Glueball Spectrum with four light dynamical fermions

TL;DR

This study investigates how light dynamical quarks influence the glueball spectrum in lattice QCD, revealing the emergence of a quark-rich scalar state and minor effects on tensor and pseudoscalar states.

Contribution

First calculation of glueball spectrum with four light dynamical fermions using gluonic operators, comparing to pure gauge theory results.

Findings

An additional light scalar state appears with dynamical quarks.

The lightest states in tensor and pseudoscalar channels are minimally affected by dynamical quarks.

The additional scalar state has a large quark content, confirmed by $N_f=2+1+1$ simulations.

Abstract

We perform a calculation of the glueball spectrum for $N_f=4$ degenerate dynamical fermions with masses corresponding to light pions. We do so by making use of ensembles produced within the framework of maximally twisted fermions by the Extended Twisted Mass Collaboration (ETMC). We obtain masses of states that fall into the irreducible representations of the octahedral group of rotations in combination with the quantum numbers of charge conjugation $C$ and parity $P$; the above quantum numbers result in 20 distinct irreducible representations. We implement the Generalized Eigenvalue Problem (GEVP) using a basis that consists only of gluonic operators. The purpose of this work is to investigate the effect of light dynamical quarks on the glueball spectrum and how this compares to the statistically more accurate spectrum of $SU(3)$ pure gauge theory. Given that glueball states may have broad widths and thus need to be disentangled from all the relevant mixings, we use large ensembles of the order of ${\sim {~\cal O}}(20 {\rm K})$ configurations. Despite the large ensembles, the statistical uncertainties allow us to extract the masses for only a few irreducible representations; namely $A_1^{++}$, $A_1^{-+}$, $E^{++}$ as well as $T_2^{++}$. The results for the scalar $A_1^{++}$ representation show that an additional state appears as the lightest state in the scalar $A_1^{++}$ channel of the glueball spectrum, while the next two excited states are consistent with the lightest two states of the pure gauge theory. To further elucidate the nature of this additional state we perform a calculation using $N_f=2+1+1$ configurations and this demonstrates that it possesses a large quark content. Finally, the ground states of the $E^{++}$ and $T_2^{++}$ tensor channels and of the $A_1^{-+}$ pseudoscalar channel show, at most, minor effects due to the inclusion of dynamical quarks.