Glueball relevant study on isoscalars from $N_f=2$ lattice QCD

Abstract: We perform a glueball-relevant study on isoscalars based on anisotropic $N_f=2$ lattice QCD gauge configurations. In the scalar channel, we identify the ground state obtained through gluonic operators to be a single-particle state through its dispersion relation. When $q\bar{q}$ operator is included, we find the mass of this state does not change, and the $q\bar{q}$ operator couples very weakly to this state. So this state is most likely a glueball state. For pseudoscalars, along with the exiting lattice results, our study implies that both the conventional $q\bar{q}$ state $\eta_2$ (or $\eta'$ in flavor $SU(3)$) and a heavier glueball-like state with a mass of roughly 2.6 GeV exist in the spectrum of lattice QCD with dynamical quarks.