Calculation of the Gluon Distribution Function Using Alternative Method for the Proton Structure Function

A calculation of the proton structure function F2(x,Q^2) is reported with an approximation method that relates the reduced cross section derivative and the F2(x, Q^2) scaling violation at low x by using quadratic form for the structure function. This quadratic form approximation method can be used to determine the structure function F2 (x, Q^2) from the HERA reduced cross section data taken at low x. This new approach can determine the structure functions F2(x,Q^2) with reasonable precision even for low x values which have not been investigated. We observe that the Q^2 dependence is quadratic over the full kinematic covered range. To test the validity of our new determined structure functions, we find the gluon distribution function in the leading order approximation with our new calculation for the structure functions and compare them with the QCD parton distribution functions.     

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.     

Small-x behavior of parton distributions from the observed Froissart energy dependence of the deep-inelastic-scattering cross sections

We fit the reduced cross section for deep-inelastic electron scattering data to a three parameter ln2s fit, A + beta ln2(s/s0), where s = (Q2/x)(1-x) + m2, and Q2 is the virtuality of the exchanged photon. Over a wide range in Q2 (0.11 < or = Q2 < or = 1200 GeV2) all of the fits satisfy the logarithmic energy dependence of the Froissart bound. We can use these results to extrapolate to very large energies and hence to very small values of Bjorken x-well beyond the range accessible experimentally. As Q2-->infinity, the structure function F2(p)(x,Q2) exhibits Bjorken scaling, within experimental errors. We obtain new constraints on the behavior of quark and antiquark distribution functions at small x.     

Analytic Derivation of the Longitudinal Proton Structure Function FL(x,Q2) and the Reduced Cross Section σr(x,Q2) at the Leading Order and the Next-to-leading Order Approximations

International Journal of Theoretical Physics - We present a set of formulas to extract the longitudinal proton structure function FL(x, Q2) and the reduced cross section σr(x, Q2) by using...     

Analytic expression for the joint x and Q2 dependences of the deep-inelastic structure functions

We obtain a good analytic fit to the joint Bjorken-x and Q2 dependences of ZEUS data on the deep-inelastic structure function F(2)(p)(x,Q2). At fixed virtuality Q2, as we showed previously, our expression is an expansion in powers of ln(1/x) that satisfies the Froissart bound. Here we show that for each x, the Q2 dependence of the data is well described by an expansion in powers of lnQ2. The resulting analytic expression allows us to predict the logarithmic derivatives (partial differential(n)F(2)(p)/(partial differentiallnQ2)n)x for n=1,2 and to compare the results successfully with other data. We extrapolate the proton structure function F(2)(p)(x,Q2) to the very large Q2 and the very small x regions that are inaccessible to present-day experiments and contrast our expectations with those of conventional global fits of parton distribution functions.     

Longitudinal Structure Function FL at Small x Extracted from the Berger–Block–Tan Parametrization of F2

JETP Letters - The longitudinal structure function FL(x, Q2) is extracted at low values of the Bjorken variable x from the Berger-Block-Tan parametrization of F2(x, Q2). The obtained structure...     

Emission in the final state in processes with the production of charged pions and light leptons

The Drell-Yan form is proposed for the decay widths of heavy quarks and cross sections for high-energy scattering with the production of charged pions and light leptons including radiative corrections in the final state in the leading logarithmic approximation. The corresponding spectral distributions are given in terms of the convolution of the cross section (decay width) in the Born approximation with the structure functions of pions and leptons. The pion structure function is given in the explicit form.     

Measurement of the charged pion electromagnetic form factor

Separated longitudinal and transverse structure functions for the reaction 1H(e,e(')pi(+))n were measured in the momentum transfer region Q2 = 0.6--1.6 (GeV/c)(2) at a value of the invariant mass W = 1.95 GeV. New values for the pion charge form factor were extracted from the longitudinal cross section by using a recently developed Regge model. The results indicate that the pion form factor in this region is larger than previously assumed and is consistent with a monopole parametrization fitted to very low Q2 elastic data.     

Local Duality Predictions for x approximately 1 Structure Functions

Recent data on the proton F2 structure function in the resonance region suggest that local quark-hadron duality works remarkably well for each of the low-lying resonances, including the elastic, to rather low values of Q2. We derive model-independent relations between structure functions at x approximately 1 and elastic electromagnetic form factors, and predict the x-->1 behavior of nucleon polarization asymmetries and the neutron to proton structure function ratios from available data on nucleon electric and magnetic form factors.     

Effects of QCD Vacuum and the Instanton Induced-Contributions to the Nucleon Structure Functions

The instanton induced cross section in deep inelastic kinematics is a subject which people are tendentious to investigate it. Instanton induced contributions are well defined for the nucleon structure function. The non-perturbative contribution to the quark distributions of structure function, F2 (x, Q2 ), is considered within an instanton model for the QCD vacuum. We find that the structure function may possess numerically large non-perterbative contributions which are related to the violation of chirality and correspond to the correction of parton distribution of the leading twist. It is shown that the instantons give a negative contribution to the structure function at the NLO approximation. A comparison between our results, considering instantaon effect, and the case when we do not take this effect is done. Taking into account the instanton size, ρ, via the modified running coupling constant we get to a good agreement between our results at the NLO and NNLO approximations and the available experimental data, specially at the low values of the Bjorken variable x0.1 which confirms the validity of our calculations.     

Geometric scaling for the total gamma(*)p cross section in the low x region

We observe that the saturation model of deep inelastic scattering predicts a geometric scaling of the total gamma(*)p cross section in the region of small Bjorken variable x. The geometric scaling in this case means that the cross section is a function of only one dimensionless variable tau = Q(2)R(2)(0)(x), where the function R(0)(x) decreases with decreasing x. We show that the experimental data from HERA in the region x<0.01 confirm the expectations of this scaling over a very broad region of Q(2). We suggest that the geometric scaling is more general than the saturation model.     

Soft-gluon resummation and the valence parton distribution function of the pion

We determine the valence parton distribution function of the pion by performing a new analysis of data for the Drell-Yan process π- N → μ+ μ- X. Compared to previous analyses, we include next-to-leading-logarithmic threshold resummation effects in the calculation of the Drell-Yan cross section. As a result of these, we find a considerably softer valence distribution at high momentum fractions x than obtained in previous next-to-leading-order analyses, in line with expectations based on perturbative-QCD counting rules or Dyson-Schwinger equations.     

Studying the Sivers and Boer-Mulders Function with Lattice QCD

Transverse momentum dependent parton distribution functions (TMDs) characterize the intrinsic momentum distribution of quarks inside the nucleon. However, they also encode final or initial state interactions of the processes in which they are measured, such as semi-inclusive deep inelastic scattering (SIDIS) or the Drell–Yan process (DY). Consequently certain TMDs are process-dependent and predicted to be equal but opposite in sign for SIDIS and DY. Extending our method on the lattice to non-local operators with U-shaped Wilson lines, we can study these naively time-reversal odd TMDs, in particular the Sivers- and the Boer-Mulders function. We express our results in terms of Fourier-transformed TMDs that appear naturally in the Fourier transformed cross section of, e.g., SIDIS, and in Bessel-weighted asymmetries. We discuss the method, its limitations and preliminary results from an exploratory calculation using lattices generated by the MILC and LHP collaborations.     

Determination of the pion charge form factor at Q2=1.60 and 2.45 (GeV/c)2

The 1H(e,e'pi+)n cross section was measured at four-momentum transfers of Q2=1.60 and 2.45 GeV2 at an invariant mass of the photon nucleon system of W=2.22 GeV. The charged pion form factor (F(pi)) was extracted from the data by comparing the separated longitudinal pion electroproduction cross section to a Regge model prediction in which F(pi) is a free parameter. The results indicate that the pion form factor deviates from the charge-radius constrained monopole form at these values of Q2 by one sigma, but is still far from its perturbative quantum chromodynamics prediction.     

2H(e,e(')p)n reaction at high recoil momenta

The 2H(e,e(')p)n cross section was measured in Hall A of the Thomas Jefferson National Accelerator Facility near the top of the quasielastic peak (x(Bj)=0.964) at a four-momentum transfer squared, Q(2)=0.665 (GeV/c) (2) (omega=0.368 GeV, W=2.057 GeV), and for recoil momenta up to 550 MeV/c. The measured cross section deviates by 1-2sigma from a state-of-the-art calculation at low recoil momenta. At high recoil momenta the cross section is well described by the same calculation; however, in this region, final-state interactions and interaction currents are predicted to be large, and alternative choices of nucleon-nucleon potential and nucleon current operator may result in significant spread in the calculations.     

高Q2电子原子核单举准弹性散射截面的计算方法

电子与原子核碰撞实验是通过中高能探针探测原子核结构的方法。本文提供了一个高Q2单举准弹性电子原子核散射截面的计算方法,此方法是基于核子-核子短程关联的经验公式与弱束缚近似下的氘核散射截面模型。在弱束缚近似下,氘核可以看成是由近似自由质子与中子组成,质子与中子的短程关联可以忽略,氘核结构函数可以写成质子与中子结构函数线性组合,从而可以得到氘核的散射截面。根据氘核散射截面以及短程关联的经验公式,可以得到考虑短程关联的原子核A > 2的散射截面。我们将计算得到的散射截面与已有的实验和及Bosted拟合方法的结果比较,发现本文的方法在大x和Q2 > 2 GeV2区域得到的结果与实验结果符合得较好并且对于一些重原子核,尤其是4He核,明显优于Bosted方法的结果。The electron nucleus collision experiments are approaches measuring the structure of nuclei by using intermediate and high energy probe. This paper shows a calculation method of inclusive electron nucleus quasielastic scattering cross section at high Q2 which based on a empirical formula of Nucleon-Nucleon Short Range Correlation (NN-SRC) and a model of electron deuteron quasi-elastic cross section in Weak-Binding Approximation (WBA). In WBA, the deuteron can be regarded as the combination of quasi-free proton and neutron and the short range correlation between them can be ignored. Therefore the structure function of deuteron can be written as the linear combination of that of proton and neutron, then one can get the cross section of deuteron. According to the cross section of deuteron and the empirical formula, one can obtain the cross section of nuclei A > 2 which considers NN-SRC effect. We compare our calculation results with existing experiments and the results calculated by Bosted' fit method, then find that our results match the experiments at high x and Q2 > 2 GeV2 and better significantly than the Bosted's results for some heavier nucleus, especially 4He.     

微扰QCD演化过程中存在遮蔽效应的一个证据

核子的纵向结构函数F_L以及虚光子吸收的纵向和横向散射截面的比值R_L在小X区域主要取决于胶子的分布函数.而胶子的初始分布函数的形式决定了在演化过程中是否要考虑遮蔽效应.利用新的动力学演化方程分析了F_L和R_L,发现在部分子演化过程中存在遮蔽现象.     

Perturbative QCD analysis of local duality in a fixed w2 framework

We study the Q2 dependence of large x F2 nucleon structure function data, with the aim of providing a perturbative QCD based, quantitative analysis of parton-hadron duality. As opposed to previous analyses at fixed x, we use a framework in fixed W2. We uncover a breakdown of the twist-4 approximation with a renormalon type improvement at O(1/Q(4)) which affects the initial evolution of parton distributions.     

One-photon-exchange processes and inelastic form factors

The general form of cross section for one-photon-exchange processes is given. For unpolarized target and projectile the total cross section is determined by two characteristic functions or form factors, for each, target and projectile. For a projectile without strong, but with electromagnetic interaction one can measure the differential cross section and thereby determine both form factors for any target in the region of kinematical variables available by such scattering experiments. These kinematical regions are investigated. One can insert these measured form factors in cross section calculations for other one-photon-exchange processes. As an example we show that for 2 GeV-W-Meson production by neutrinos on a target the kinematical region of form factors which enter the cross section calculation is covered by electron scattering up to 6 GeV. The impulse approximation is used to estimate form factors for electronnucleus scattering in a special kinematical region.