Test of Low-Energy Theorems forH1(γ→,π0)H1in the Threshold Region

The photon asymmetry in the reaction ${}^1\mathrm{H}(\overrightarrow{\gamma },{\pi }^0{)}^1\mathrm{H}$ close to threshold has been measured for the first time with the photon spectrometer TAPS using linearly polarized photons from the tagged-photon facility at the Mainz Microtron MAMI. The total and differential cross sections were also measured simultaneously with the photon asymmetry. This allowed determination of the $S$-wave and all three $P$-wave amplitudes. The values obtained at threshold are $E_{0+}=[-1.33\mathrm{}\pm 0.08(\mathrm{stat})\pm 0.03(\mathrm{syst}\left)\right]\times {10}^{-3\mathrm{}}{/m}_{{\pi }^{+}}$, $P_1=[9.47\pm 0.08(\mathrm{stat})\pm 0.29(\mathrm{syst}\left)\right]\times {10}^{-3\mathrm{}}{q/m}_{{\pi }^{+}}^2$, $P_2=[-9.46\mathrm{}\pm 0.1(\mathrm{stat})\pm 0.29(\mathrm{syst}\left)\right]\times {10}^{-3\mathrm{}}{q/m}_{{\pi }^{+}}^2$, and $P_3=[11.48\pm 0.06(\mathrm{stat})\pm 0.35(\mathrm{syst}\left)\right]\times {10}^{-3\mathrm{}}{q/m}_{{\pi }^{+}}^2$.