Exclusive $\rho^{0}$ Production in Polarized DIS at SMC

Preliminary spin cross section asymmetries for exclusive $\rho^{0}$ lepto-production, $\vec{\mu} + \vec{N} \to \mu' + N + \rho^{0} (\rho^{0} \to \pi^{+} \pi^{-})$, are reported. These asymmetries have been determined for the first time by the Spin Muon Collaboration (SMC) at low Q^2 (photoproduction) and at large Q^2 (DIS) for different $p_T^2$ intervals in the kinematic range $0.01 <Q^2< 60 GeV^2$ and $140 < W^2 < 310 GeV^2$ (<W> \simeq 15 GeV) for the full SMC data set. About 100 K $\rho^{0}$'s have been selected for $0.62 < m (\pi^{+} \pi^{-}) < 1.07 GeV/c^2$ and $|I|< 0.05$. Within the statistical precision, no significant asymmetries have been observed at low $Q^{2}$ in the preliminary results.