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We investigate the glueball spectrum for $N_f=4$ fermions corresponding tolow pion masses of $m_\pi \sim 250$MeV. We do so by making use ofconfigurations produced with maximally twisted fermions within the framework ofthe Extended Twisted Mass Collaboration (ETMC). We extract states that belongto irreducible representations of the octahedral group of rotations $R$ incombination with the quantum numbers of charge conjugation $C$ and parity $P$,i.e. $R^{PC}$. We implement the Generalized Eigenvalue Problem (GEVP) using abasis consisting only of gluonic operators. The purpose of this work is toinvestigate the effect of light dynamical quarks on the glueball spectrum andhow this compares to the statistically more accurate spectrum of the pure gaugetheory. We employed large ensembles of the order of ${\sim {~\cal O}}(10 {\rmK})$ configurations for each of three different lattice spacings. Our resultsdemonstrate that in the scalar channel $A_1^{++}$ we obtain an additional,lightest state due to the inclusion of light dynamical quarks while the nexttwo states are consistent with the lightest two states in the pure gaugetheory. By contrast the mass of the lightest tensor glueball $J^{PC}=2^{++}$appears to be insensitive to the inclusion of sea quarks, as is the mass of thelightest pseudoscalar. In addition we perform an investigation of the low lyingspectrum of the representation $A_1^{++}$ for $N_f=2+1+1$ twisted mass quarkswith low masses and demonstrate that the extra lowest state depends strongly onthe pion mass. This suggests that the ground state of the scalar glueball has alarge quark content, possibly representing the decay of a glueball to twopions.

The glueball spectrum with $N_f=4$ light fermions