  Multiple high precision $\beta$-decay measurements are being carried out
these days on various nuclei, in search of beyond the Standard Model
signatures. These measurements necessitate accurate standard model theoretical
predictions to be compared with. Motivated by the experimental surge, we
present a formalism for such a calculation of $\beta$-decay observables, with
controlled accuracy, based on a perturbative analysis of the theoretical
observables related to the phenomena, including high order nuclear recoil and
shape corrections. The accuracy of the corrections is analyzed by identifying a
hierarchy of small parameters, related to the low momentum transfer
characterizing $\beta$-decays. Furthermore, we show that the sub-percent
uncertainties, targeted by on-going and planned experiments, entail an accuracy
of the order of 10\% for the solution of the nuclear many body problem, which
is well within the reach of modern nuclear theory for light to medium mass
nuclei.
