Heavy quarkonium systems for the deformed unequal scalar and vector Coulomb–Hulthén potential within the deformed effective mass Klein–Gordon equation using the improved approximation of the centrifugal term and Bopp’s shift method in RNCQM symmetries

In this study, the analytical solutions of the Klein–Gordon equation for any [Formula: see text] states of the modified effective mass potential under the modified unequal scalar and vector Coulomb–Hulthén potential (MUSVCH-P) are derived by using an approximation method to the centrifugal potential term in the symmetries of relativistic noncommutative three-dimensional real space (RNC: 3D-RS). The new analytical expressions for eigenvalues of the energy spectrum and the new mass of mesons, such as charmonium and bottomonium that have the quark and antiquark flavor, have been estimated by using Bopp’s shift method, and perturbation theory. The energy state equation depends on the global parameters characterizing the noncommutativity space and the potential parameter [Formula: see text] in addition to the Gamma function and the discreet atomic quantum numbers [Formula: see text]. The expression for the new energy spectra is applied to obtain the new mass spectra of heavy quarkonium systems (charmonium and bottomonium) in the symmetries of (RNC: 3D-RS). The comparisons show that our theoretical results are in very good agreement with the reported works.

Effects of the hyperscaling violation and dynamical exponents on the imaginary potential and entropic force of heavy quarkonium via holography

The imaginary potential and entropic force are two important different mechanisms to characterize the dissociation of heavy quarkonia. In this paper, we calculate these two quantities in strongly coupled theories with anisotropic Lifshitz scaling and hyperscaling violation exponent using holographic methods. We study how the results are affected by the hyperscaling violation parameter $$ \theta $$ θ and the dynamical exponent z at finite temperature and chemical potential. Also, we investigate the effect of the chemical potential on these quantities. As a result, we find that both mechanisms show the same results: the thermal width and the dissociation length decrease as the dynamical exponent and chemical potential increase or as the hyperscaling violating parameter decreases.

Next-to-leading-order QCD corrections to heavy quark fragmentation into $${}^1S^{(1,8)}_0$$ quarkonia

Within NRQCD factorization framework, in this work we compute, at the lowest order in velocity expansion, the next-to-leading-order (NLO) perturbative corrections to the short-distance coefficients associated with heavy quark fragmentation into the $${}^1S_0^{(1,8)}$$ 1 S 0 ( 1 , 8 ) components of a heavy quarkonium. Starting from the Collins and Soper’s operator definition of the quark fragmentation function, we apply the sector decomposition method to facilitate the numerical manipulation. It is found that the NLO QCD corrections have a significant impact.