The First Calculation for the Mass of the Ground $4^{++}$ Glueball State on Lattice

TL;DR

This paper presents a lattice calculation of the ground $4^{++}$ glueball mass, providing a precise estimate that challenges previous interpretations of the $\xi(2230)$ resonance as a glueball.

Contribution

The study is the first to compute the mass of the ground $4^{++}$ glueball state on the lattice in the quenched approximation.

Findings

Mass of $4^{++}$ glueball is 3.65 GeV.

Results exclude $\xi(2230)$ as a $4^{++}$ glueball.

Provides a benchmark for future lattice glueball studies.

Abstract

Under the quenched approximation, we perform a lattice calculation for the mass of the ground $4^{++}$ glueball state in $E^{++}$ channel on a $D=3+1$ lattice. Our calculation shows that the mass of this state is $M_G(4^{++})=3.65(6)(18)GeV$, which rules out the $4^{++}$ or mainly $4^{++}$ glueball interpretation for $\xi(2230)$.