  In view of various field-theoretic reasons, in the present work, we study the
question of if the usual dimensional regularization can be extended to quantum
field theories with an ultraviolet cutoff (Poincare-breaking scale) in a way
preserving all the properties of the dimensional regularization. And we find
that it can indeed be. The resulting extension gives a framework in which the
power-law and logarithmic divergences get detached to involve different scales.
This new regularization scheme, the detached regularization as we call it,
enables one to treat the power-law and logarithmic divergences differently and
independently. We apply the detached regularization to the computation of the
vacuum energy and to two well-known QFTs namely the scalar and spinor
electrodynamics. As a case study, we consider Fujikawa's subtractive
renormalization in the framework of the detached regularization, and show its
effectiveness up to two loops by specializing to scalar self energy. We discuss
various application areas of the detached regularization.
