Double-spin asymmetry in exclusive $\rho^{0}$ meson production

The longitudinal double-spin asymmetry $A^{\rho}_{1}$ extracted from exclusive muoproduction of $\rho^{0}$ mesons, $\mu+N\rightarrow\mu+N'+\rho^{0}$, is studied using 2002 and 2003 data from the COMPASS experiment. The studied reaction is incoherent $\rho^{0}$ production on polarized deuterons. The dependence of $A^{\rho}_{1}$ on $Q^{2}$ and $x_{Bj}$ is presented in a wide kinematical range of 3 $+$ 10%$^{-3} < Q^{2} <$ GeV$^{2}$ and 5 $+$ 10$^{-5} < x_{Bj} <$ 0.05. The presented results are the $first$ measurements of $A^{\rho}_{1}$ at small $Q^{2} (Q^{2} <$ 0.1 GeV $^{2})$ and small $x_{Bj} (x_{Bj} <$ 3 $+$ 10$^{-3})$. The asymmetry is consistent with zero in the whole studied kinematical range.