Charm annihilation effects on the hyperfine splitting in charmonium

TL;DR

This paper investigates the impact of disconnected diagrams on hyperfine splitting in charmonium, providing nonperturbative estimates in quenched and unquenched QCD to improve high-precision spectrum calculations.

Contribution

It offers the first nonperturbative estimates of disconnected diagram effects on charmonium hyperfine splitting in both quenched and unquenched lattice QCD.

Findings

Disconnected contributions are small but non-negligible.

Light modes in unquenched ensembles complicate signal extraction.

Results obtained at lattice spacings of approximately 0.09 fm and 0.06 fm.

Abstract

In calculations of the hyperfine splitting in charmonium, the contributions of the disconnected diagrams are considered small and are typically ignored. We aim to estimate nonperturbatively the size of the resulting correction, which may eventually be needed in high precision calculations of the charmonium spectrum. We study this problem in the quenched and unquenched QCD cases. On dynamical ensembles the disconnected charmonium propagators contain light modes which complicate the extraction of the signal at large distances. In the fully quenched case, where there are no such light modes, the interpretation of the signal is simplified. We present results from lattices with $a\approx 0.09$ fm and $a\approx 0.06$ fm.