CKM Matrix Element |Vcb| in a QCD potential model with Three loop effects

This study investigates the Isgur–Wise function (IWF) and the Cabibbo–Kobayashi–Maskawa (CKM) matrix element [Formula: see text] within the framework of a Quantum Chromodynamics (QCD) potential model. The linear plus coulomb Cornell potential, [Formula: see text] is considered for heavy flavour meson, incorporating three-loop corrections to the strong coupling constant [Formula: see text] in the V-scheme. Using the Asymptotic Matching Method (AMM) together with Dalgarno’s Perturbation Theory (DPT), we derive the wave function of the [Formula: see text] meson in the infinite mass limit. Based on this wave function, the CKM matrix element [Formula: see text] is evaluated through its direct relation with the Isgur–Wise function and the semileptonic decay rate. This approach deepens the understanding of heavy–light meson dynamics and provides an improved model dependent estimate of the CKM matrix element, yielding [Formula: see text] validating the well-known standard model predictions.