Double-polarization observables in the reaction $vec{e}p rightarrow evec{p}gamma{}$ have been measured at $Q^2=0.33 (GeV/c)^2$. The experiment was performed at the spectrometer setup of the A1 Collaboration using the 855 MeV polarized electron beam p
rovided by the Mainz Microtron (MAMI) and a recoil proton polarimeter. From the double-polarization observables the structure function $P_{LT}^perp$ is extracted for the first time, with the value $(-15.4 pm 3.3 (stat.)^{+1.5}_{-2.4} (syst.)) GeV^{-2}$, using the low-energy theorem for Virtual Compton Sattering. This structure function provides a hitherto unmeasured linear combination of the generalized polarizabilities of the proton.
The cross section of the $ep to e p gamma$ reaction has been measured at $Q^2 = 0.33$ (GeV/c)$^2$. The experiment was performed using the electron beam of the MAMI accelerator and the standard detector setup of the A1 Collaboration. The cross section
is analyzed using the low-energy theorem for virtual Compton scattering, yielding a new determination of the two structure functions $P_LL}-P_{TT}/epsilon$ and $P_{LT}$ which are linear combinations of the generalized polarizabilities of the proton. We find somewhat larger values than in the previous investigation at the same $Q^2$. This difference, however, is purely due to our more refined analysis of the data. The results tend to confirm the non-trivial $Q^2$-evolution of the generalized polarizabilities and call for more measurements in the low-$Q^2$ region ($le$ 1 (GeV/c)$^2$).
