Study of ${\pi }^0$ pair production in single-tag two-photon collisions

We report a measurement of the differential cross section of ${\pi }^0$ pair production in single-tag two-photon collisions, $\gamma^* \gamma \to \pi^0 \pi^0$,in$e^+ e^-$scattering\mathrm{.}Thecrosssectionismeasuredfor$Q^2$ up to 30 GeV${}^2$, where $Q^2$ is the negative of the invariant mass squared of the tagged photon, in the kinematic range 0.5 GeV < W < 2.1 GeV and $|\cos \theta^*|$ < 1.0 for the total energy and pion scattering angle, respectively, in the ${\gamma }^{\ast }\gamma$ center-of-mass system. The results are based on a data sample of 759 fb${}^{-1}$ collected with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. The transition form factor of the $f_0(980)$ and that of the $f_2(1270)$ with the helicity-0, -1, and -2 components separately are measured for the first time and are compared with theoretical calculations.