Parton Distributions in Nucleon on the Basis of a Relativistic Independent Quark Model

Abstract

At a low resolution scale with $Q^2=μ^2$ corresponding to the nucleon bound state; deep inelastic unpolarized structure functions $F_1(x,μ^2)$ and $F_2(x,μ^2)$ are derived with correct support using the symmetric part of the hadronic tensor under some simplifying assumptions in the Bjorken limit. For doing this; the nucleon in its ground state has been represented by a suitably constructed momentum wave packet of its valence quarks in their appropriate SU(6) spin flavor configuration with the momentum probability amplitude taken phenomenologically in reference to the independent quark model of scalar-vector harmonic potential. The valence quark distribution functions $u_v(x,μ^2)$ and $d_v(x,μ^2)$, extracted from the structure function $F_1(x,μ^2)$ in a parton model interpretation, satisfy normalization constraints as well as the momentum sum-rule requirements at a bound state scale of $μ^2=0.1 GeV^2$. QCD evolution of these distribution functions taken as the inputs; yields at $Q_0^2=15 GeV^2; xu_v(x,Q_0^2)$ and $xd_v(x,Q_0^2)$ in good qualitative agreement with the experimental data. The gluon distribution $G(x,Q_0^2)$ and the sea-quark distribution $q_s(x,Q_0^2)$; which are dynamically generated using the leading order renormalization group equation; also match reasonably well with the available experimental data.