Glueball spectrum from $N_f=2$ lattice QCD study on anisotropic lattices

The lowest-lying glueballs are investigated from $N_f=2$ QCD study on aniostropic lattices. Only the gluonic operators built from Wilson loops are involved in calculating the corresponding correlation functions. In the tensor channel, we obtain the ground state mass to be 2.367(35) GeV and 2.380(61) GeV at $m_\pi\sim 938$ MeV and $650$ MeV, respectively. In the pseudoscalar channel, when we use the gluonic operator whose continuum limit has the form of $\epsilon_{ijk}TrB_iD_jB_k$, we obtain the ground state mass to be 2.559(50) GeV and 2.605(52) GeV at the two pion masses. These results are in agreement with the corresponding glueball masses in the quenched approximation and show little dependence of pion masses. In contrast, if we use the topological charge density as field operators for the pseudoscalar, the masses of the lowest state are much lighter (around 1GeV) and compatible with the expected masses of the flavor singlet $q\bar{q}$ meson. This provides a strong hint that the operator $\epsilon_{ijk}TrB_iD_jB_k$ and the topological charge density couple very differently to the glueball states and $q\bar{q}$ mesons. In the scalar channel, the ground state masses extracted from the correlation functions of gluonic operators are determined to be around 1.4-1.5 GeV, which are close to the ground state masses from the correlation functions of the quark bilinear operators. In all cases, the mixing between glueballs and conventional mesons remains to be investigated in the future.