Longitudinal Structure Function F L of Proton from Regge Like Behaviour of Structure Function at Small-x

The evolutions of longitudinal structure function F _L from quantum chromodynamics (QCD) evolution equation in next-to-leading order at small-x is presented using the Regge like behaviour of the structure function. The proposed simple analytical expression for F _L structure function provides the t- and x-evolution equations to study the behaviour of F _L structure function at small-x. The calculated results are compared with the data of H1, ZEUS collaborations and results of Block model, Donnachie–Landshoff model. Our calculated results can be described within the framework of perturbative QCD.     

Evolutions of Longitudinal Structure Function F L upto Next-to-Next-to-Leading Orders at Small-x

We compute the longitudinal structure function F _L of proton from its QCD (Quantum Chromodynamics) evolution equation in next-to-next-to-leading order (NNLO) approximation at small-x. Here we use Taylor series expansion method to solve the evolution equation for small-x and the obtained simple analytical expressions for F _L provide t- and x-evolution equations for the computation of the longitudinal structure function. Finally, we compare our results with the recent H1, ZEUS experimental data and results of MSTW, CT10 parameterizations and Block, Donnachie-Landshoff (DL) models. Our results are in good agreement with the data and the related fittings and parameterizations, which can also be described within the framework of perturbative QCD.     

Solution of Evolution Equation for Longitudinal Structure Function F L upto Next-to-Next-to-Leading Order and Its t-Evolution at Small-x

The aim of the present paper is to calculate longitudinal structure function F _L from QCD (Quantum Chromodynamics) evolution equation in next-to-next-to-leading order (NNLO) at small-x. The calculation of F _L is important for the phenomenological study of gluon distribution function inside the nucleon. Here we use Taylor Series Expansion method to solve the evolution equation for small-x and thus obtain t-evolution of F _L structure function. The calculated results are compared with H1 and ZEUS data and results of Block and Donnachie-Landshoff (DL) models.     

Nonlinear correction to the longitudinal structure function at small x

We computed the longitudinal proton structure function F_L, using the nonlinear Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (NLDGLAP) evolution equation approach at small x . For the gluon distribution, the nonlinear effects are related to the longitudinal structure function. As the very small-x behavior of the gluon distribution is obtained by solving the Gribov, Levin, Ryskin, Mueller and Qiu (GLR-MQ) evolution equation with the nonlinear shadowing term incorporated, we show that the strong rise that corresponds to the linear QCD evolution equations can be tamed by screening effects. Consequently, the obtained longitudinal structure function shows a tamed growth at small x . We computed the predictions for all details of the nonlinear longitudinal structure function in the kinematic range where it has been measured by the H1 Collaboration and made comparisons with the computation by Moch, Vermaseren and Vogt at the second order with input data from the MRST QCD fit.     

Fractal Inspired Models of quark and gluon distributions and longitudinal structure function FL (x, Q2) at small x

In recent years, Fractal Inspired Models of quark and gluon densities at small x have been proposed. In this paper, we investigate longitudinal structure function F _L (x, Q ²) within this approach. We make predictions using the Quantum Chromodynamics (QCD) based approximate relation between the longitudinal structure function and the gluon density. As the Altarelli-Martinelli equation for the longitudinal structure function cannot be applied to Model I due to the presence of a singularity in the Bjorken x-space we consider Model II only. The qualitative feature of the prediction of Model II is found to be compatible with the QCD expectation.     

Extraction of Structure Function and Gluon Distribution Function at Low-x from Cross Section Derivative by Regge Behavior

An approximation method based on Regge behavior is presented. This new method relates the reduced cross section derivative and the structure function Regge behavior at low x. With the use of this approximation method, the C and λ parameters are calculated from the HERA reduced cross section data taken at low-x. Also, we calculate the structure functions F₂(x,Q²) even for low-x values, which have not been investigated. To test the validity of calculated structure functions, we find the gluon distribution function in the Leading order approximation based on Regge behaviour of structure function and compare to the NLO QCD fit to H1 data and NLO parton distribution function.     

Longitudinal Proton Structure Function at LO and NLO Approximations

The purpose of this paper is to calculate the longitudinal structure function of proton through the well-known equation F _L =F ₂?2xF ₁. To determine this structure function, we need to identify parton distribution functions to find F ₂. In this case, the valon model and DGLAP equations are utilized to obtain the parton distributions. Our calculations are carried out in two approximations LO and NLO. The results at the NLO approximation are in better agreement with the experimental data.     

A phenomenological analysis of the longitudinal structure function at small <Emphasis Type="Italic">x</Emphasis> and low <Emphasis Type="Italic">Q</Emphasis><Superscript>2</Superscript>

The longitudinal structure function in deep-inelastic scattering is one of the observables from which the gluon distribution can be unfolded. Consequently, this observable can be used to constrain the QCD dynamics at small x. In this work we compare the predictions of distinct QCD models with the recent experimental results for F _L(x,Q ²) at small x and low Q ² obtained by the H1 Collaboration. We focus mainly on the color dipole approach, selecting those models which include saturation effects. Such models are suitable at this kinematical region and also resum a wide class of higher-twist contributions to the observables. Therefore, we investigate the influence of these corrections to F _L in the present region of interest.Received: 23 June 2004, Revised: 13 July 2004, Published online: 14 September 2004     

Equivalent Method of Solving Quantum Efficiency of Reflection-Mode Exponential Doping GaAs Photocathode

The mathematical expression of the electron diffusion and drift length LDE of exponential doping photocathode is deduced. In the quantum efficiency equation of the reflection-mode uniform doping cathode, substituting LDE for LD, the equivalent quantum efficiency equation of the reflection-mode exponential doping cathode is obtained. By using the equivalent equation, theoretical simulation and experimental analysis shows that the equivalent index formula and formula-doped cathode quantum efficiency results in line. The equivalent equation avoids complicated calculation, thereby simplifies the process of solving the quantum efficiency of exponential doping photocathode.     

A Strength Softening Phase Transition Observed in Shocked （Mg0.92,Fe0.08）SiO3 Perovskite at About 83 GPa

We report the experimental data of Hugoniot longitudinal sound velocity VL for natural （Mg0.92,Fe0.08）SiO3 enstatite sample at about 40-140 GPa, consisting of three new data and five previously reported data but revised by our new Hugoniot equation of state parameters. Three segments, separated by two discontinuities, appear in the VL-PH （shock pressure） plot. Analyses show that the first discontinuity at about 64 GPa, with a sharp increase of VL of about 21%, is judged to be a phase transition from enstatite to Pbnm perovskite （PV）; while the second one at about 83 GPa, with a dramatic decrease of VL of about 23%, is likely caused by a subtle structural change from Pbnm PV to tetragonal PV, accompanied by material strength softening due to melting of oxygen sublattices. This strength softening evidence is obtained first from shock wave experiments, and probably has profound implications for probing into the origin of low seismic velocity anomaly in the Earth＇s lower mantle and thus constraining the geophysical and geochemical models for the Earth＇s lower mantle.     

F L structure function and heavy quark contributions

In this paper we obtain the heavy-quark contribution to the longitudinal structure functions F _L (x, Q ²). Since F _L structure functions contains rather large heavy flavor contributions in the small x region, we need to use the massive operator matrix elements, which contribute to the heavy flavor Wilson coefficients in unpolarized deeply inelastic scattering in the region Q ²?>?>?m ². The method of QCD analysis, based on the Jacobi polynomials method, is also described. Our results for longitudinal structure function are in good agreement with the available experimental data.     

Measurement of the longitudinal structure function and the smallx gluon density of the proton

At HERA energies the smallx region (x?10^?2) can be explored atQ ² values large enough that leading twist QCD calculations are valid. We show how measurement of the longitudinal structure function,F _L (x,Q ²), can lead to accurate measurement of the gluon structure function at such smallx values. Experimental systematic errors are discussed fully and requirements for the measurement outlined. We conclude that it should be possible to distinguish between the widely varying gluon distributions which are currently allowed.     

Low-x QCD with CMS at the LHC

The physics of gluon saturation and non-linear evolution at small values of parton momentum fraction x in the proton and nucleus is discussed in the context of experimental results at HERA and RHIC. The rich physics potential of low-x QCD studies at the LHC is discussed and some measurements in pp, pA and AA collisions accessible with the compact muon solenoid (CMS) experiment are presented. PACS 12.38.-t; 24.85.+p; 25.75.-q     

Common Features in Electronic Structure of the Oxypnictide Superconductors from Photoemission Spectroscopy

High resolution photoemission measurements are carried out on non-superconducting LaFeAsO parent com- pound and various superconducting RFeAs（O1-ZFx） （R=La, Ce and Pr） compounds. It is found that the parent LaFeAsO compound shows a metallic character. By extensive measurements, several common features are identified in the electronic structure of these Fe-based compounds： （1） 0.2 eV feature in the valence band, （2） a universal 13-16 meV feature, （3） near EF spectral weight suppression with decreasing temperature. These uni- versal features can provide important information about band structure, superconducting gap and pseudogap in these Fe-based materials.     

AN INVESTIGATION OF THE EFFECTS OF CHARGED BOSONIC PARTONS (DIQUARKS) IN e-P DEEP INELASTIC SCATTERING

We point out the possible existence of bosonic charged partons (diquarks) withinnucleons. A certain form of the structure functions of diquarks inside nucleons is as-sumed and the functions are suitably parametrized. Then, by combining their effectswith the usual QCD calculations, we get a better theoretical fit to the experimental R=(σ_L)/(σ_T) value in e-p deep inelastic scattering.     

Two-loop QCD corrections to the coefficient functions of the deep inelastic structure functionsF 2 andF L

We present the analytic two-loop perturbative QCD corrections in the leading twist approximation to the coefficient functions of the operator product expansion for the second to tenth moments of the nonsinglet and singlet deep inelastic structure functionsF ₂ andF _L .     

Stability and Growth Modes of Ni--C Clusters: A Study based on All-Electron Density Function Theory

Growth modes of the free-standing NiCN （N ≤ 8） and Ni2CN （N ≤ 8） dusters are investigated by the allelectron density functional theory. The results reveal that there are two competing modes for the growth of these clusters： the linear chain and the ring structure without transannular bonds. The lowest-energy geometries of NiCN （N ≤ 8） are the linear chains with the Ni atom at one end, except for NiC2 and NiCT. The Ni2CN （N ≤ 8） clusters all prefer to the linear chains with the two Ni atoms at the two ends. Miilliken population analysis indicates that the total spin of the lowest-energy cluster show significant odd-even alternation. The NiMCN （M = 1,2） clusters with the even N are one and those with the odd-N are zero.     

Element Substitution Effect in Transition Metal Oxypnictide Re(O1-xFx)TAs (Re=rare earth, T=transition metal)

Different element substitution effects in transition metal oxypnictide Re(O_1-xF_x)TAs, with Re=La, Ce, Nd, Eu, Gd, Tm, T=Fe, Ni, Ru, are studied. Similarto the La- or Ce-based systems, we find that the pure NdOFeAs shows a strong resistivity anomaly near 145K, which is ascribed to the spin-density-wave instability. Electron doping by F increases T_c to about 50K. While in the case of Gd, Tc is reduced below 10K. The tetragonal ZrCuSiAs-type structure could not be formed for Eu or Tm substitution in our preparing process. For the Ni-based case, although both pure and F-doped LaONiAs are superconducting, no superconductivity is found when La is replaced by Ce in both the cases, instead a ferromagnetic ordering transition is likely to form at low temperature in the undoped sample. We also synthesize LaO_1-xF_xRuAs and CeO_1-xF_xRuAs compounds. The metallic behaviour is observed down to 4K.     

Structural Stability of CaCuMn6O12 under High Pressure and Low Temperature

In situ high pressure energy-dispersive x-ray synchrotron radiation diffraction and resistance experiments are carried out on CaCuMn6O12. Its crystal structure is stable in the measured pressure range. The equation of state of CaCuMn6O12 is obtained from the V/Vo - P relationship （V and Vo are the volumes at pressure P and at atmosphere）. The bulk modulus Bo is calculated based on the Birch-Murnaghan equation. Low temperature x-ray diffraction shows no phase transition occurring down to 160K.