Nuclear effects on the longitudinal structure function at small x

We discuss the longitudinal structure function in nuclear DIS at small x  . We work within the framework of universal parton densities obtained in DGLAP analyses at NLO. We show that the nuclear effects on the longitudinal structure function closely follow those on the gluon distribution. The error analyses available from newest sets of nuclear PDFs also allow to propagate the uncertainties from present data. In this way, we evaluate the minimal sensitivity required in future experiments for this observable to improve the knowledge of the nuclear glue. We further discuss the uncertainties on the extraction of F₂$F_2$ off nuclear targets, introduced by the usual assumption that the ratio FL/F₂$F_L/F_2$ is independent of the nuclear size. We focus on the kinematical regions relevant for future lepton–ion colliders.     

Nuclear structure function at large x and ΛQCD

We explain that due to the presence of the short-range nucleon correlations in nuclei the theoretical pattern of Bjorken scaling violation at x > 0.7 is expected to be simpler here than in lepton-nucleon scattering. Consequently, lepton-nucleus scattering is better suited for the accurate determination of Λ_QCD if nuclear effects are properly accounted for. On the contrary if they are ignored (as it is often done at present) Λ_QCD is considerably underestimated.     

Analytical approach for the approximate solution of the longitudinal structure function with respect to the GLR-MQ equation at small x

We show that the nonlinear corrections to the longitudinal structure function can be tamed the singularity behavior at low x values, with respect to GLR-MQ equations. This approach can determined the shadowing longitudinal structure function based on the shadowing corrections to the gluon and singlet quark structure functions. Comparing our results with HERA data show that at very low x this behavior completely tamed by these corrections.     

Distribution of valence quarks in hadrons at small x in QCD

Valence u- and d-quark distributions in nucleons and pions at small x corresponding to ? and ω Regge pole exchanges have been obtained on the basis of the QCD sum rule method.     

Regge behaviour of structure functions and evolution of gluon structure function upto next-to-leading order at low-x

Evolution of gluon structure function from Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations upto next-to-leading order at low-x is presented assuming the Regge behaviour of structure functions. We compare our results of gluon structure function with GRV 98 global parameterization and show the compatibility of Regge behaviour of structure functions with PQCD.     

The magnetic susceptibility of Hg−xMnxSe for small x

The magnetic susceptibility of Hg_1?xMn_xSe semimetals for x ? 0.031 and 2.3 ? T ? 250 K is presented. The samples show Curie-Weiss behaviour in several temperature regions. S_eff at high temperatures exceeds that at low temperatures. θ_p is antiferromagnetic (θ_p < 0) for all x at low T, but θ_p is positive at high T for low x. The coupling mechanism considered is long-range and caused by virtual band transitions across the zero-gap.     

Constraining the nuclear gluon distribution in eA processes at RHIC

A systematic determination of the gluon distribution is of fundamental interest in understanding the parton structure of nuclei and the QCD dynamics. Currently, the behavior of this distribution at small x   (high energy) is completely undefined. In this Letter we analyze the possibility of constraining the nuclear effects present in xgA$x{g}_A$ using the inclusive observables which would be measured in the future electron-nucleus collider at RHIC. We demonstrate that the study of nuclear longitudinal and charm structure functions allows to estimate the magnitude of shadowing and antishadowing effects in the nuclear gluon distribution.     

Regge behaviour of structure function and gluon distribution at low-x in leading order

We present a method to find the gluon distribution from the proton structure function data at low-x assuming the Regge behaviour of the gluon distribution function at this limit. We use the leading order (LO) Altarelli–Parisi (AP) evolution equation in our analysis and compare our result with those of other authors. We also discuss the limitations of the Taylor expansion method in extracting the gluon distribution from the structure function used by those authors. Received: 2 January 2000 / Revised version: 23 February 2000 / Published online: 6 July 2000     

The scattering effects of the redistribution function RIII(x′, n′; x, n) on spectral line formation

The effects of frequency and angular redistribution on line formation are examined in static isothermal atmospheres for scattering described by the redistribution function R_III(x′, n′; x, n). For an optically thin atmosphere, it is found that the emergent line intensities obtained using R_III are essentially the same as R_I and R_II. In the case of a semi-infinite atmosphere, the emergent line intensities obtained using R_III, whether angle-averaged or angle-dependent, did not differ substantially from the complete redistribution results.     

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.     

Singlet structure function g<Subscript>1</Subscript> at small x and small Q<Superscript>2</Superscript>

Explicit expressions for the singlet spin structure function g₁ at small x and small Q² are obtained with a total resummation of the leading logarithmic contributions. It is shown that g₁ practically does not depend on x in this kinematic region. In contrast, it would be interesting to investigate its dependence on the invariant energy 2pq, because g₁, being positive at small 2pq, can turn negative at greater values of this variable. The position of the turning point is sensitive to the ratio of the initial quark and gluon densities, so its experimental detection would enable one to estimate this ratio. PACS 12.38.Cy     

Shadowing correction to the gluon distribution behavior at small x

We determined the saturation exponent of the gluon distribution using the solution of the QCD nonlinear Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (NLDGLAP) evolution equation at small x . 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. The form of the initial condition for the equation is determined. We find, with decreasing x , the emergence of a singular behavior and the eventual taming (at R = 5 GeV^-1) and the essential taming (at R = 2 GeV^-1) of this singular behavior by the shadowing term. The nonlinear gluon density functions are calculated and compared with the results for the integrated gluon density from the Balitsky-Kovchegov (BK) equation for the different values of Q². It is shown that the results for the gluon density function are comparable with the results obtained from the BK equation solution. Also we show that for each x , the Q²-dependence of the data is well described by gluon shadowing corrections to the GLR-MQ equation. The resulting analytic expression allows us to predict the logarithmic derivative \( {\frac{{\partial F^{s}_{2} (x,Q^{2})}}{{\partial \ln Q^{2}}}}\) and to compare the results with H1 data and a QCD analysis fit.     

X-ray spectroscopic study of the valence band structure of Cd1−xMnxTe, x = 0.6

The valence band structure of Cd_1?xMn_xTe (x = 0.6) was studied by soft X-ray emission spectroscopy using a 11.5 m concave grating grazing incidence spectrometer in conjunction with a high power rotating anode, which provided the radiation for flourescence excitation. The position of the Mn 3d⁵ states within the energy band system could be identified unambiguously; they form a band near the top of the CdTe valence band. The results are discussed with regard to recently published photoemission data.     

Optical correlation of functions distorted as f(x′)=>f(xa)

The use of coordinate transformation preprocessing is used to produce a space-variant correlator invariant to functions distorted as f(x′)=f(x^a). Such distortions arise in non-linear scanning devices, imaging from curved surfaces, aberrations in an imaging system, and in the Doppler shift of target with non-uniform motion.     

The gluon form factor to higher orders: Gluon-gluon annihilation at small Qt

We study the region of small transverse momenta in the dynamics of the gluon-gluon annihilation channel. This is done by evaluating the gluon form factor at the single non-leading infrared and collinear logarithmic accuracy to all orders in α_s. An explicit expression for the gluon form factor is obtained. The results are compared with those for the analogous quark case.     

Correlation with large transverse momentum photons and the gluon structure function

The inclusive two-particle cross section for the production of largep _T photons and opposite side charged hadrons in proton-proton collisions is examined in detail in the framework of QCD. The model, with the parametrization as in our previous work, agrees with the measured single photon spectra. Quantitative predictions are made for two-particle distributions to be measured at the ISR. The contributions due to the photon bremsstrahlung and the effects coming from the intrinsic constituent motion are estimated. It is shown that indeed the direct subprocess gluon+quark→photon+quark gives the dominant contribution in the experimentally relevant region of phase space, and that direct information about the gluon structure function can be obtained from such measurements.     

Small x resummation and the Odderon

We present a general argument which suggests that the Bartels–Lipatov–Vacca Odderon intercept should be equal to one to all orders in the perturbation theory. The argument is based on the validity of the so-called omega-expansion in the high energy limit. It can be further supported by the analogous pattern observed in the case of the anomalous dimensions which is a consequence of the momentum sum rule. In addition, we conjecture that the BFKL kernel should satisfy the transverse momentum sum rule. Finally, it is shown that the higher order kinematical effects do not change the BLV Odderon intercept.     

Asymmetries in Largep T photoproduction and the polarized gluon structure function

QCD predictions for asymmetries in largep _T polarized photon reactions on a polarized target are given. Taking cross-section differences is shown to yield new tests of QCD. Double inclusive cross section measurements provide a direct way to measure the distribution function of polarized gluons in the proton.     

QCD calculation of expected large xT 3-jet structure at Isabelle

We investigate in perturbative QCD the magnetude and shape of the large x_T(?0.5) 3-transverse jet thrust spectrum from pp collisions. We show that in this valence subprocess dominated region the shape of the spectrum is determined unambiguously by QCD. At Isabelle energies and the lowest acceptable x_T the magnitude of the cross section should allow observation of such 3-jet events but with rather low statistics.