Potential description of the charmonium from lattice QCD

Abstract

We present spin-independent and spin-spin interquark potentials for charmonium states, that are calculated using a relativistic heavy quark action for charm quarks on the PACS-CS gauge configurations generated with the Iwasaki gauge action and 2+1 flavors of Wilson clover quark. The interquark potential with finite quark masses is defined through the equal-time Bethe-Salpeter amplitude. The light and strange quark masses are close to the physical point where the pion mass corresponds to $M_{\pi }\approx 156(7)$ MeV, and charm quark mass is tuned to reproduce the experimental values of ${\eta }_c$ and $J/\psi$ states. Our simulations are performed with a lattice cutoff of $a^{-1}\approx 2.2$ GeV and a spatial volume of $(3\mathrm{fm}{)}^3$. We solve the nonrelativistic Schrödinger equation with resulting charmonium potentials as theoretical inputs. The resultant charmonium spectrum below the open charm threshold shows a fairly good agreement with experimental data of well-established charmonium states.

Comments: 12 pages, 4 figures, the Proceedings of the Conference "XIth Quark Confinement and the Hadron Spectrum", September 8 to 12, Saint-Petersburg State University, Russia