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September 10, 2025

Improved Wave Function for Heavy-light Mesons in QCD Potential Model Approach and Parameterization of the Cornell Potential

AAAbdul AzizUniversity of Nizwa SRSabyasachi RoyGuy's and St Thomas' NHS Foundation Trust ADAtri DeshamukhyaAssam University

Key Points

The findings show an improved wave function for heavy-light mesons in QCD potential models, enhancing potential accuracy.
Using Schrödinger equation solutions, the range of the scale factor c of the Cornell potential is defined in relation to heavy-flavor mesons.
Exploration of inter quark separations identifies critical distances that influence perturbation choices in the Cornell potential.
Insights into the interplay between linear and Coulombic terms can inform future meson modeling in quantum chromodynamics.

Abstract

Wereport improved wave function for mesons in QCD potential model approach using multiplicative method for solution of Schr¨odinger equation for the extreme cases of inter quark separations (r → 0 and r → ∞). Using the wave function we find the range of the scale factor c of the Cornell potential with reference to the mass scale of B and D sectors heavy-flavoured mesons. With our computed range of c, we also explore the critical inter quark separation which should govern the choice of parent-child terms in perturbation method out of the linear and Coulombic terms of the Cornell potential.

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