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Register a new userFaddeev approach to confined three-quark problems
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We propose a method that allows for the efficient solution of the three-body Faddeev equations in the presence of infinitely rising confinement interactions. Such a method is useful in calculations of nonrelativistic and especially semirelativistic constituent quark models. The convergence of the partial wave series is accelerated and possible spurious contributions in the Faddeev components are avoided. We demonstrate how the method works with the example of the Goldstone-boson-exchange chiral quark model for baryons.
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A method is presented that allows to solve the Faddeev integral equations of the semirelativistic constituent quark model. In such a model the quark-quark interaction is modeled by a infinitely rising confining potential and the kinetic energy is taken in a relativistic form. We solve the integral equations in Coulomb-Sturmian basis. This basis facilitate an exact treatment of the confining potentials.
{bf Background} Deuteron induced reactions are widely used to probe nuclear structure and astrophysical information. Those (d,p) reactions may be viewed as three-body reactions and described with Faddeev techniques. {bf Purpose} Faddeev-AGS equations in momentum space have a long tradition of utilizing separable interactions in order to arrive at sets of coupled integral equations in one variable. However, it needs to be demonstrated that observables calculated based on separable interactions agree exactly with those based on nonseparable forces. {bf Methods} Momentum space AGS equations are solved with separable and nonseparable forces as coupled integral equations. {bf Results} Deuteron-alpha scattering is calculated via momentum space AGS equations using the CD-Bonn neutron-proton force and a Woods-Saxon type neutron(proton)-$^4$He force, for which the Pauli-forbidden S-wave bound state is projected out. Elastic as well as breakup observables are calculated and compared to results in which the interactions in the two-body sub-systems are represented by separable interactions derived in the Ernst-Shakin-Thaler (EST) framework. {bf Conclusions} We find that the calculations based on the separable representation of the interactions and the original interactions give results that are in excellent agreement. Specifically, integrated cross sections and angular distributions for elastic scattering agree within $approx$ 1%, which is well below typical experimental errors. In addition, the five-fold differential cross sections corresponding to breakup of the deuteron agree extremely well.
Two different types of orthogonality condition models (OCM) are equivalently formulated in the Faddeev formalism. One is the OCM which uses pairwise orthogonality conditions for the relative motion of clusters, and the other is the one which uses the orthogonalizing pseudo-potential method. By constructing a redundancy-free T-matrix, one can exactly eliminate the redundant components of the total wave function for the harmonic-oscillator Pauli-forbidden states, without introducing any limiting procedure. As an example, a three-alpha-particle model interacting via the deep alpha alpha potential by Buck, Friedrich and Wheatley is investigated.
A selfconsistent thermodynamic $T$-matrix approach is deployed to study the microscopic properties of the quark-gluon plasma (QGP), encompassing both light- and heavy-parton degrees of freedom in a unified framework. The starting point is a relativistic effective Hamiltonian with a universal color force. The input in-medium potential is quantitatively constrained by computing the heavy-quark (HQ) free energy from the static $T$-matrix and fitting it to pertinent lattice-QCD (lQCD) data. The corresponding $T$-matrix is then applied to compute the equation of state (EoS) of the QGP in a two-particle irreducible formalism including the full off-shell properties of the selfconsistent single-parton spectral functions and their two-body interaction. In particular, the skeleton diagram functional is fully resummed to account for emerging bound and scattering states as the critical temperature is approached from above. We find that the solution satisfying three sets of lQCD data (EoS, HQ free energy and quarkonium correlator ratios) is not unique. As limiting cases we discuss a weakly-coupled solution (WCS) which features color-potentials close to the free energy, relatively sharp quasiparticle spectral functions and weak hadronic resonances near $T_{rm c}$, and a strongly-coupled solution (SCS) with a strong color potential (much larger than the free energy) resulting in broad non-quasiparticle parton spectral functions and strong hadronic resonance states which dominate the EoS when approaching $T_{rm c}$.
The Faddeev equations for the $Xi NN$ bound-state problem are solved where the three $S$=$-2$ baryon-baryon interactions of Julich-Bonn-Munchen chiral EFT, HAL QCD and Nijmegen ESC08c are used. The $T$-matrix $T_{Xi N, Xi N}$ obtained within the original $LambdaLambda$-$Xi N$-$SigmaSigma$ $/$ $Xi N$-$Lambda Sigma$-$SigmaSigma$ coupled-channel framework is employed as an input to the equations. We found no bound state for Julich-Bonn-Munchen chiral EFT and HAL QCD but ESC08c generates a bound state with the total isospin and spin-parity $(T,J^{pi})=(1/2, 3/2^+)$ where the decays into $LambdaLambda N$ are suppressed.
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