Bethe-Salpeter wave functions of $\eta_c(2S)$ and $\psi(2S)$ states from full lattice QCD

Understand

We discuss the internal structure of radially excited charmonium mesons based on the equal-time and Coulomb gauge Bethe-Salpeter (BS) amplitudes, which are obtained in lattice QCD.

• Our simulations are performed with a relativistic heavy-quark action for the charm quark on the 2+1 flavor PACS-CS gauge configurations at the lightest pion mass, $M_{\pi}=156(7)$ MeV.
• The variational method is applied to the study of optimal charmonium operator for ground and first excited states of $S$-wave charmonia.
• We successfully calculate the BS wave functions of $\eta_c(2S)$ and $\psi(2S)$ states, as well as $\eta_c(1S)$ and $J/\psi$ states, and then estimate the root-mean-square radii of both the $1S$ and $2S$ charmonium states.