Effects of The Initial Hadron in $B\to J/\psi+X$

In the framework of HQET inclusive decays of b-flavored hadrons can be handled as decays of the free b-quark approximately. We analyse the correction to this approximation for the inclusive decays into a polarized $J/\psi$,the correction is characterized by two matrix elements defined in HQET. For the $J/\psi$ we use NRQCD to parameterize the formation of the $c\bar c$ pair into $J/\psi$. Numerically the correction is remarkably large, it can be at the level of 30% and it is mainly due to the Fermi-motion of the $b$-quark. With this correction we give a new determination for combinations of two NRQCD matrix elements.