2S and 3S State Masses and decay constants of heavy-flavour mesons in a non-relativistic QCD potential model with three-loop effects in V-scheme
Rashidul Hoque, B. J. Hazarika, D. K. Choudhury
Abstract
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 , $$D_s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>D</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> , B, $$B_s,$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> $$B_c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> , $$\eta _c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>η</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> and $$\eta _b$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>η</mml:mi> <mml:mi>b</mml:mi> </mml:msub> </mml:math> 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 2 S and 3 S 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.