Doubly charged Higgs from e–γ scattering in the 3-3-1 Model

The solution of the Dirac equation with a generalized harmonic oscillator potential is used to extract the constituent bare parton densities. The results are firstly in spatial space which are converted to momentum space, using the Fourier transformation. The final results are presented in terms of the Bjorken x-variable. Employing the effective chiral quark model and the related convolutions, the parton densities inside the proton are obtained. Choosing an appropriate radius of proton, they indicate reasonable behavior. Although the initial framework is completely theoretical, the results for the sea and valence quark densities and also the ratio of d to u valence quarks inside the proton are in good agreement with the available experimental data and some theoretical models.     

A new approach to calculate the gluon polarization

We derive the Leading-Order (LO) master equation to extract the polarized gluon distribution G(x,Q ²)=xδg(x,Q ²) from polarized proton structure function, g^p₁(x,Q²)g^{p}_{1}(x,Q^{2}). By using a Laplace-transform technique, we solve the master equation and derive the polarized gluon distribution inside the proton. The test of accuracy which is based in our calculations on two different methods, confirms that we achieve to the correct solution for the polarized gluon distribution. To determine the polarized gluon distribution xδg(x,Q ²) more accurately, we only need to have more experimental data on the polarized structure functions, g₁^p(x,Q²)g_{1}^{p}(x,Q^{2}). Our result for polarized gluon distribution is in good agreement with some phenomenological models.     

The Leading-Order Charm Quark Contribution to the Next-to-Leading-Order Proton Structure Function Using {\cal A}=3 Mirror Nuclei as Input Valence Quarks

The charm quark contribution to the proton structure function (SF) is investigated in the leading-order (LO) QCD at small x region. A next-to-leading order (NLO) QCD analysis for the proton SF is made within the renormalization scheme of the radiation parton evolution model (DGLAP). The valence quark distribution is obtained from the relativistic quark-exchange calculation for the mirror nuclei, i.e., ³He and ³H, which is based on a realistic model. The inverse Mellin technique is performed to extract the parton distribution in the (x, Q ²)-plane. The calculated F ₂ ^c (x, Q ²) and F ₂ ^p (x, Q ²) as well as the longitudinal SF, F _L ^p (x, Q ²) are compared with the experimental data available at present, namely H1, ZEUS, and HERMES at HERA ring as well as other theoretical models, especially the hard pomeron phenomenological model.     

The NLO Parton Distribution in the (x, Q 2)-Plane: A Relativistic Quark-Exchange Approach to A = 3 Mirror Nuclei

A next-to-leading order QCD analysis of polarized and unpolarized structure functions of the proton in the (x, Q²)-plane is discussed within the scheme of the radiation parton formalism. The valence quark distribution is obtained from the application of the relativistic quark-exchange model to A = 3 mirror nuclei, i.e., ³He and ³H. The sea quark and gluon distributions are calculated using the inverse Mellin technique in the NLO approximation. A comparison is made with the corresponding available experimental data. We find a good fit for F₂^p(x, Q²) to the data. It is shown that our new NLO calculation improves our previous works. We argue that the valence quark scenario at some μ₀² ≪ Q² is a reasonable assumption in the framework of the DGLAP evolution equation. In agreement with the data, it is demonstrated that the asymmetry A₁^p(x, Q²) has no significant Q²-dependence as we go to the small x, even at NLO limit. Finally we argue that for small x ≤ 0.2 it is a good approximation to consider ³He and ³H structure functions as those of neutrons and protons, respectively.     

Target mass correction on the 3He polarized structure function

Target mass correction (TMC) is employed to amend the polarized helium structure functions, ³He . The structure function can be obtained via the convolution of the light cone momentum distribution with the polarized structure of the proton and neutron. The calculation of the polarized structure function of the nucleon is based on the constituent quark model. The analytical result for ³He polarized structure function at low values of Q² is not in good agreement with the available experimental data. The reliability of calculations is increased using TMC effect. New comparison confirms a better agreement with the experimental data.     

How can we properly define the Q2 dependent parton distribution function in QCD?

We discuss how we can properly define the Q² dependent parton distribution functions in quantum chromodynamics within the framework of the operator product expansion and renormalization group techniques. It is proposed that the moments of the parton distribution functions at Q² should be defined as the hadronic expectation values of the twist-2 operators renormalized at Q². The integro-differential equations for the parton densities obtained by Altarelli and Parisi are reproduced in the leading logarithmic approximation. An application of our present formalism will be given in the case of a longitudinal structure function.     

Highlights and perspectives of the JLab spin physics program

Nucleon spin structure has been an active, exciting and intriguing subject of interest for the last three decades. Recent precision spin-structure data from Jefferson Lab have significantly advanced our knowledge of nucleon structure in the valence quark (high-x) region and improved our understanding of higher-twist effects, spin sum rules and quark-hadron duality. First, results of spin sum rules and polarizabilities in the low to intermediate Q ² region are presented. Comparison with theoretical calculations, in particular with Chiral Perturbation Theory (ChPT) calculations, are discussed. Surprising disagreements of ChPT calculations with experimental results on the generalized spin polarizability, δ _LT, were found. Then, precision measurements of the spin asymmetry, A ₁, in the high-x region are presented. They provide crucial input for global fits to world data to extract polarized parton distribution functions. The up and down quark spin distributions in the nucleon were extracted. The results for Δd/d disagree with the leading-order pQCD prediction assuming hadron helicity conservation. Results of precision measurements of the g ₂ structure function to study higher-twist effects are presented. The data indicate a significant higher-twist (twist-3 or higher) effect. The second moment of the spin structure functions and the twist-3 matrix element d ₂ results were extracted. The high Q ² result was compared with a Lattice QCD calculation. Results on the resonance spin-structure functions in the intermediate Q ² range are presented, which, in combination with DIS data, enable a detailed study of quark-hadron duality in spin-structure functions. Finally, an experiment to study neutron transversity and transverse spin asymmetries is discussed. A future plan with the 12 GeV energy upgrade at JLab is briefly outlined.     

Nonperturbative parton distributions and the proton spin problem

The Lorentz contracted form of the static wave functions is used to calculate the valence parton distributions for mesons and baryons, boosting the rest frame solutions of the path integral Hamiltonian. It is argued that nonperturbative parton densities are due to excitedmultigluon baryon states. A simplemodel is proposed for these states ensuring realistic behavior of valence and sea quarks and gluon parton densities at Q² = 10 (GeV/c)². Applying the same model to the proton spin problem one obtains Σ₃ = 0.18 for the same Q².     

The role of screening corrections in smallx-behaviour of structure functions

We consider the influence of shadowing effects on the proton structure function in the small-x interval. The gluon-gluon shadowing are noticeable in the HERA kinematical region while the screening of the quark component of the structure function effects negligibly the gluon distribution. The only noticeable effect is the decreasing of sea quark densities at small-x. The explicit form of the gluon distribution in the proton depends significantly on the form of used boundary condition atQ ²=Q ₀ ² . We consider also difference of results obtained with the help of Kuraev-Lipatov-Fadin and Altarelli-Parisi evolution equations.     

Pion parton distributions in a nonlocal Lagrangian

We use phenomenological nonlocal Lagrangians, which lead to nontrivial forms for the quark propagator, to describe the pion. We define a procedure based on previous studies on nonlocal Lagrangians for the calculation of the pion parton distributions at low Q². The obtained parton distributions fulfill all the wishful properties. Using a convolution approach we incorporate the composite character of the constituent quarks. We evolve, using the Renormalization Group, the calculated parton distributions to the experimental scale and compare favorably with the data and draw conclusions.     

Structure functions of bound nucleons: From the EMC effect to nuclear shadowing

We describe the nuclear structure functions in the whole range of the Bjorken variablex, by combining various effects in a many-step procedure. First, we present a QCD motivated model of nucleons, treated, in the limit of vanishingQ ², as bound states of three relativistic constituent quarks. Gluons and sea quarks are generated radiatively from the input valence quarks. All parton distributions are described in terms of the confinement (or nucleon's) radius. The results for free nucleons are in agreement with the experimental determinations. The structure functions of bound nucleons are calculated by assuming that the main effect of nucleon binding is stretching of nucleons. The larger size of bound nucleons lowers the valence momentum and enhances the radiatively generated glue and sea densities. In the small-x region the competitive mechanism of nuclear shadowing takes place. It also depends on the size of the nucleons. By combining stretching, shadowing and Fermi motion effects (the latter confined to very largex), the structure function ratio is well reproduced. Results are also presented for theA-dependence of the momentum integral of charged partons, the nuclear gluon distribution and the hadron-nuclei cross sections.     

Model for nucleon gluon and sea quark structure functions at allx and allQ 2 from the correspondence between QCD and DTU

We propose a simple parametrization of the nucleon gluon and sea quark structure functions at allx, and allQ ². We use the DTU parton model to fix the parametrization at a reference point (Q ₀ ² =1.25 GeV² andA ²=0.01 GeV²) and we mimic the QCD evolution by replacing the dimensioned parameters of the DTU parton model by functions depending onQ ².     

Current and constituent quarks: Their implications for resonance excitations polarized and unpolarized inelastic structure functions

The transformation between constituent and current quarks is discussed and applied to the calculation of matrix elements for nucleon to resonance transitions induced by arbitrary currents belonging to an octet. In particular, previous results on πN and γN transitions are subsumed while weak interactions (ΔQ = 0 or 1) and longitudinal photon induced transitions are discussed for the first time. The implications of a non-trivial Melosh transformation upon previous calculations in quark parton models of the non-diffractive component of the deep inelastic structure functions are discussed. The magnitudes of the unpolarized structure functions are found to be unchanged but for the polarized structure functions significant corrections to previous calculations are discovered. In particular it is found that it is not necessary that the polarization asymmetry A^γP be positive in the deep inelastic region. Our approach is valid for all Q², even for photoproduction, and is not restricted to deep inelastic scattering in contrast to earlier parton model calculations. The saturation of various current algebra sum rules is discussed.     

On the Q2 dependence of parton fragmentation functions

The Q² dependences of parton fragmentation functions are calculated using lowest-order quantum chromodynamics (QCD). The resulting scaling deviations have a simple intuitive form when a suitable valence-sea decomposition is employed for the quark fragmentation functions.     

Scaling and non-scaling in a rest frame quark-parton model of the proton

Electron-proton deep inelastic scattering is treated as the incoherent scattering of electrons by bound Dirac partons in the proton rest frame. An approximate bound state wave function is used for the initial parton, while the final parton is considered free. A good fit is obtained to the structure function F₁(x,Q²) in the range x > 0.15, Q² > 2 GeV. The subsequent prediction for F₂(x,Q²) is not as good, indicating a small additional contribution by longitudinal photons for W < 2.5 GeV. The parton momentum distribution is found to contain transverse momentum of 400–600 MeV, increasing with x.     

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.     

The Constituent Quark Exchange Model for the Bound State Nucleons

The aim of present article is to compare the different bound state parton distributions in the protons with those coming from the free protons experimental data and to investigate the effect of quark structure of protons on each other. So, the constituent quark model (CQM), in which the quarks are assumed to be the complex objects and was originally proposed by Altarelli et al. (ACMP), is used in the frame work of the quark exchange model (QEM) to calculate the parton distributions of bound protons. Unlike our previous works, the effect of sea quarks and gluons are included in the QEM. Our results are in agreement with those of Glück et al. (GRV) when we ignore the binding and the Fermi motion effects for the constituent quarks. In this case, we get more sea-quarks and gluons with respect to the bound state constituents quarks calculation. It is also shown that the QEM, which is a realistic formalism gives better result with respect to the Isgur and Karl et al. model which is a field theoretical approach. The ratio of the structure functions of neutron to proton is also calculated with the assumption of isospin symmetry and it is compared with the available data and our previous works.     

Nuclear shadowing in Glauber–Gribov theory with Q 2-evolution

We consider deep inelastic scattering off nuclei in the Regge limit within the Glauber–Gribov model. Using unitarized parton distribution functions for the proton, we find sizeable shadowing effects on the nuclear total and longitudinal structure functions, $F_{2}^{A}$ and $F_{L}^{A}$ , in the low-x limit. Extending a fan-diagram analysis for the large-mass region of coherent diffraction off nuclei to high Q ², we also find significant shadowing effects in this kinematical regime. Finally, we discuss the shortcomings of our approach and possible extensions of the model to other kinematical regimes.