The differential cross section for the process $\gamma \gamma \to \eta {\pi }^0$ has been measured in the kinematic range $0.84\mathrm{GeV}<W<4.0\mathrm{GeV}$, $|\cos {\theta }^{*}|<0.8$, where $W$ and ${\theta }^{*}$ are the energy and ${\pi }^0$ (or $\eta$) scattering angle, respectively, in the $\gamma \gamma$ center-of-mass system. The results are based on a $223{\mathrm{fb}}^{-1}$ data sample collected with the Belle detector at the KEKB $e^{+}{e}^{-}$ collider. Clear peaks due to the $a_0(980)$ and $a_2(1320)$ are visible. The differential cross sections are fitted in the energy region $0.9\mathrm{GeV}<W<1.46\mathrm{GeV}$ to obtain the parameters of the $a_0(980)$. Its mass, width and ${\Gamma }_{\gamma \gamma }\mathcal{B}(\eta {\pi }^0)$ are measured to be ${982.3}_{-0.7-4.7}^{+0.6+3.1}\mathrm{MeV}/c^2$, $75.6\pm {1.6}_{-10.0}^{+17.4}\mathrm{MeV}$ and ${128}_{-2-43}^{+3+502}\mathrm{eV}$, respectively. The energy and angular dependences above 3.1 GeV are compared with those measured in the ${\pi }^0{\pi }^0$ channel. The integrated cross section over $|\cos {\theta }^{*}|<0.8$ has a $W^{-n}$ dependence with $n=10.5\pm 1.2\pm 0.5$, which is slightly larger than that for ${\pi }^0{\pi }^0$. The differential cross sections show a ${sin}^{-4}{\theta }^{*}$ dependence similar to $\gamma \gamma \to {\pi }^0{\pi }^0$. The measured cross section ratio, $\sigma (\eta {\pi }^0)/\sigma ({\pi }^0{\pi }^0)=0.48\pm 0.05\pm 0.04$, is consistent with a QCD-based prediction.

• Received 8 June 2009

DOI:https://doi.org/10.1103/PhysRevD.80.032001