Abstract
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 , B, B_s,B_c, eta _c and eta _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.
Highlights
The non-relativistic predictions of Potential Models with a non-relativistic Hamiltonian for the heavy-light and heavyheavy mesons are found to be in fair agreement with the updated experimental data, theoretical results like QCD sum rule [1,2], Lattice results [3] and relativistic harmonic confinement model (RHCM) [53]
V-scheme is a standard way of taking into account the higher order effects of QCD, which are expressed as power series in the running strong coupling constant αM S in M S-scheme
The mass and the decay constant of heavy-flavour pseudoscalar meson including only spin–spin interaction are given in [26,27] as: MP = m1 + m2 + En,l + Hss where, m1 and m2 are the masses of quark–antiquark and αs is the strong coupling constant identified as αV in the present work, En,l is the non-relativistic binding energy between the quark–antiquark composition and the van Royen–Weisskopf formula [54] for the decay of pseudo-scalar meson is, fP =
Summary
The non-relativistic predictions of Potential Models with a non-relativistic Hamiltonian for the heavy-light and heavyheavy mesons are found to be in fair agreement with the updated experimental data, theoretical results like QCD sum rule [1,2], Lattice results [3] and relativistic harmonic confinement model (RHCM) [53]. We have obtained a total first order corrected wavefunction for 2S and 3S states using Dalgarno’s method of perturbation [30] with linear part of the Cornell potential [19,31] as perturbation in co-ordinate space. This wavefunction is used to estimate the masses and decay constants of heavy-light and heavy-heavy pseudo-scalar mesons in this improved QCD Potential model approach. The rest of the paper is organised as follows: Sect. 2 contains formalism, Sect. 3 contains results while Sect. 4 includes the conclusion
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