Sea quark densities in the nucleon, based on the constituent quark model are analyzed. To model the asymmetry of these densities, the meson cloud or alternatively chiral quark model (χQM) is used. Valence quark densities of the meson which are required to extract the sea quark densities in the constituent quarks are obtained using the phenomenological valon model. In addition to the standard perturbative QCD approach which uses the [Formula: see text] scheme with a physical choice of renormalization scale, the calculations are also performed using the complete RG-improvement (CORGI) approach. To avoid a physically unacceptable Q2 behavior of the sea densities inside the constituent quarks, we assume that the free parameter which exists in the vertex function of the boson–quark splitting function, is Q2-dependent. Using the unsymmetrized sea densities of the nucleon which result from convoluting the constituent density in a nucleon with the quark density in the constituent quark, the Gottfried sum rule (GSR) is calculated using the standard perturbative and CORGI approaches. The CORGI result is closer to the reported experimental value for the GSR. The extracted sea and valence quark density in a nucleon, using χQM and also the CORGI approach, have been compared with available experimental data and what was obtained, based on χQM in the standard approach. This comparison confirms the anticipated better agreement of the CORGI approach with the data.
Sea quark distributions in the NLO approximation, based on the phenomenological valon model or constituent quark model are analyzed. We use the parametrized inverse Mellin transform technique to perform a direct fit with available experimental data and obtain the unknown parameters of the distributions. We try to extend the calculation to the NLO approximation for the singlet and nonsinglet cases in DIS phenomena. We do also the same calculation for electron–positron annihilation. The resulting sea distributions are effectively independent of the process used. The approach of complete RG improvement (CORGI) is employed and the results are compared with the standard approach of perturbative QCD in the [Formula: see text] scheme with a physical scale. The comparisons with data are in good agreement. As is expected, the results in the CORGI approach indicate a better agreement to the data than the NLO calculation in the standard approach.
We employ the polarized chiral constituent quarks to extract the polarized structure function of the nucleon. The polarized valon model is used to calculate the spin dependence of parton distribution functions of meson. The connection between the polarized structure of the proton and the Goldstone bosons, using the chiral quark model (χQM) is analyzed and the spin dependence of the parton distribution functions for pion and kaon, is obtained thoroughly. These functions are evolved to high Q2 values, using the singlet, nonsinglet and quark–gluon moments (ΔMS, ΔMNS, ΔMgq) which are convoluted with the polarized valon distributions. The polarized valon distributions for meson are computed, based on a phenomenological method and a comparison between polarized and unpolarized parton distribution functions for pion and kaon are performed. As a consequence of the χQM, the SU (3)f symmetry breaking for the spin dependent of the nucleon sea distributions is achieved. The required polarized parton distributions of the proton will be obtained from the parton distribution functions of the polarized meson via the related convolution integral which are existed in the χQM. Following that the analytical result for the proton's spin structure function, [Formula: see text], is obtained and compared with experimental data. Finally, the parton orbital angular momentum of meson are introduced and the total spin of the meson, based on this quantity and the first moment of distributions for gluon and singlet sectors, are obtained.
The polarized distribution functions of mesons, including pion, kaon and eta, using the proton structure function, are calculated. We are looking for a relationship between the polarized distribution of mesons and the polarized structure of nucleons. We show that the meson polarized parton distributions leads to zero total spin for mesons, considering the orbital angular momentum of quarks and gluons inside the meson. Two separate Monte Carlo algorithms are applied to compute the polarized parton distributions of the kaon. Via the mass dependence of quark distributions, the distribution function of the eta meson is obtained. A new method by which the polarized sea quark distributions of protons are evolved separately -which cannot be performed easily using the standard solution of DGLAP equations -is introduced. The mass dependence of these distributions is obtained, using the renormalization group equation which makes their evolutions more precise. Comparison between the evolved distributions and the available experimental data validates the suggested solutions for separate evolutions.In Part 1, we calculate the bare quark distributions using the proton polarized structure function g p 1 (x), using data from [10]. Then we compute the ratio of the polarized valence data of kaons to that of pions, δq K val /δq π val , using the data for their unpolarized ratio, q K val /q π val [11], based on two separate Monte Carlo algorithms. We also calculate the polarized valence ratio of eta mesons to pions, δq η val /δq π val , using the mass dependence of the valence quark distribution inside the meson. Substituting these ratios into the chiral quark model (χQM) equations and fitting with experimental data (or any reasonable phenomenological model), the polarized distribution functions in pion, kaon and eta mesons at low energy scales will be obtained. Following that, the evolution of the PDFs, employing the DGLAP equations, can be done straightforwardly [12][13][14][15]. Using these evolved PDFs, we can extract the values of the orbital angular momentum of quarks and gluons inside mesons [6].In Part 2, the PPDFs of the proton, using the distributions extracted for mesons, are calculated. The valence PPDF of the proton can be evolved easily using the non-singlet moment δM NS . Since the DGLAP equations can thoroughly evolve only the sea quark distribution, however, the evolution of the separated sea quarks is more complicated. There are reasonable methods to separate the evolution of sea quarks [16] but in this work we use the running mass and renormalization equation to make the sea quark distribution functions depend on the quark masses. Thereby, the eigenvalues of the evolution operator become non-degenerate. The sea quark distributions at low scale Q 2 0 , arising from χQM , are unsymmetrized. The different eigenvalues of the evolution operator, which are obtained as a result of the new method introduced in this paper, makes the evolution of sea quark densities more distinctive than what we obtained in [17]. Two bounda...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.