A Solvable Model for Many Quark Systems in QCD Hamiltonians

Motivated by a canonical, QCD Hamiltonian we propose an effective Hamiltonian to represent an arbitrary number of quarks in hadronic bags. The structure of the effective Hamiltonian is discussed and the BCS-type solutions that may represent constituent quarks are presented. The single particle orbitals are chosen as 3-dimensional harmonic oscillators and we discuss a class of exact solutions that can be obtained when a subset of single-particle basis states is restricted to include a certain number of orbital excitations. The general problem, which includes all possible orbital states, can also be solved by combining analytical and numerical methods.Comment: 24 pages, 2 figures, research articl

Analysis of a QCD Hamiltonian in the low energy regime

We present a QCD motivated Hamiltonian for the light quark sector. Inspired from self-consistent analysis of the Coulomb interaction, we implement an interaction of the form (-a/r + br) between color sources, which already consider gluonic dynamics by the linear potential contribution. A prediagonalization of the kinetic energy term followed by the implementation of the Tamm-Dancoff method are used to obtain the eigenvalues of the Hamiltonian. A variational analysis is implemented to obtain the optimized basis for the low energy meson spectrum. The potential parameter is compared to the reported lattice string tension with relatively good agreement. The obtained energies are located close to the experimental values and further improvements are discussed.Facultad de Ciencias Exacta

QCD at low energy: the use of many-body methods

The exact diagonalization of the kinetic energy-term of the QCD-Hamiltonian, at low energy and restricted to a finite volume, is resumed. The Coulomb interaction term, approximated by a sum of a 1/r and a linear potential, is added. Only quarks and anti-quarks are considered, while the gluons are taken into account effectively via the linear potential. The Tamm-Dankoff method is applied to obtain the meson spectrum of a simplified QCD- Hamiltonian at low energy. The current status and first results of our research-program are presented.Facultad de Ciencias Exacta

Analysis of a QCD Hamiltonian in the low energy regime

We present a QCD motivated Hamiltonian for the light quark sector. Inspired from self-consistent analysis of the Coulomb interaction, we implement an interaction of the form (-a/r + br) between color sources, which already consider gluonic dynamics by the linear potential contribution. A prediagonalization of the kinetic energy term followed by the implementation of the Tamm-Dancoff method are used to obtain the eigenvalues of the Hamiltonian. A variational analysis is implemented to obtain the optimized basis for the low energy meson spectrum. The potential parameter is compared to the reported lattice string tension with relatively good agreement. The obtained energies are located close to the experimental values and further improvements are discussed.Facultad de Ciencias Exacta

QCD at low energy: the use of many-body methods

The exact diagonalization of the kinetic energy-term of the QCD-Hamiltonian, at low energy and restricted to a finite volume, is resumed. The Coulomb interaction term, approximated by a sum of a 1/r and a linear potential, is added. Only quarks and anti-quarks are considered, while the gluons are taken into account effectively via the linear potential. The Tamm-Dankoff method is applied to obtain the meson spectrum of a simplified QCD- Hamiltonian at low energy. The current status and first results of our research-program are presented.Facultad de Ciencias Exacta

Use of a non-relativistic basis for describing the low energy meson spectrum

We justify the use of harmonic oscillator eigenfunctions for expanding the fermionic fields of an effective field theory and evaluate its utility for solving a Hamiltonian inspired by the QCD formalism in the Coulomb Gauge. Since the functions involved in such expansion are non-relativistic, the Talmi-Moshinsky transformations can be used to recover the translational invariance of the center of mass of the mesonic states. Finally, many-body methods and an a posteriori flavor mixing procedure are used to compute a preliminary spectrum for the mesons below 1 GeV.Facultad de Ciencias Exacta

TDA and RPA pseudoscalar and vector solutions for the low energy regime of a motivated QCD Hamiltonian

We present the low energy meson spectrum of a Coulomb gauge QCD motivated Hamiltonian for light and strange quarks. We have used the harmonic oscillator as a trial basis and performed a pre-diagonalization of the kinetic energy term in order to get an effective basis where quark and anti-quark degrees of freedom are defined. For the relevant interactions between quarks and anti-quarks, we have implemented a confining interaction between color sources, in order to account in an effective way for the gluonic degrees of freedom. The low energy meson spectrum is obtained from the implementation of the TDA and RPA many-body-methods. The physical states have been described as TDA and RPA collective states with a relatively good agreement. Particularly, the particle-hole correlations of the RPA ground state improve the RPA pion-like state (159.7 MeV) close to its physical value while the TDA one remains at a higher energy (269.2 MeV).Facultad de Ciencias Exacta