Excited charmonium spectrum from anisotropic lattices

TL;DR

This paper calculates the excited charmonium spectrum using anisotropic lattice QCD, identifying exotic hybrid states and orbitally excited mesons with continuum extrapolation across multiple lattice spacings.

Contribution

The study provides a detailed relativistic lattice QCD calculation of the excited charmonium spectrum, including exotic hybrids, with continuum limit results and finite volume validation.

Findings

Exotic hybrid $1^{-+}$ at 4.428 GeV

Exotic hybrids $0^{+-}$ and $2^{+-}$ at 4.70 and 4.895 GeV

Spectrum includes orbitally excited mesons up to L=3

Abstract

We present our final results for the excited charmonium spectrum from a quenched calculation using a fully relativistic anisotropic lattice QCD action. A detailed excited charmonium spectrum is obtained, including both the exotic hybrids (with $J^{PC} = 1^{-+}, 0^{+-}, 2^{+-}$) and orbitally excited mesons (with orbital angular momentum up to 3). Using three different lattice spacings (0.197, 0.131, and 0.092 fm), we perform a continuum extrapolation of the spectrum. We convert our results in lattice units to physical values using lattice scales set by the $^1P_1-1S$ splitting. The lowest lying exotic hybrid $1^{-+}$ lies at 4.428(41) GeV, slightly above the $D^{**}D$ (S+P wave) threshold of 4.287 GeV. Another two exotic hybrids $0^{+-}$ and $2^{+-}$ are determined to be 4.70(17) GeV and 4.895(88) GeV, respectively. Our finite volume analysis confirms that our lattices are large enough to accommodate all the excited states reported here.