Speaker
Description
We carry out the first lattice calculation of the charm quark density-density correlations for $1S$ and $1P$ conventional charmonia, as well as charmoniumlike states $\eta_{c1}(1^{-+})$ and $h_{c0}(0^{+-})$, which provide {\it ab initio} information about the internal spatial structures of these states. The spatial distributions of the charm quark and antiquark ($c\bar{c}$) in $1S$ and $1P$ states exhibit clear relativistic effects that can be understood neatly in the Dirac theory of quarks with a Cornell-type potential. For the charmoniumlike hybrid $\eta_{c1}(1^{-+})$ and $h_{c0}(0^{+-})$, the $c\bar{c}$ component is compact with a spatial size comparable with those of charmonia. Specifically, $\eta_{c1}$ can be viewed as an $S$-wave bound state of a color octet $1^{--}$ $c\bar{c}$ component and a $1^{+-}$ gluonic (chromomagnetic) component. The calculation is performed in $N_f=2$ lattice QCD with a pion mass around 420~MeV and at a single lattice spacing of about 0.136(2) fm. The systematic uncertainties should be investigated through more sophisticated lattice setups in the future.