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Register a new userA Covariant model for the nucleon and the $Delta$
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The covariant spectator formalism is used to model the nucleon and the $Delta$(1232) as a system of three constituent quarks with their own electromagnetic structure. The definition of the ``fixed-axis polarization states for the diquark emitted from the initial state vertex and absorbed into the final state vertex is discussed. The helicity sum over those states is evaluated and seen to be covariant. Using this approach, all four electromagnetic form factors of the nucleon, together with the {it magnetic} form factor, $G_M^*$, for the $gamma N to Delta$ transition, can be described using manifestly covariant nucleon and $Delta$ wave functions with {it zero} orbital angular momentum $L$, but a successful description of $G_M^*$ near $Q^2=0$ requires the addition of a pion cloud term not included in the class of valence quark models considered here. We also show that the pure $S$-wave model gives electric, $G_E^*$, and coulomb, $G^*_C$, transition form factors that are identically zero, showing that these form factors are sensitive to wave function components with $L>0$.
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A possibility of the construction of a periodic table for the excited baryon spectrum is shown in the frame of a relativistic chiral quark model based on selection rules derived from the one-pion exchange mechanism. It is shown that all the $N^*$ and $Delta^*$ resonances appearing in the $pi N$ scattering data and strongly coupling to the $pi N$ channel are identified with the orbital configurations $(1S_{1/2})^2(nlj)$. Baryon resonances corresponding to the orbital configuration with two valence quarks in excited states couple strongly to the $pi pi N$-channel, but not to the $pi N$ channel. At low energy scale up to 2000 MeV, the obtained numerical estimations for the SU(2) baryon states (up to and including F-wave $N^*$ and $Delta^*$ resonances) within the schematic periodic table are mostly consistent with the experimental data. It is argued that due-to the overestimation of the ground state N(939) and Roper resonance N(1440) almost by the same amount and that the Roper resonance is a radial excitation of the N(939), the lowering mechanism for the both baryon states must be the same. The same mechanism is expected in the $Delta$ sector. At higher energies, where the experimental data are poor, we can extend our model schematically and predict seven new $N^*$ and four $Delta^*$ resonances with larger spin values.
The covariant parton model is generalized to describe quark correlators in a systematic way. Previous results are reproduced for the T-even leading-twist transverse momentum dependent parton distribution functions (TMDs), and for the first time all T-even twist-3 TMDs are evaluated in this model. We apply the approach to evaluate the fully unintegrated quark correlator which allows us to understand the model-specific relations between different TMDs. We verify the consistency of the approach, present numerical results and compare to available TMD parametrizations.
A convergence of the valence quark self-energies in the 1S, 2S, $1P_{1/2}$, $1P_{3/2}$ orbits induced by pion and gluon field configurations, is shown in the frame of a relativistic chiral quark model. It is shown that in order to reach a convergence, one needs to include contribution of the intermediate quark and anti-quark states with the total momentum up to $j=25/2$. It is argued that a restriction to the lowest mode when estimating the self-energy is not good approximation.
We present a calculation of the three-quark core contribution to the mass of the Delta-baryon in a Poincare-covariant Faddeev framework. A consistent setup for the dressed-quark propagator, the quark-quark and quark-diquark interactions is used, where all the ingredients are solutions of their respective Dyson-Schwinger or Bethe-Salpeter equations in rainbow-ladder truncation. We discuss the evolution of the Delta mass with the current-quark mass and compare to the previously obtained mass of the nucleon.
We solve a nonlocal generalisation of the NJL model in the Hartree approximation. This model has a separable interaction, as suggested by instanton models of the QCD vacuum. The choice of form factor in this interaction is motivated by the confining nature of the vacuum. A conserved axial current is constructed in the chiral limit of the model and the pion properties are shown to satisfy the Gell-Mann--Oakes--Renner relation. For reasonable values of the parameters the model exhibits quark confinement.
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