By M. Ottel
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Extra info for Baryons as Relativistic Bound States of Quark and Diquark [thesis]
116) depending on q may safely be dropped. The operator W2 now takes the form W2 = L2 + 2L·S + S2 , ∂ ∂ ∂ L2 = 2pi i − p2 ∆p + pi pj i j , ∂p ∂p ∂p ∂ 2(L·S)αα′ ,ββ ′ ,γγ ′ = −ǫijk pj k (Σi )αα′ ⊗ δββ ′ ⊗ δγγ ′ + ∂p δαα′ ⊗ (Σi )ββ ′ ⊗ δγγ ′ + δββ ′ ⊗ (Σi )γγ ′ , (S2 )αα′ ,ββ ′ ,γγ ′ = 41 (9 δαα′ ⊗ δββ ′ ⊗ δγγ ′ + 2 Σi αα′ ⊗ (Σi )ββ ′ ⊗ δγγ ′ + δββ ′ ⊗ (Σi )γγ ′ 2 δαα′ ⊗ (Σi )ββ ′ ⊗ (Σi )γγ ′ . 126) . 3: Classification of the components of the nucleon Faddeev amplitude in terms of eigenfunctions of L2 and S2 in the rest frame of the bound state.
The solutions in the scalar diquark sector suffered from the large constituent quark masses that set a wrong scale within the nucleon, as seen by the results for the magnetic moments. The inclusion of the attractive axialvector diquark channel now allows for solutions with smaller quark masses and smaller binding energy for the scalar diquark. The diquark normalization (or coupling) constant gs drops for this reason and therefore the nucleon binding energy becomes smaller in the scalar channel, but the additional binding provided by the axialvector diquark compensates this effect to yield the physical nucleon mass.
52) the traces over the color and flavor parts yield no additional factors, see eqs. 55). In the following, we will solve the baryon bound state problem with the coupling constants gs and ga fixed in the indicated manner, keeping in mind that the Bethe-Salpeter normalization condition determines these values only on-shell. When calculating diquark contributions to the nucleon electric form factors, we will see that the Ward identity provides for an indirect off-shell constraint on gs and ga . However, the ratio between the constants fixed either on- or off-shell will be of the order of unity.
Baryons as Relativistic Bound States of Quark and Diquark [thesis] by M. Ottel