Residual Mean Field Model of Valence Quarks in the Nucleon

Abstract

We develop a non-perturbative model for valence parton distribution functions (PDFs) based on the mean field interactions of valence quarks in the nucleonic interior. The main motivation for the model is to obtain a mean field description of the valence quarks as a baseline to study the short range quark-quark interactions that generate the high $x$ tail of PDFs. The model is based on the separation of the valence three-quark cluster and residual system in the nucleon. Then the nucleon structure function is calculated within the effective light-front diagrammatic approach introducing nonperturbative light-front valence quark and residual wave functions. Within the model a new relation is obtained between the position, $x_p$, of the peak of $xq_V(x)$ distribution of the valence quark and the effective mass of the residual system, $m_R$, in the form: $x_{p} \approx {1\over 4} (1-{m_R\over m_N})$ at starting $Q^2$. This relation explains the difference in the peak positions for d- and u- quarks through the expected difference of residual masses for valence d- and u- quark distributions. The parameters of the model are fixed by fitting the calculated valence quark distributions to the phenomenological PDFs. This allowed us to estimate the overall mean field contribution in baryonic and momentum sum rules for valence d- and u- quarks. Finally, the evaluated parameters of the non-perturbative wave functions of valence 3q-cluster and residual system can be used in calculation of other quantities such as nucleon form factors, generalized partonic and transverse momentum distributions.