Dimensional reduction in non-supersymmetric theories

Abstract

It is shown that regularisation by dimensional reduction is a viable alternative to dimensional regularisation in non-supersymmetric theories.

Regularization schemes and higher order corrections

“…The DRED scheme is primarily used as a supersymmetric regulator and is quite cumbersome for non-supersymmetric calculations. It is, however, closely related to the FDH scheme and has been demonstrated [8,9,23,24] The calculation of the V boson decay rate provides another instance of the equivalence the CDR and DRED schemes at the four-loop level [23]. The ability to obtain the correct result using the DRED scheme required a delicate balance of the many extra couplings and their renormalization effects upon one another.…”

“…Because the effects of external evanescent states can be removed (or indeed never seen) by imposing a four-dimensionality restriction, and because the effects of internal evanescent states therefore contribute at order ε at one loop, it appears that one can simply ignore the distinction between gauge and evanescent terms. In contrast, because the DRED scheme must deal with external evanescent terms from the beginning, its advocates were forced to develop a successful renormalization program [8,9]. Extensive testing [8,9,23,24] has shown that this program works to at least the fourth order and that it handles the effects of both internal and external evanescent contributions.…”

“…A successful renormalization program for the DRED scheme [8,9] applies the principle of minimal subtraction to the evanescent Green functions (that is, Green functions with external evanescent states)…”

“…The evanescent coupling still contributes to Green functions with only physical external states, but the contribution is rendered finite by the prescribed renormalization program [8,9,23,24]. Because the evanescent coupling, α e renormalizes differently than the gauge coupling α s , the two cannot be identified, even at the end of the calculation.…”

“…The arguments which establish the validity of the HV scheme carry over to the CDR scheme and establish that it too is a valid regularization scheme. After some initial confusion over the proper renormalization procedure [6][7][8] for the DRED scheme, it was established that it too is a proper, unitary regularization scheme [8] and that it is indeed equivalent to the CDR scheme [9]. The FDH scheme has never been subjected to such stringent examination.…”