A Non-perturbative Model of Mean Field Valence Quarks
May 06, 2020
May 26, 2020
We present a new approach for the calculation of the valence quark distributions in the nucleon based on the scenario in which the spectrum of the valence quarks at $x>0.05$ is generated through three main mechanisms: interaction of valence quarks with the mean field generated by the residual nucleon system, two and three quark short range interactions through gluon exchanges. In the current report we present the first phase of the project in which we develop a non-perturbative model for valence quark interaction in the mean field of the nucleonic interior to describe their distribution in the moderate x region ($0.05\le x \le 0.4$). The short range quark-quark interaction effects in our approach generate the high $x$ tail of valence quark distributions. The presented non-perturbative model is based on the picture in which three relativistic valence quarks occupy the nucleon core at distances of $\le 0.5$ Fm while interacting in the mean field generated by the residual nucleon system. The calculations are based on the assumption of the a factorization of the internal interaction of short-range three valence quarks with the long-range interaction of these quarks with the residual system. The theoretical approach is based on effective light-front diagrammatic approach which allows us to introduce the valence quark and residual system wave functions in a consistent way The parameters of these wave functions are fixed by the position of the peak of the $xf_q(x)$ distribution of valence quarks at $Q_0$ corresponding to the charm-quark mass. With few parameters we achieved a very reasonable description of the up and down valence quark distributions in the moderate $x$ region ($x\le 0.4$), where one expects the mean field dynamics to dominate. The model, however, systematically underestimates the high $x$ region where enhanced contributions from partonic short-range correlations are expected.
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