  The production of vector mesons in SIDIS is a particularly interesting
channel to study the polarized fragmentation and related phenomena. Preliminary
COMPASS results for the first measurement of inclusive $\rho^0$ Collins and
Sivers transverse-spin asymmetries are presented here for the first time. The
analysis is based on the data-set collected by COMPASS in $2010$ using a $160\,
\rm{GeV}/c$ $\mu^+$ beam and a transversely polarized $NH_3$ target. The
asymmetries are extracted as function of Bjorken-$x$, of the total transverse
momentum of the oppositely charged hadron pair and of the fraction of available
energy $z$ carried by the pair. Indications for positive Collins and Sivers
asymmetries are obtained as expected from models.

High Energy Physics - Experiment;High Energy Physics - Phenomenology