By M. Ottel
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Extra resources for Baryons as Relativistic Bound States of Quark and Diquark [thesis]
Using scalar diquarks only, it reads in the rest frame (SΓ)αβγ = Sˆ1 ς Sˆ2 (σˆ p) ς (gs V ) (γ5C)βγ . 157) α The two scalar functions Sˆ1 and Sˆ2 (related to the wave function) describe upper and lower component of the effective nucleon spinor. Likewise only the two functions S1 and S2 enter the decomposition of the vertex function. We will start out with investigations of the various forms of the scalar function V (x) that parametrizes the diquark-quark vertex, see eqs. 63). Furthermore we pick σ = 1/2 for the momentum distributing parameter in the diquarkquark vertex.
131) Applying the operators L2 and S2 , eqs. 123), to the Faddeev amplitude (SΓ∆ )αβγ , this decomposition is seen to yield eigenfunctions of the spin and orbital angular momentum operators. 4. The strength of the partial waves is determined by the scalar functions ˆ i (p2 , p·P ). D In contrast to the nucleon, only one s wave (described by D1 ) is found. Two d waves that survive the non-relativistic limit are given by D5 and D7 , and one d wave can be attributed to the virtual time component of the axialvector diquark, D3 .
3 The diquark-quark Bethe-Salpeter equation Equipped with the separable form of the two-quark correlations, eq. 43), and the functional form of the scalar and axialvector diquark correlations in eqs. 5 To complete the model definition, we have to specify the functional form of the quark propagator. We take it to be a free fermion propagator with a constituent mass mq , S(p) = ip / − mq C(p2 , m = mq ) p2 + m2q with C(p2 , m = mq ) = 1. 64) We will sum up the four nearly mass-degenerate states ∆++ , ∆+ , ∆0 , ∆− under the label ∆ in the following.