  We carry out a systematic classification and computation of next-to-leading
order kinematic power corrections to the fully differential cross section in
the parton shower. To do this we devise a map between ingredients in a parton
shower and operators in a traditional effective field theory framework using a
chain of soft-collinear effective theories. Our approach overcomes several
difficulties including avoiding double counting and distinguishing
approximations that are coordinate choices from true power corrections.
Branching corrections can be classified as hard-scattering, that occur near the
top of the shower, and jet-structure, that can occur at any point inside it.
Hard-scattering corrections include matrix elements with additional hard
partons, as well as power suppressed contributions to the branching for the
leading jet. Jet-structure corrections require simultaneous consideration of
potential 1 -> 2 and 1 -> 3 branchings. The interference structure induced by
collinear terms with subleading powers remains localized in the shower.
