  The goal of this paper is to assign an intrinsic meaning to the space of
quantum parameters $\operatorname{Par}_G$ appearing in the geometric Langlands
program of Beilinson-Drinfeld. We introduce tame twistings, a variant of
twisted differential operators (TDOs) for which regularity of twisted $\mathscr
D$-modules is well-defined. Our main result is that for a proper curve $X$,
$\operatorname{Par}_G$ is precisely the moduli space of factorization tame
twistings on the affine Grassmannian.
