Kapitza Inspired Effective Interaction for the Exotic State X(3872): A Coupled-Channel Potential Model Study

Abstract

The X(3872) remains one of the most intriguing exotic hadrons, lying extremely close to the $D^0{\bar{D}}^{\ast 0}$ threshold. We construct an effective potential consisting of Coulomb, linear confinement and a Kapitza-inspired term representing the averaged effect of fast gluonic fluctuations. Numerical solution of the Schrödinger equation shows that this term provides effective attraction in the intermediate-distance region, yielding a ground-state mass of $3871.7\pm 0.9$ MeV in excellent agreement with experiment. Coupled-channel analysis indicates a dominant molecular component ($\sim 65\%-72\%$) with a significant compact tetraquark core ($\sim 28\%-35\%$). We also present predictions for low-lying excited states. The model offers a physically motivated mechanism for threshold tuning.