Contribution of disconnected diagrams to the hyperfine splitting of charmonium

TL;DR

This study investigates the impact of disconnected diagrams on the hyperfine splitting in charmonium using lattice QCD, revealing significant effects at strange quark masses but minimal influence at charm quark masses.

Contribution

It provides the first detailed lattice QCD analysis of OZI-suppressed disconnected diagrams' effects on charmonium hyperfine splitting across various quark masses.

Findings

Disconnected diagrams increase pseudoscalar meson mass near strange quark mass.

No significant disconnected contribution observed in the vector channel.

Effect diminishes as quark mass approaches charm mass.

Abstract

We discuss the contribution of OZI-suppressed diagrams to the hyperfine splitting of charmonium in lattice QCD. We study valence quark mass regions from strange to charm quark masses. No contribution of the disconnected diagram is seen in the vector meson channel. In the pseudo-scalar channel and for valence quark masses around the strange quark, the disconnected contribution induces a considerable increase of the meson mass. This contribution quickly decreases as the quark mass increases. For charmonium the effect is very small although a decrease of the pseudoscalar mass induced by the disconnected contribution cannot be ruled out.