Abstract
We apply a dynamical three-constituent quark light-front model to study the proton. The dynamics is based on the notion of a diquark (bound or virtual) as the dominant interaction channel, which paramaterizes a contact interaction between the quarks in order to build the three-body Faddeev Bethe-Salpeter equations for the valence state, and we focus on the totally symmetric part of the wave function. The Dirac electromagnetic form factor is used to fix the model parameters, and the valence wave function is obtained. From that we investigate its Ioffe-time image, non-polarized longitudinal and transverse momentum distributions, and the double momentum distribution.
Highlights
The complex nucleon wave function on the null plane ðxþ 1⁄4 t þ z 1⁄4 0Þ expressed in the Fock space in terms of its constituent degrees of freedom, namely quarks and gluons at a given scale μ and strongly interacting, provides the image through the associated probability densities [1,2,3]
We observe an exponential damping of the probability density with the relative separation between the Ioffe time of the two quarks, and the damping is expected to be more sizable if confinement is incorporated as it is effective at large distances
The trapezoid shaped boundary observed for model II can be associated with the strong damping of the parton distribution functions (PDFs) above x ∼ 0.6 seen in Fig. 5 and to its peak around x ∼ 0.35, these two properties compete to provide the form seen in the upper panel of Fig. 6
Summary
The complex nucleon wave function on the null plane ðxþ 1⁄4 t þ z 1⁄4 0Þ expressed in the Fock space in terms of its constituent degrees of freedom, namely quarks and gluons at a given scale μ and strongly interacting, provides the image through the associated probability densities [1,2,3]. GTMDs are associated to matrix elements of bilocal partonic field operators with separation in all three light-front coordinates defined onto the null-plane hypersurface They are off-forward matrix elements between hadron states, which depend on the partons longitudinal transverse momentum components. × hp; λjOðy; z1ÞOð0; z2Þjp; λi; ð6Þ λ which has been obtained for the nucleon by recent LQCD calculations for different operator structures [22] Despite such efforts, it is useful to obtain the DPDFs at the nucleon scale and identifying properties of the LF wave function, as for example using anti–de Sitter/QCD approach [23] and LF constituent quark models (see, e.g., [24]). We aim to explore the proton bound-state structure in terms of constituent quarks degrees of freedom by calculating the valence LF wave function, where our focus is to study its Ioffe time representation, as well as the different one- and two-quark momentum distributions. The work is completed by two appendices: in Appendix A the derivation of the main dynamical integral equation of the model is given, and in Appendix B is presented the adopted numerical method to solve it
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