Decay rates of charmonia within a quark-antiquark confining potential

Abstract

In this work, we investigate the spectroscopy and decay rates of charmonia within the framework of nonrelativistic Schrödinger equation by employing an approximate inter quark-antiquark potential. The spin hyperfine, spin-orbit and tensor components of the one gluon exchange interaction are employed to compute the spectroscopy of the excited S states and few low-lying P and D waves. The resultant wave functions at zero inter quark separation as well as some finite separation are employed to predict the di-gamma, di-leptonic and di-gluon decay rates of charmonia states by using the conventional Van Royen-Weisskopf formula. The di-gamma and di-leptonic decay widths are also computed by incorporating the relativistic corrections of order v 4 within the NRQCD formalism. We have observed that the NRQCD predictions with their matrix elements computed at finite radial separation yielded results which are found to be in better agreement with experimental value for both di-gamma and di-leptonic decays. The same scenario is seen in the case when di-gamma and di-leptonic decay widths are computed with Van Royen-Weisskopf formula. It is also observed that the di-gluon decay width with the inclusion of binding energy effects are in better agreement with the experimental data available for 1S-2S and 1P. The di-gluon decay width of 3S and 2P waves waves are also predicted. Thus, the present study of decay rates clearly indicates the importance of binding energy effects.

Charmonium Properties Using the Discrete Variable Representation (DVR) Method

“…The Schrödinger equation for most of the q q potentials (including the Cornell potential) cannot be solved analytically; hence, numerical solutions are called for. Some of the methods found in literature for solving the Schrödinger equation for q q systems are numerical methods based on Runge-Kutte approximation [28,29], Numerov matrix method [30][31][32], asymptotic iteration method [33][34][35], Fourier grid Hamiltonian method [36], variational method [37,38], etc. Another method for numerically solving the Schrödinger equation is the discrete variable representation (DVR) method.…”

Decay Constants of S Wave Heavy Quarkonia

“…Lattice QCD provides great hope in this direction and significant results are being reported [1,2]. Various other approaches widely used in the literature to study hadronic systems include QCD sum rules [14][15][16][17][18][19], nonrelativistic and relativistic potential models [20][21][22][23][24][25][26][27][28][29][30][32][33][34][35][36], effective field theory [37][38][39] and formalisms based on Bethe-Salpeter equation and Dyson-Schwinger equation [40][41][42][43][44][45][46][47][48][49]. Among theses QCD inspired potential models have been largely successful in explaining hadronic properties.…”

Status of quarkonia-like negative and positive parity states in a relativistic confinement scheme

“…There are various issues related to higher excited states which are still to be resolved. In this context, phenomenological models either non-relativistic quark model (NRQM) or the relativistic quark model have been developed to study the properties of heavy mesons (Charmonium and Bottomonium) [21,22,23]. 1 − e + e − → γ(π + π − J/ψ) BABAR [28,29]CLEO [30] , Belle [26] e + e − → (π + π − J/ψ) CLEO [31] e + e − → (π 0 π 0 J/ψ) CLEO [31] Y (4330) 4320.0 ± 10.4 ± 7.0 1 − e + e − → γ(π + π − J/ψ) BESIII [7] Y (4360) 4361 ± 13 1 − e + e − → γ(π + π − ψ(2S)) BABAR [32] , Belle [ In the present study we compute the masses of charmonium -like and bottomonium-like states in a relativistic frame work.…”