Constraint equations for heavy-to-light currents in soft-collinear effective theory

A complete basis for the next-to-next-to leading order heavy-to-light currents in the soft-collinear effective theory is constructed. Reparametrization invariance is imposed by deriving constraint equations. Their solutions give the set of allowed Dirac structures as well as relations between the Wilson coefficients of operators that appear at different orders in the power expansion. The completeness of reparametrization invariance constraints derived on a projected surface is investigated. We also discuss the universality of the ultrasoft Wilson line with boundary conditions.