Lattice study of the masses of singlet $0^{++}$ mesons

We compute the masses of the flavor singlet $0^{++}$ mesons using ($n_f=2$) unquenched lattice QCD with the Iwasaki and Wilson gauge actions. Both fermionic and glueball interpolating operators are used to create the states. The mass of the lightest $0^{++}$ meson is suppressed relative to the mass of the $0^{++}$ glueball in quenched QCD at an equivalent lattice spacing. The low value for mass of the lightest flavor singlet $0^{++}$ meson obtained in our calculation could be due to either: that the mass of the meson is much lower than that of the $0^{++}$ glueball in quenched QCD, or due to the effect of lattice artifacts. We present arguments for the first option, but we are unable to rule out the explanation due to lattice artifacts.

Figure 1

Singlet scalar meson effective mass plot from fermionic and gluonic operators from U355 with momentum zero.

Figure 2

Singlet scalar meson effective mass plot from fermionic and gluonic operators from C410 with momentum zero.

Figure 3

Singlet scalar meson effective mass plot from fermionic and gluonic operators from C390 with momentum zero.

Figure 4

Scalar meson masses (for U355) versus momentum for both flavor-singlet ($f_0$) and nonsinglet ($a_0$). The straight lines show the expected slope for a relativistic mass-energy relationship. The lowest $\pi \pi$ thresholds are also illustrated.

Figure 5

Compilation of FS $0^{++}$ masses versus $a^2$. The quenched data are from lattice calculations that use the Wilson gauge action [7, 61, 62, 63, 64].

Figure 6

FS $0^{++}$ mass from this calculation compared to the quenched $0^{++}$ glueball mass from Necco [34].

Figure 7

FS $0^{++}$ mass as a function of pion mass squared.

Figure 8

Two pion threshold for the FS scalar meson as a function of pion mass squared.

Figure 9

The quark structure of the disconnected contribution ($Q$) and the triangle contribution ($T$) to the transition $f_0\to \pi \pi$.

Figure 10

The relative contribution of the disconnected contribution ($Q$) (vacuum subtracted) and the triangle contribution ($T$) to the transition $f_0\to \pi \pi$ with all states at zero momentum for lattice U355.