obtained by taking the number and weight averages of the moments for the monodisperse case. The most probable values of r, which cannot be obtained by the latter method, are found to be 1/k and 2/k, respectively, using the above distributions.     

Nuclear Orientation Studies of Magnetism in Single Crystal Pr0.5Nd0.5Ni

The angular distributions of -rays from ¹⁴²Pr, ¹⁴⁷Nd and ¹⁴⁴Pm in Pr_0.5Nd_0.5Ni were investigated by means of low-temperature nuclear orientation. The results show that the Pr and Nd electronic moments order along the c- and a-axis, respectively. Pm ions introduced as a very dilute magnetic impurity, preferentially align with the Nd ions.     

Determination of the b -quark mass and nonperturbative parameters in semileptonic B -meson decays at BABAR⋆

Knowing the mass of the b -quark is essential to the study of the structure and decays of B -mesons as well as to future tests of the Higgs mechanism of mass generation. We present recent preliminary measurements of the b -quark mass and related nonperturbative parameters from moments of kinematic distributions in charmed and charmless semileptonic B -meson decays. Their determination from charmless semileptonic B -meson decays is the first measurement in this mode. The data were collected by the BABAR detector at the PEP-II asymmetric-energy e ⁺ e ^- -collider at the Stanford Linear Accelerator Center at a center-of-mass energy of 10.58GeV. Original article based on material presented at HADRON 2007.     

Leading and higher twists in proton,neutron and deuteron unpolarized structure functions F<Subscript>2</Subscript>

We summarize the results of a recent global analysis of proton and deuteron F₂ structure function world data performed over a large range of kinematics, including recent measurements done at JLab with the CLAS detector. From these data the lowest moments (n≤10) of the unpolarized structure functions are determined with good statistics and systematics. The Q² evolution of the extracted moments is analyzed in terms of an OPE-based twist expansion, taking into account soft-gluon effects at large x. A clean separation among the leading- and higher-twist terms is achieved. By combining proton and deuteron measurements the lowest moments of the neutron F₂ structure function are determined and its leading-twist term is extracted. Particular attention is paid to nuclear effects in the deuteron, which become increasingly important for the higher moments. Our results for the non-singlet, isovector (p-n) combination of the leading-twist moments are used to test recent lattice simulations. We also determine the lowest few moments of the higher-twist contributions, and find these to be approximately isospin independent, suggesting the possible dominance of ud correlations over uu and dd in the nucleon.     

Random Matrix Theory and ζ(1/2+it)

We study the characteristic polynomials Z(U, θ) of matrices U in the Circular Unitary Ensemble (CUE) of Random Matrix Theory. Exact expressions for any matrix size N are derived for the moments of |Z| and Z/Z ^*, and from these we obtain the asymptotics of the value distributions and cumulants of the real and imaginary parts of log Z as N→∞. In the limit, we show that these two distributions are independent and Gaussian. Costin and Lebowitz [15] previously found the Gaussian limit distribution for Im log Z using a different approach, and our result for the cumulants proves a conjecture made by them in this case. We also calculate the leading order N→∞ asymptotics of the moments of |Z| and Z/Z ^*. These CUE results are then compared with what is known about the Riemann zeta function ζ (s) on its critical line Re s= 1/2, assuming the Riemann hypothesis. Equating the mean density of the non-trivial zeros of the zeta function at a height T up the critical line with the mean density of the matrix eigenvalues gives a connection between N and T. Invoking this connection, our CUE results coincide with a theorem of Selberg for the value distribution of log ζ(1/2+iT) in the limit T→∞. They are also in close agreement with numerical data computed by Odlyzko [29] for large but finite T. This leads us to a conjecture for the moments of |ζ(1/2+it) |. Finally, we generalize our random matrix results to the Circular Orthogonal (COE) and Circular Symplectic (CSE) Ensembles. Received: 20 December 1999 / Accepted: 24 March 2000     

Isotropic and nematic phase N.M.R. spectra of tellurophen

In molecular beam experiments the preferred spatial orientation or polarization of the rotational angular momentum of reactively scattered molecules can be determined by deflection in an inhomogeneous electric field. The apparatus, experimental method, and analysis procedure are described and illustrated with data obtained for the K + HBr, Cs + HBr, and Cs + HI reactions. The experiments employ a new field design which eliminates the non-adiabatic change of quantization axis that handicapped a previous polarization study. A simple normalization procedure provides ‘reduced deflection profiles’ which are very insensitive to substantial variations in the experimental parameters, including the deflection field strength, beam position in the field, collimating slit widths, dipole moment, and distributions of rotational and translational energy. These reduced profiles yield 2 x> and 4 x>, the first two moments of the probability distribution of polarization, where x is the angle between the rotational angular momentum and the initial relative velocity vector. The experimental results indicate marked polarization, corresponding to 2 x> < 0·10, and agree well with theoretical moments calculated from a statistical phase-space treatment.     

Moments of charge distributions in the reaction92Mo+92Mo at 14.7 MeV/u

First and second moments of primary charge distributions were determined as a function of the total kinetic energy loss in the reaction⁹²Mo+⁹²Mo at an incident energy of 14.7 MeV/u. Up to energy losses of 200 MeV no significant drift of the first moments is observed. The second moments are in agreement with predictions of a stochastic model derived at lower bombarding energies.