Meson polarized distribution function and mass dependence of the nucleon parton densities

Abstract

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...