In this work,we investigate the masses of a few heavy-light mesons with variational method,taking into account the two-loop effects in the static Cornell potential. Specifically,we consider two wave-function,Gaussian and Coulomb. Our analysis suggests that phenomenologically such approach is more successful in the Heavy flavoured meson sector than the stationary state perturbation theory and other approximation methods.

We make an analysis of three -loop effects of the strong coupling constant in the study of masses and decay constants of the heavy-flavour pseudo-scalar mesons (PSM) D, $$D_s$$ D s , B, $$B_s,$$ B s , $$B_c$$ B c , $$\eta _c$$ η c and $$\eta _b$$ η b in a non-relativistic QCD potential model using Dalgarno’s perturbation theory (DPT). The first order mesonic wavefunction is obtained using Dalgarno’s perturbation theory. The three-loop effects of strong coupling constant are included in the wave function in co-ordinate space and then used to examine the static and dynamic properties of the heavy-flavour mesons for 2S and 3S higher states. The results are compared with the other models available and are found to be compatible with available experimental values. In V-scheme, the three-loop effects on masses and decay constants of heavy-flavour mesons show a significant result.

In this paper, we incorporate three-loop contributions in the strong coupling constant and study their effects in the wave functions, masses and decay constants of heavy–light pseudo-scalar mesons (PSM) [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] in V-scheme. In this work, we use the standard linear plus inverse distance QCD potential in association with Dalgarno’s method of perturbation theory for linear parent option. Detailed comparison is done with the results from Lattice QCD, QCD sum rules, light-front quark model (LFQM), relativistic harmonic confinement model (RHCM) and recent PDG data.

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