Structure Function of the Bound Proton in the Dressed-quark Exchange Formalism

The idea of the dressed quark scenario, in the context of the quark exchange model has been used to obtain the bound parton distribution functions as well as the bound proton structure function. The Glück, Reya, and Vogt (GRV)’s parton distribution functions, where they have a good agreement with the experimental data in the whole range of (x, Q²)-region, have been used to extract the amount of the momentum carried by each parton inside the proton; therefore, by using these values, the different parton densities inside the constituent quark have been calculated. To extract the parton distribution functions in the bound proton, the phenomenological constituent quark exchange formalism and the nuclear convolution theorem have been used. By considering these densities, the structure function of the bound proton, \({F_{2}^{P}}(x,Q^{2})\), inside the light nuclei like helium-3 or tritium has been calculated at low- and high-Q² values. The correctness of the calculations has been tested through computing the difference of the proton-neutron structure functions as well as the ratio of the neutron to the proton structure functions, in which they are well known from experimental data. The results of the present study are in an agreement with both the available and relevant experimental data and the theoretical predictions.

     

Spinor fields in the theory of relativity and a generalization of Heisenberg's nonlinear spinor equation

Some years ago it was shown that the nonlinear term of Heisenberg's spinor equation can be derived by torsion of the Minkowski space (Cartan space). This result is applied in the investigations of this paper. As the Heisenberg equation does not show any connection with recent phenomenological theories in high energy physics, like the parton or quark model, the problems of the metric of space-time are discussed from the aspect of fundamental axioms of topology (Hausdorff space). It will be shown that Feynman's relativistic parton theory can be derived by means of a quantised de Sitter space, where the constant curvature can assume only discrete values. It is also possible to derive the Dirac equation from the same mathematical considerations. A nonlinear spinor equation will be formulated which contains the parton theory and the nonlinear term of the Heisenberg equation as different approaches in the theory of elementary particles.     

Equivalence of the “Wilson expansion” and a generalized parton model

For a target made with constituents which interact via an asymptotically free theory, it is possible to define some parton densities in the deep inelastic region and at any order of the running coupling constant. These densities depend only on the structure of the target and their Q² dependence is governed by master equations. At first order the result of Altarelli and Parisi is recovered. The scattering of any current off the target is described by a convolution of these parton densities with some charge densities, depending on the couplings of the current to the partons. All those results are equivalent to those of the Wilson operator formalism. Some explicit examples are given.     

The scale dependent nuclear effects in parton distributions for practical applications

The scale dependence of the ratios of parton distributions in a proton of a nucleus A and in the free proton, , is studied within the framework of the lowest order leading-twist DGLAP evolution. By evolving the initial nuclear distributions obtained with the GRV-LO and CTEQ4L sets at a scale , we show that the ratios are only moderately sensitive to the choice of a specific modern set of free parton distributions. We propose that to a good first approximation, this parton distribution set-dependence of the nuclear ratios can be neglected in practical applications. With this result, we offer a numerical parametrization of for all parton flavours i in any , and at any and any for computing cross sections of hard processes in nuclear collisions. Received: 10 August 1998 / Published online: 27 April 1999     

Probing the color glass condensate in an electron-ion collider

Perturbative quantum chromodynamics (pQCD) predicts that the small-x gluons in a hadron wavefunction should form a color glass condensate (CGC), characterized by a saturation scale Q_s(x,A), which is energy and atomic number dependent. In this paper, we study the predictions of CGC physics for electron-ion collisions at high energies. We consider that the nucleus at high energies acts as an amplifier of the physics of high parton densities and estimate the nuclear structure function F₂^A(x,Q²), as well as the longitudinal and charm contributions, using a generalization for nuclear targets of the Iancu–Itakura–Munier model that describes the ep HERA data quite well. Moreover, we investigate the behavior of the logarithmic slopes of the total and longitudinal structure functions in the kinematical region of the future electron-ion collider eRHIC.     

Interpretation of the NuTeV experiment

The NuTeV neutrino measurement of the Weinberg angle differs by 3 standard deviations from measurements at the Z pole. We review the status of various possibilities to explain this result, including contributions from physics outside the standard model; effects of radiative corrections; nuclear corrections to parton distributions; isospin-violating effects; and effects due to strange quarks.     

When is a heavy quark not a parton? Charged Higgs production and heavy quark mass effects in the QCD-based parton model

Several issues pertaining to the application of the QCD-based parton model to new physics processes involving heavy partons are described and quantitatively studied using charged Higgs boson production as a prime example. The naive parton model predictions are found to over-estimate the actual cross section by a factor of 2 to 5, depending on the top-quark and Higgs masses. The role of the top quark as a “parton” is examined by a detailed study of the cancellation between the straight parton model contribution and a subtraction term required by QCD corrections. The accuracy of the zero-mass method for evaluating the first-order QCD correction is assessed (in light of the potentially large mass of the top quark) by a quantitative analysis of the cancellation of mass singularities between the correction terms. A pragmatic procedure for calculation based on a renormalization scheme without the heavy quark-parton is formulated and compared with the usual perturbative QCD formalism. The energy ranges over which heavy quarks (or other particles) should or should not be naturally treated as “partons” are delineated. Properly evolved parton distribution functions relevant to the specific renormalization schemes considered are employed for all the numerical studies in order to ensure consistency in the QCD framework.     

Nucleon/nuclei polarized structure function,using Jacobi polynomials expansion

We use the constituent quark model to extract polarized parton distributions and finally polarized nucleon structure function.Due to limited experimental data which do not cover whole(x,Q2)plane and to increase the reliability of the fitting,we employ the Jacobi orthogonal polynomials expansion.It will be possible to extract the polarized structure functions for Helium,using the convolution of the nucleon polarized structure functions with the light cone moment distribution.The results are in good agreement with available experimental data and some theoretical models.     

Electron-ion collider in China

Lepton scattering is an established ideal tool for studying inner structure of small particles such as nucleons as well as nuclei. As a future high energy nuclear physics project, an Electron-ion collider in China (EicC) has been proposed. It will be constructed based on an upgraded heavy-ion accelerator, High Intensity heavy-ion Accelerator Facility (HIAF) which is currently under construction, together with a new electron ring. The proposed collider will provide highly polarized electrons (with a po- larization of 80%) and protons (with a polarization of 70%) with variable center of mass energies from 15 to 20 GeV and the luminosity of (2–3)×10³³ cm−2•s−1. Polarized deuterons and Helium-3, as well as unpolarized ion beams from Carbon to Uranium, will be also available at the EicC.The main foci of the EicC will be precision measurements of the structure of the nucleon in the sea quark region, including 3D tomography of nucleon; the partonic structure of nuclei and the parton interaction with the nuclear environment; the exotic states, especially those with heavy flavor quark contents. In addition, issues fundamental to understanding the origin of mass could be addressed by measurements of heavy quarkonia near-threshold production at the EicC. In order to achieve the above-mentioned physics goals, a hermetical detector system will be constructed with cutting-edge technologies.This document is the result of collective contributions and valuable inputs from experts across the globe. The EicC physics program complements the ongoing scientific programs at the Jefferson Laboratory and the future EIC project in the United States. The success of this project will also advance both nuclear and particle physics as well as accelerator and detector technology in China.     

Comparisons Between Additional Parton Evolution and Q2-Rescaling Models Based on Recombination Effect

Comparisons between the additional parton evolution (APE) model and Q²-rescaling (QR) model based on the recombination effect are made by means of investigating deep-inelastic (DIS) structure functions F₂^A, nuclear Drell-Yan process and nuclear gluon distributions. While explaining experimentally measured F₂^A(x) structure functions, the difference in the recombination results of the two models mainly lies in their sensitivity to input parton distributions and Q²-dependence. In predicting the nuclear Drell-Yan ratio, the APE model gives more reasonable results in the small x region than those of the QR model. The two motlels offer similar predictions of the nuclear gluon ratio G_sn(x)/G_c(x) which are extracted from the inelastic J/ψ production process.     

Multiple parton scattering in nuclei: twist-four nuclear matrix elements and off-forward parton distributions

Multiple parton scatterings inside a large nucleus generally involve higher-twist nuclear parton matrix elements. The gluon bremsstrahlung induced by multiple scattering depends not only on direct parton matrix elements but also on momentum-crossed ones, due to the Landau–Pomeranchuk–Migdal interference effect. We show that both types of twist-four nuclear parton matrix elements can be factorized approximately into the product of twist-two nucleon matrix elements in the limit of extremely large nuclei, A→∞, as assumed in previous studies. Due to the correlative nature of the twist-four matrix elements under consideration, it is actually the off-forward parton distributions that appear naturally in this decomposition, rather than the ordinary diagonal distributions probed in deeply-inelastic scattering. However, we argue that the difference between these two distribution classes is small in certain kinematic regimes. In these regions, the twist-four nuclear parton matrix elements are evaluated numerically and compared to the factorized form for different nuclear sizes within a schematic model of the two-nucleon correlation function. The nuclear size dependence is found to be A^4/3 in the limit of large A, as expected. We find that the factorization is reasonably good when the momentum fraction carried by the gluon field is moderate. The deviation can be more than a factor of 2, however, for small gluon momentum fractions, where the gluon distribution is very large.     

核子(强子)结构和性质的QCD研究

核子 (强子 )是夸克、胶子的束缚态 ,由量子色动力学 QCD描述。由于 QCD的基本特性(高能标度下的渐近自由、低能标度下色禁闭及动力学手征对称性破缺 ) ,对核子 (强子 )结构和性质的 QCD图象是标度相关的 .在高能标度下描述强子的是与探测强子结构的硬过程相联系的QCD部分子模型 .强子的夸克、胶子结构信息通过 QCD部分子求和规则得到 .QCD微扰论是适用的理论 .在低能标度时 ,必须发展 QCD非微扰途径来描述核子 (强子 )物理 .这里简要地讨论各种非微扰途径 (格点 QCD、Dyson- Schwinger方程、有效场论、QCD求和规则 )的某些结果和进展 ,并指出 QCD真空结构在描述低能标度下强子物理中担任重要角色 . The nucleon (hadron) is the bound state of guarks and gluons, which is described by the quantum chromodynamics (QCD). Due to the basic properties of QCD (the asymptotic freedom at the high energy scale, the color confinement and the dynamical chiral symmetry breaking at the low energy scale), the QCD picture for the nucleon’s (hadron’s) structure and property is scale dependent. At high energy scale, the QCD parton model, which is relative to the hard process for testing the...     

The anomalous behaviour of nuclear structure functions revisited

The anomalous behaviour of the nuclear structure functions is discussed in the framework of a simple statistical parton model, where the nucleus is treated as a bag of uncorrelated partons. We show that the model reproduces correctly the main features of the effect and, to some extent, it is even successful at the numerical level. The characteristic prediction of the model (to be tested experimentally) is a saturation law: for largeA (=nuclear mass number) the anomalous nuclear behaviour of the structure functions is described by a universal (i.e.A-independent) function of the Bjorken variable.     

Nuclear shadowing and Drell-Yan production on heavy nuclei

The suggestion that nuclear shadowing in deep inelastic scattering is primarily a parton phenomenon is extended to the Drell-Yan reaction on heavy nuclei. The nuclear structure functions required to describe the latter process are found to be compatible with those obtained from an analysis of the shadowing data, and lend weight to the hypothesis that this is indeed a parton phenomenon.     

改进的部分子演化模型及其对EMC效应和核Drell－Yan过程的解释

用解析方法证明了部分子演化模型可为双重Ｘ重新标度模型提供物理基础，进而利用修正的Ａｌｔｅｒａｌｌｉ－Ｐａｒｉｓｉ方程描述小ｘ区域的核遮蔽和反遮蔽效应，以改进部分子演化模型，使我们不必引入核遮蔽因子便可统一地描述ＥＭＣ效应、核遮蔽和反遮蔽效应．最后，利用改进的部分子演化模型相当好地解释了核Ｄｒｅｌｌ－Ｙａｎ过程的实验数据．     

Factorisation scale independence,the connection between alternative explanations of the EMC effect and QCD predictions for nuclear properties

We examine different models for deep inelastic scattering in nuclei in the context of the operator product expansion where the operator matrix elements involve a factorisation scale characterising the separation of short or long distance physics. By exploiting the independence of physical quantities upon this scale we can connect seemingly different models for the nucleus such as dynamical rescaling and the standard convolution models of nuclear physics, allowing nuclear properties to be simply expressed in terms of the anomalous dimensions of QCD. We discuss how non-convolution contributions may also be described by dynamical rescaling and we show how to extend dynamical rescaling to describe spin dependent quantities.     

A New Effect in the QCD Fusion of Nuclear Partons

The parton fusion in nucleus at the leading order of recombination is investigated based on perturbative QCD. We compute various cut diagrams including the nuclear parton fusion, and find that the parton-fusion effects depend on the nuclear QCD structure.     

Extraction of the x-dependence of the non-perturbative QCD b-quark fragmentation distribution component

Using recent measurements of the b-quark fragmentation distribution obtained in events, registered at the Z pole, the non-perturbative QCD component of the distribution has been extracted independently of any hadronic physics modelling. This distribution depends only on the way the perturbative QCD component has been denned. When the perturbative QCD component is taken from a parton shower Monte Carlo, the non-perturbative QCD component is rather similar with those obtained from the Lund or Bowler models. When the perturbative QCD component is the result of an analytic NLL computation, the non-perturbative QCD component has to be extended in a non-physical region and thus cannot be described by any hadronic modelling. In the two examples, used to characterize these two situations, which are studied at present, it happens that the extracted non-perturbative QCD distribution has the same shape, being simply translated to higher-x values in the second approach, illustrating the ability of the analytic perturbative QCD approach to account for softer gluon radiation than with a parton shower generator.     

A pQCD-based approach to parton production and equilibration in high-energy nuclear collisions

A pQCD-based model for parton production and equilibration in ultrarelativistic heavy-ion collisions is reviewed. The model combines pQCD processes including initial and final state radiations together with string phenomenology for nonperturbative soft processes. Nuclear effects on the initial parton production, such as multiple parton scattering and nuclear shadowing of parton distribution functions are considered. Comparisons with existing data are made and further tests of the model to constrain model parameters are proposed. With the obtained space-time history of the parton production, evolution of the minijet gas toward a fully equilibrated parton plasma is studied. Direct probes of the early parton dynamics, such as pre-equilibrium photon and dilepton production, open charm production, J/ψ suppression and jet quenching are also reviewed.