Gluons in charmoniumlike states

TL;DR

This study decomposes the mass components of charmoniumlike states using lattice QCD, revealing that mass splittings mainly originate from gluon contributions and that exotic states have a larger light quark and gluon component than conventional charmonia.

Contribution

It provides the first lattice QCD analysis of mass decomposition and internal structure of exotic charmoniumlike states, highlighting differences from conventional states.

Findings

Mass contributions from quark masses are similar across states.

Mass splittings are mainly due to gluon trace anomaly.

Exotic states have a lower charm quark momentum fraction, indicating more light quark and gluon content.

Abstract

The mass components of charmoniumlike states are investigated through the decomposition of QCD energy-momentum tensor (EMT) on lattice. The quark mass contribution $\langle H_m\rangle$ and the momentum fraction $\langle x\rangle$ of valence charm quark and antiquark are calculated for conventional $1S,1P,1D$ charmonia and the exotic $1^{-+}$ charmoniumlike state, based on the $N_f=2+1$ gauge configurations generated by the RBC/UKQCD collaboration. It is found that $\langle H_m\rangle$ is close to each other and around 2.0 to 2.2 GeV for these states, which implies that the mass splittings among these states come almost from the gluon contribution of QCD trace anomaly. The $\langle x\rangle$ of the $1^{-+}$ state is only around 0.55, while that in conventional charmonia is around 0.7 to 0.8. This difference manifests that the proportion of light quarks and gluons in the $1^{-+}$ charmoniumlike state is significantly larger than conventional states.