  For a commutative ring $R$, we define the notions of deformed Picard
algebroids and deformed twisted differential operators on a smooth, separated,
locally of finite type $R$-scheme and prove these are in a natural bijection.
We then define the pullback of a sheaf of twisted differential operators that
reduces to the classical definition when $R=\mathbb{C}$. Finally, for modules
over twisted differential operators, we prove a theorem for the descent under a
locally trivial torsor.
