Hadron spectra from a non-relativistic model with confining harmonic potential

Abstract

Espectros de Hadrons a partir de um modelo não relativístico com potencial harmônico confinante Abstract Hadron spectra and other properties of quark systems are studied in the framework of a non-relativistic spin-independent phenomenological model. The chosen confining potential is harmonic, which allowed us to obtain analytical solutions for both meson and baryon (of equal constituent quarks) spectra. The introduced parameters are fixed from the low-lying levels of heavy quark mesons. The requirement of flavor independence is imposed, and it restricts the possible choices of inter-quark potentials. The hyper-spherical coordinates are considered for the solution of the three-body problem. Espectros de Hadrons e outras propriedades de sistemas de quarks são estudados do ponto de vista de um modelo fenomenológico não-relativístico independente de spin. O potencial confinante escolhidoé harmônico, o qual nos permite obter soluções analíticas tanto para os espectros dos mésons quanto para os dos bárions (de iguais quarks constituintes). Os parâmetros introduzidos são fixos a partir dos primeiros estados excitados dos mésons pesados. A condição de independência de saboré imposta, o que restringe as possíveis escolhas de potenciais inter-quarks. As coordenadas hiper-esféricas são consideradas para a solução do problema de três corpos.

Study of Heavy Quarkonium with Energy Dependent Potential

“…These exhibit flavor dependence. Parameters of set A correspond to energy independent potential and are compared with the parameters obtained by Ryes et al [16] for harmonic oscillator plus inverse square potential. Parameters of set B are for energy dependent potential used in present work.…”

“…The combination of harmonic oscillator and inverse square potential was first of all adopted by Joshi and Mitra [14] in a theory based on the Schrodinger equation for studying the heavy meson spectroscopy. Later it has been used by Iyer et al [15] and Ryes et al [16] in the study of hadron spectroscopy. In all these studies a better fit was obtained for the potential with a term proportional to 1/r 2 because it has singularity for r  0 that improves the behavior in this region.…”

Study of Baryon Spectroscopy Using a New Potential Form

“…The mathematical description of a threebody system is more complicated than that of a two-body system. Several methods have been used by different authors to solve three-body problems [11,15]. In order to describe the baryon as a bound state of three constituent quarks, we define the configuration of three particles by the center of mass, , and two Jacobi coordinates and as…”

“…Some authors have used the Cornell potential (Coulomb-type plus linear term) to study the resonance states of and Δ baryons [8][9][10][11][12][13][14]. The harmonic oscillator potential has been used to study the interaction between three identical particles [15]. In the present work, the digamma-function is used as the interaction potential between constituent quarks of baryon systems.…”

$$\rho J/\Psi $$ scattering in an improved many-body potential

“…We report a comparison of incorporating the QCD-motivated improved overlap factor f with the more popular sum of two-body approach, along with those of almost a full use of the realistic Cornell potential and of replacing this by a computationally convenient quadratic potential. A quadratic potential is frequently used [29][30][31][32] in the hadronic physics including the nucleon-nucleon interaction. In the old Isgur-Karl model, still used in ref.…”