Process $\eta \to {\pi }^0\gamma \gamma$ in the Nambu-Jona-Lasinio model

The decay width of the process $\eta \to {\pi }^0\gamma \gamma$ is calculated in the framework of the Nambu-Jona-Lasinio model. The momentum dependence of quark loops is taken into account. Three types of diagrams are considered: quark box, scalar ($a_0$) and vector $(\rho ,\omega )$ pole diagrams. The obtained estimations are in satisfactory agreement with recent experimental data.

Figure 1

Diagrams contributing to the amplitude of the process $\eta \to {\pi }^0\gamma \gamma$.

Figure 2

Invariant mass distribution of the two-photons of the scalar meson contribution(dots), vector meson contributions(short dash), $\mathrm{\text{scalar}}+\mathrm{\text{vector mesons}}(\mathrm{\text{dash}}\mathrm{\text{−}}\mathrm{\text{dot}})$, quark box(long dash) and total(continuous line) for the set I.

Figure 3

Invariant mass distribution of the two-photons of the scalar meson contribution(dots), vector meson contributions(short dash), $\mathrm{\text{scalar}}+\mathrm{\text{vector mesons}}(\mathrm{\text{dash}}\mathrm{\text{−}}\mathrm{\text{dot}})$, quark box(long dash) and total(continuous line) for the set II.

Figure 4

Invariant mass distribution of the two-photons of the total contributions for the set I (dashes), set II (dots) together with the results of the chiral unitary approach [20].