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Authors
Bing An Li
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The mixing between the $f_2(1270)$, the $f_2(1525)$, and the $2^{++}$ glueball is determined and tested. The mass and the hadronic decay widths of the $G_2$ and the branching ratio $B(J/psirightarrowgamma G_2)$ are predicted.
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We have revisited glueball mixing with the pseudoscalar mesons in the MIT bag model scheme. The calculation has been performed in the spherical cavity approximation to the bag using two different fermion propagators, the cavity and the free propagators. We obtain a very small probability of mixing for the eta at the level of $0.04-0.1% and a bigger for the eta at the level of 4-12%. Our results differ from previous calculations in the same scheme but seem to agree with the experimental analysis. We discuss the origin of our difference which stems from the treatment of our time integrations.
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 $qbar{q}$ operator is included, we find the mass of this state does not change, and the $qbar{q}$ 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 $qbar{q}$ 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.
We develop an inverse matrix method to solve for resonance masses from a dispersion relation obeyed by a correlation function. Given the operator product expansion (OPE) of a correlation function in the deep Euclidean region, we obtain the nonperturbative spectral density, which exhibits resonance structures naturally. The value of the gluon condensate in the OPE is fixed by producing the $rho$ meson mass in the formalism, and then input into the dispersion relations for the scalar, pseudoscalar and tensor glueballs. It is shown that the low-energy limit of the correlation function for the scalar glueball, derived from the spectral density, discriminates the lattice estimate for the triple-gluon condensate from the single-instanton estimate. The spectral densities for the scalar and pseudoscalar glueballs reveal a double-peak structure: the peak located at lower mass implies that the $f_0(500)$ and $f_0(980)$ ($eta$ ad $eta$) mesons contain small amount of gluonium components, and should be included into scalar (pseudoscalar) mixing frameworks. Another peak determines the scalar (pseudoscalar) glueball mass around 1.50 (1.75) GeV with a broad width about 200 MeV, suggesting that the $f_0(1370)$, $f_0(1500)$ and $f_0(1710)$ ($eta(1760)$) mesons are the glue-rich states. We also predict the topological susceptability $chi_t^{1/4}=75$-78 MeV, deduced from the correlation function for the pseudoscalar glueball at zero momentum. Our analysis gives no resonance solution for the tensor glueball, which may be attributed to the insufficient nonperturbative condensate information in the currently available OPE.
We calculate the scattering cross section between two $0^{++}$ glueballs in $SU(2)$ Yang-Mills theory on lattice at $beta = 2.1, 2.2, 2.3, 2.4$, and 2.5 using the indirect (HAL QCD) method. We employ the cluster-decomposition error reduction technique and use all space-time symmetries to improve the signal. In the use of the HAL QCD method, the centrifugal force was subtracted to remove the systematic effect due to nonzero angular momenta of lattice discretization. From the extracted interglueball potential we determine the low energy glueball effective theory by matching with the one-glueball exchange process. We then calculate the scattering phase shift, and derive the relation between the interglueball cross section and the scale parameter $Lambda$ as $sigma_{phi phi} = (2 - 51) Lambda^{-2}$ (stat.+sys.). From the observational constraints of galactic collisions, we obtain the lower bound of the scale parameter, as $Lambda > 60$ MeV. We also discuss the naturalness of the Yang-Mills theory as the theory explaining dark matter.
The lowest-lying glueballs are investigated in lattice QCD using $N_f=2$ clover Wilson fermion on anisotropic lattices. We simulate at two different and relatively heavy quark masses, corresponding to physical pion mass of $m_pisim 938$ MeV and $650$ MeV. The quark mass dependence of the glueball masses have not been investigated in the present study. Only the gluonic operators built from Wilson loops are utilized in calculating the corresponding correlation functions. In the tensor channel, we obtain the ground state mass to be 2.363(39) GeV and 2.384(67) GeV at $m_pisim 938$ MeV and $650$ MeV, respectively. In the pseudoscalar channel, when using the gluonic operator whose continuum limit has the form of $epsilon_{ijk}TrB_iD_jB_k$, we obtain the ground state mass to be 2.573(55) GeV and 2.585(65) GeV at the two pion masses. These results are compatible with the corresponding results in the quenched approximation. 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 $qbar{q}$ meson. This indicates that the operator $epsilon_{ijk}TrB_iD_jB_k$ and the topological charge density couple rather differently to the glueball states and $qbar{q}$ mesons. The observation of the light flavor singlet pseudoscalar meson can be viewed as the manifestation of effects of dynamical quarks. 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 is 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 further clarified in the future.
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