Equivalence of Dimensional Reduction and Dimensional Regularisation

For some years there has been uncertainty over whether regularisation by dimensional reduction (DRED) is viable for non-supersymmetric theories. We resolve this issue by showing that DRED is entirely equivalent to standard dimensional regularisation (DREG), to all orders in perturbation theory and for a general renormalisable theory. The two regularisation schemes are related by an analytic redefinition of the couplings, under which the $\b$-functions calculated using DRED transform into those computed in DREG. The $S$-matrix calculated using DRED is numerically equal to the DREG version, ensuring that both schemes give the same physics.