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Register a new userA Euclidean bridge to the relativistic constituent quark model
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${bf Background}$ Knowledge of nucleon structure is today ever more of a precision science, with heightened theoretical and experimental activity expected in coming years. At the same time, a persistent gap lingers between theoretical approaches grounded in Euclidean methods (e.g., lattice QCD, Dyson-Schwinger Equations [DSEs]) as opposed to traditional Minkowski field theories (such as light-front constituent quark models). ${bf Purpose}$ Seeking to bridge these complementary worldviews, we explore the potential of a Euclidean constituent quark model (ECQM). This formalism enables us to study the gluonic dressing of the quark-level axial-vector vertex, which we undertake as a test of the framework. ${bf Method}$ To access its indispensable elements with a minimum of inessential detail, we develop our ECQM using the simplified quark $+$ scalar diquark picture of the nucleon. We construct a hyperspherical formalism involving polynomial expansions of diquark propagators to marry our ECQM with the results of Bethe-Salpeter Equation (BSE) analyses, and constrain model parameters by fitting electromagnetic form factor data. ${bf Results}$ From this formalism, we define and compute a new quantity --- the Euclidean density function (EDF) --- an object that characterizes the nucleons various charge distributions as functions of the quarks Euclidean momentum. Applying this technology and incorporating information from BSE analyses, we find the dressing effect on the protons axial-singlet charge to be small in magnitude and consistent with zero. ${bf Conclusions}$ The scalar quark $+$ diquark ECQM is a step toward a realistic quark model in Euclidean space, and urges additional refinements. The small size we obtain for the impact of the dressed vertex on the axial-singlet charge suggests that models without this effect are on firm ground to neglect it.
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The results for the elastic nucleon form factors and the electromagnetic transition amplitudes to the Delta(1232) resonance, obtained with the Hypercentral Constituent Quark Model with the inclusion of a meson cloud correction are briefly presented. The pion cloud effects are explicitly discussed.
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A preliminary investigation of the anti-K N interaction is performed within a chiral constituent quark model by solving the resonating group method (RGM) equation. The model parameters are taken from our previous work, which gave a satisfactory description of the S-, P-, D-, F-wave KN scattering phase shifts. The channel-coupling between anti-K N, pi Lambda and pi Sigma is considered, and the scattering phase shifts as well as the bound-state problem of anti-K N are dynamically studied. The results show that the S-wave anti-K N interaction in the isospin I=0 channel is attractive, and in the extended chiral SU(3) quark model such an attraction can make for an anti-K N bound state, which appears as a pi Sigma resonance in the coupled-channel calculation, while the chiral SU(3) quark model cannot accommodate the existence of an anti-K N bound state. It seems that the vector meson exchanges are necessary to be introduced in the quark-quark interactions if one tries to explain the Lambda(1405) as an anti-K N bound state or a pi Sigma - anti-K N resonance state.
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