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

TL;DR

This study uses lattice QCD to compute Bethe-Salpeter wave functions of excited charmonium states, providing insights into their internal structure and validating potential models for these mesons.

Contribution

First lattice QCD calculation of BS wave functions for excited charmonium states, supporting the potential model description of charmonium below open-charm threshold.

Findings

Root-mean-square radii for 1S and 2S states estimated.

Quark kinetic mass and interquark potentials from 2S states agree with 1S states.

Potential description remains valid for excited charmonium states.

Abstract

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. We also examine whether a series of the BS wave functions from the ground state to excited states can be described by a single set of the spin-independent and spin-dependent interquark potentials with a unique quark mass. It is found that the quark kinetic mass and, both the central and spin-spin charmonium potentials, determined from the $2S$ wave functions, fairly agree with the ones from the $1S$ wave functions. This strongly supports the validity of the potential description for the charmonium system, at least, below open-charm threshold.