A new study of relativistic and nonrelativistic for new modified Yukawa potential via the BSM in the framework of noncommutative quantum mechanics symmetries: An application to heavy-light mesons systems

Abstract

In this article, the deformed Dirac equation was solved with a new modified Yukawa potential within three tensor interactions (Coulomb-like, Yukawa-like, and Hulthén-type potentials) (NMYTTIs). This study is scrutinized by taking into consideration the noncommutative space-space effect within the relativistic and nonrelativistic regimes using the parametric of Bopp’s shift method and standard perturbation theory with the help of an approximation to the centrifugal term. In the framework of the spin and pseudospin (p-spin) symmetry, we obtain the global new energy eigenvalue which equals the energy eigenvalue in usual relativistic QM under the new modified Yukawa potential plus the corrected of energy induced with three infinitesimal additive parts of the relativistic Hamiltonian corresponds to the spin-orbit interaction, the new modified Zeeman and the rotational Fermi term. The new values that we get appeared sensitive to the quantum numbers (j,k,l,lps,s,sps,m,mps) and (j,l,s,m) (within the relativistic and nonrelativistic regimes, respectively), the potential depths (A,B,C), the range of the potential α, and noncommutativity parameters (η,σ,χ). The present results are applied for calculating the mass spectra of heavy mesons such as heavy-light mesons HLM such as cc¯, bb¯, bc¯, bs¯, cs¯ and bq¯, q=(u,d). Our results excellent agree perfectly with the ones in works of literature.