Properties of bottomonium in a semi-relativistic model

Abstract

Using a semi-relativistic potential model we investigate the spectra and decays of the bottomonium (b b) system. The Hamiltonian of our model consists of a relativistic kinetic energy term, a vector Coulomb-like potential and a scalar confining potential. Using this Hamiltonian, we obtain a spinless wave equation, which is then reduced to the form of a single particle Schrodinger equation. The spin dependent potentials are introduced as a perturbation. The three-dimensional harmonic oscillator wave function is employed as a trial wave function and the b b mass spectrum is obtained by the variational method. The model parameters and the wave function that reproduce the the b b spectrum are then used to investigate some of their decay properties. The results obtained are then compared with the experimental data and with the predictions of other theoretical models.

Observation of theχb1(3P)andχb

“…These values can be compared to the predictions of theoretical calculations [39][40][41][42][43][44][45][46][47][48][49][50]. Out of 19 ∆M predictions, 18 range from 8 to 18 MeV, mostly depending on the potentials describing the bb nonperturbative interaction.…”

Approach to calculation of mass spectra and two-photon decays of cc¯ mesons in the framework of Bethe-Salpeter equation

“…Further, our results for the cc mass spectra suggest that the perturbative incorporation of OGE with the use of analytically derived harmonic oscillator wave functions is closer to reality than some of the previous approaches [46,47], where they used harmonic oscillator wave functions only as trial wave functions, which did not take into account the importance of the Coulomb potential for heavy quarkonium systems.…”

“…Further, the present approach is in line with some earlier works [43][44][45] where the OGE (Coulomb) term was treated perturbatively for charmed mesons and baryons. Similarly, in a recent work [46] the 3D harmonic oscillator wave functions were used as trial wave functions for obtaining the cc spectrum and their decays, where these trial wave functions did not take into account the importance of the Coulomb potential for heavy quarkonium systems. A similar treatment was followed earlier in Ref.…”

“…This is especially so for orbital excitations of these states, where the centrifugal effects [43] ensure that the c −c separation is large enough to feel the effect of the confining term more strongly than the Coulomb term. We further wish to state that some earlier works [43][44][45] have treated the onegluon-exchange (OGE) (Coulomb) term perturbatively for charmed mesons and baryons, while other works [46,47] did not take into account the importance of the Coulomb term for heavy quarkonium systems.…”

Properties of Charmonium States in a Phenomenological Approach

“…These QCD inspired potential models use a short range part motivated by perturbative QCD (Coulomb like or one gluon exchange potential) [20,[22][23][24][25][26][27][28][29][30] and a phenomenological long range part accounting for confinement (i.e. linear, logarithmic or quadratic potential) [31][32][33][34][35][36][37][38]. Our Model uses the NRQM formalism for the study of low lying charmonium states using a Hamiltonian which has the heavy quark potential from the instanton vacuum depending on r, the inter quark distance.…”