6533b857fe1ef96bd12b5121

RESEARCH PRODUCT

Three-body forces in the quark model

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The constituent quark model has been very useful for the description of many physical properties of baryons, achieving in most cases a fair agreement with the experimental data 1 The model is based on a non relativistic QCD-inspired dynamics including a harmonic oscillator (h.o.) confinement potential and a spin dependent (hyperfine) interaction. The use of Lovelace coordinates p, ~ avoides any problem with the center of mass motion, while the h.o. potential provides a simple basis for ana ly t ica l calculations, which is a very important feature for many applications, like the evaluation of form factors and Meson Exchange Currents 2. On the other hand the h.o. spectrum is too degenerate with respect to the experimental one and the typical h.o. behaviour of the 3q-wave functions leads to a strong damping of the form factors at medium momentum transfer. All the potentials quoted above have a two-body character. However, there are some indications that 3q forces may play a relevant role. In fact, a Born-Oppenheimer treatment of the confinement potential in QCD motivated bag models leads quite naturally to 3q forces 3 and a more realistic q-behaviour for the e.m. form factors can be obtained if a 3-body potential is used in the 5chr6dinger equation for 3 quarks 4. Finally, it should be reminded that three-body forces are strictly related to the presence of a direct gluon-gluon coupling in QCD. We explore the possibility of a 3-body force model for baryons. The potential is assumed to depend on the hyperradius x=4(p2+;k 2) and the 5chrt)dlnger equation is solved In the hyperspherlcal harmonics formalism s. As in the 2-body case only Intrinsic coordinates are used and all the symmetry properties of the 3q-wave functions are st i l l valid. Various forms of the potential are considered, Including Coulomb-like logarithmic or linear confinement terms. The corresponding Intensities can be fitted to the energy spectrum, but it turns out to be difficult to reproduce both excitation energies and proton charge distribution, a situation very similar to what happens in the 2-body approach e The model provides a direct relation between the proton charge form