Extraction of helicity amplitude ratios from exclusive $\rho^0$-meson electroproduction on transversely polarized protons

Exclusive $\rho^0$-meson electroproduction is studied by the HERMES experiment, using the 27.6 GeV longitudinally polarized electron/positron beam of HERA and a transversely polarized hydrogen target, in the kinematic region 1.0 GeV$^2$ < Q$^2$ < 7.0 GeV$^2$, 3.0 GeV < W < 6.3 GeV, and -t' < 0.4 GeV$^2$. Using an unbinned maximum-likelihood method, 25 parameters are extracted. They determine the real and imaginary parts of the ratios of certain helicity amplitudes (describing$\rho^0$-meson production by a virtual photon) and the dominant amplitude $F_{0,\frac{1}{2},0,\frac{1}{2}}$ without the nucleon-helicity flip. The latter amplitude describes the production of a longitudinal $\rho^0$ meson by a longitudinal virtual photon. The transverse target polarization allows for the first time the extraction of ratios of a number of nucleon-helicity-flip amplitudes to $F_{0,\frac{1}{2},0,\frac{1}{2}}$. The ratios of nucleon-helicity-non-flip amplitudes to $F_{0,\frac{1}{2},0,\frac{1}{2}}$ are found to be in good agreement with those from the previous HERMES analysis. A comparison of the extracted amplitude ratios with the Goloskokov-Kroll model shows the necessity to add pion exchange amplitudes with positive $\pi\rho$ form factor to the amplitudes based on generalized parton distributions to improve the HERMES data description