The lowest-lying glueballs are investigated from $N_f=2$ QCD study onaniostropic lattices. Only the gluonic operators built from Wilson loops areinvolved in calculating the corresponding correlation functions. In the tensorchannel, we obtain the ground state mass to be 2.367(35) GeV and 2.380(61) GeVat $m_\pi\sim 938$ MeV and $650$ MeV, respectively. In the pseudoscalarchannel, 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 agreementwith the corresponding glueball masses in the quenched approximation and showlittle dependence of pion masses. In contrast, if we use the topological chargedensity as field operators for the pseudoscalar, the masses of the lowest stateare much lighter (around 1GeV) and compatible with the expected masses of theflavor 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 verydifferently to the glueball states and $q\bar{q}$ mesons. In the scalarchannel, the ground state masses extracted from the correlation functions ofgluonic operators are determined to be around 1.4-1.5 GeV, which are close tothe ground state masses from the correlation functions of the quark bilinearoperators. In all cases, the mixing between glueballs and conventional mesonsremains to be investigated in the future.
展开▼
