Spin Splitting Spectroscopy of Heavy Quark and Antiquarks Systems

Abstract

Phenomenological potentials describe the quarkonium systems like c c ¯ , b b , ¯ and b ¯ c where they give a good accuracy for the mass spectra. In the present work, we extend one of our previous works in the central case by adding spin-dependent terms to allow for relativistic corrections. By using such terms, we get better accuracy than previous theoretical calculations. In the present work, the mass spectra of the bound states of heavy quarks c c ¯ , b b ¯ , and 𝐵𝑐 mesons are studied within the framework of the nonrelativistic Schrödinger equation. First, we solve Schrödinger’s equation by Nikiforov-Uvarov (NU) method. The energy eigenvalues are presented using our new potential. The results obtained are in good agreement with the experimental data and are better than the previous theoretical estimates.

Approximate bound state solutions of the fractional Schr\"{o}dinger equation under the spin-spin-dependent Cornell potential

“…Also, a similar trend is observed for the l > 0 quantum states. The bottomonium masses are in good agreement with the masses obtained in existing literature [26,27,[32][33][34][35] and available experimental data [52]. The percentage errors deviation from experimental data for β = 1, α = 0.97 and β = 1, α = 0.50 were found to be 0.67% and 0.49% respectively.…”

“…In Table 4, we obtained the mass spectra of the bottomcharm meson for the s-wave and l > 0 states for the spin number s = 0 and s = 1. The masses also follow the trends of the bottomonium and charmonium and conform to the results reported in existing literature [26,34,35]. In Figure 1a-c, we plotted the potential against radial distance using the calculated parameters for the bottomonium and charmonium mesons in Table 1.…”

“…Additionally, Gupta and Mehrotra [25] evaluated the masses, decay rates, and position expectation values of heavy mesons utilizing the energy-dependent potential. Extensive works on the properties of the quarkonia systems can be found in the literature [26][27][28][29][30][31][32][33][34][35][36].…”