Description of Heavy Quark Mass by Lippmann-Schwinger Equation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Collective Perspective on Advances in Dyson-Schwinger Equation QCD

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Identification of the Mass and Stability Interval of Strong Potential in Heavy Mesons

In this paper, we have calculated the masses of mesons containing t-quark and their spins' coupling coefficients. This was achieved by solving Lippmann-Schwinger equation for the quark-antiquark bound state of heavy mesons in configuration space. Heavy meson masses submitted criteria for the strong nuclear interactive potential between two quarks. We investigated the stability of a few suitable potentials and offered the best of these potentials for heavy mesons.

Study of the (D)over-barN Interaction in a QCD Coulomb Gauge Quark Model

We study the (D) over barN interaction at low energies with a quark model inspired in the QCD Hamiltonian in Coulomb gauge. The model Hamiltonian incorporates a confining Coulomb potential extracted from a self-consistent quasiparticle method for the gluon degrees of freedom, and transverse-gluon hyperfine interaction consistent with a finite gluon propagator in the infrared. Initially a constituent-quark mass function is obtained by solving a gap equation and baryon and meson bound-states are obtained in Fock space using a variational calculation. Next, having obtained the constituent-quark masses and the hadron waves functions, an effective meson-nucleon interaction is derived from a quark-interchange mechanism. This leads to a short range meson-baryon interaction and to describe long-distance physics vector- and scalar-meson exchanges described by effective Lagrangians are incorporated. The derived effective (D) over barN potential is used in a Lippmann-Schwinger equation to obtain phase shifts. The results are compared with a recent similar calculation using the nonrelativistic quark model.

COMPLEX KOHN VARIATIONAL PRINCIPLE FOR 2-NUCLEON BOUND-STATE AND SCATTERING WITH THE TENSOR POTENTIAL

Complex Kohn variational principle is applied to the numerical solution of the fully off-shell Lippmann-Schwinger equation for nucleon-nucleon scattering for various partial waves including the coupled S-3(1), D-3(1), channel. Analytic expressions are obtained for all the integrals in the method for a suitable choice of expansion functions. Calculations with the partial waves S-1(0), P-1(1), D-1(2), and S-3(1)-D-3(1) of the Reid soft core potential show that the method converges faster than other solution schemes not only for the phase shift but also for the off-shell t matrix elements. We also show that it is trivial to modify this variational principle in order to make it suitable for bound-state calculation. The bound-state approach is illustrated for the S-3(1)-D-3(1) channel of the Reid soft-core potential for calculating the deuteron binding, wave function, and the D state asymptotic parameters. (c) 1995 Academic Press, Inc.

Short-distance part of the interaction of D mesons and nucleons

The short-distance part of the low energy interaction of D-mesons and nucleons is investigated in the context of a quark model. The quark model is based on Coulomb gauge QCD. The model contains a confining Coulomb potential and a transverse hyperfine interaction consistent with a finite gluon propagator in the infrared. The basic mechanism for the short-distance interaction between the D-mesons and nucleons is quark interchange. Using Resonating GroupMethod techniques an effective potential for the interaction between nucleons and D mesons can be obtained and used in a Lippmann-Schwinger equation to obtain differential cross-sections and phase shifts.

Heavy-light mesons scattering from nucleons: Quark-gluon and meson exchanges

We investigate the scattering of heavy-light K and D mesons by nucleons at low energies. The short-distance part of the interaction is described by quark-gluon interchange and the longdistance part is described by a one-meson-exchange model that includes the contributions of vector (ρ, ω) and scalar (σ) mesons. The microscopic quark model incorporates a confining Coulomb potential extracted from lattice QCD simulations and a transverse hyperfine interaction consistent with a finite gluon propagator in the infrared. The derived effective meson-nucleon potential is used in a Lippmann-Schwinger equation to obtain s-wave phase shifts. Our final aim is to set up a theoretical framework that can be extended to finite temperatures and baryon densities. © 2010 American Institute of Physics.

Three-Dimensional Low-Momentum Interaction in Two-Body Bound State Calculations

The deuteron binding energy and wave function are calculated by using the recently developed three-dimensional form of low-momentum nucleon-nucleon (NN) interaction. The homogeneous Lippmann-Schwinger equation is solved in momentum space by using the low-momentum two-body interaction, which is constructed from Malfliet-Tjon potential. The results for both, deuteron binding energy and wave function, obtained with low-momentum interaction, are compared with the corresponding results obtained with bare potential. © 2012 Springer-Verlag.

D̄N interaction in a color-confining chiral quark model

We investigate the low-energy elastic D̄N interaction using a quark model that confines color and realizes dynamical chiral symmetry breaking. The model is defined by a microscopic Hamiltonian inspired in the QCD Hamiltonian in Coulomb gauge. Constituent quark masses are obtained by solving a gap equation, and baryon and meson bound-state wave functions are obtained using a variational method. We derive a low-energy meson-nucleon potential from a quark-interchange mechanism whose ingredients are the quark-quark and quark-antiquark interactions and baryon and meson wave functions, all derived from the same microscopic Hamiltonian. The model is supplemented with (σ, ρ, ω, a0) single-meson exchanges to describe the long-range part of the interaction. Cross sections and phase shifts are obtained by iterating the quark-interchange plus meson-exchange potentials in a Lippmann-Schwinger equation. Once coupling constants of long-range scalar σ and a0 meson exchanges are adjusted to describe experimental phase shifts of the K+N and K0N reactions, predictions for cross sections and s-wave phase shifts for the D̄0N and D-N reactions are obtained without introducing new parameters. © 2013 American Physical Society.

Heavy Mesons Spectroscopy

In this paper, Lippmann-Schwinger equation is solved by using Martin and Cornel potentials to calculate bc̄ energy levels. The results for some energy levels which are not observable, such as those of tt̄ in its short half-life are also predicted. Our calculated energy levels are in good agreement with results of other groups. The stability interval for Yukawa-Linear potential is also studied by investigating the spectrum of eigenvalues. © 2013 Springer Science+Business Media New York.

Quebra da simetria de sabor na interação de mésons charmosos com o núcleon

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Solution of two-body bound state problems with confining potentials

The homogeneous Lippmann-Schwinger integral equation is solved in momentum space by using confining potentials. Since the confining potentials are unbounded at large distances, they lead to a singularity at small momentum. In order to remove the singularity of the kernel of the integral equation, a regularized form of the potentials is used. As an application of the method, the mass spectra of heavy quarkonia, mesons consisting from heavy quark and antiquark (Υ(bb̄), ψ(cc̄)), are calculated for linear and quadratic confining potentials. The results are in good agreement with configuration space and experimental results. © 2010 American Institute of Physics.

Integral equations of scattering in one dimension

A self-contained discussion of integral equations of scattering is presented in the case of centrally symmetric potentials in one dimension, which will facilitate the understanding of more complex scattering integral equations in two and three dimensions. The present discussion illustrates in a simple fashion the concept of partial-wave decomposition, Green's function, Lippmann-Schwinger integral equations of scattering for wave function and transition operator, optical theorem, and unitarity relation. We illustrate the present approach with a Dirac delta potential. (C) 2001 American Association of Physics Teachers.