Two-photon Transition Form Factor of $\eta_{c,b}(nS)$ and $\chi_{c0,b0}(nP)$ via Relativized Mock Meson States

Abstract

We construct relativized mock meson states for heavy quarkonium, where the Dirac spinors import kinetic relativistic correction and the dynamic wave functions are the same as those solved from Schr\"odinger equation. We find that the kinetic relativistic correction imported by Dirac spinors is crucial to study the two-photon transition form factors. Using relativized mock meson states, we give credible predictions for the two-photon transition form factors and decay widths of $\eta_{c,b}(n^1S_0)$ and $\chi_{c,b}(n^3P_0)$ ($n=1,2,3$).