The glueball spectrum with $N_f=4$ light fermions

We investigate the glueball spectrum for $N_f=4$ fermions corresponding to low pion masses of $m_\pi \sim 250$MeV. We do so by making use of configurations produced with maximally twisted fermions within the framework of the Extended Twisted Mass Collaboration (ETMC). We extract states that belong to irreducible representations of the octahedral group of rotations $R$ in combination with the quantum numbers of charge conjugation $C$ and parity $P$, i.e. $R^{PC}$. We implement the Generalized Eigenvalue Problem (GEVP) using a basis consisting 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 the pure gauge theory. We employed large ensembles of the order of ${\sim {~\cal O}}(10 {\rm K})$ configurations for each of three different lattice spacings. Our results demonstrate that in the scalar channel $A_1^{++}$ we obtain an additional, lightest state due to the inclusion of light dynamical quarks while the next two states are consistent with the lightest two states in the pure gauge theory. 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 the lightest pseudoscalar. In addition we perform an investigation of the low lying spectrum of the representation $A_1^{++}$ for $N_f=2+1+1$ twisted mass quarks with low masses and demonstrate that the extra lowest state depends strongly on the pion mass. This suggests that the ground state of the scalar glueball has a large quark content, possibly representing the decay of a glueball to two pions.