Structure of renormalization constants for theories with multiple couplings in the MS-like subtraction schemes

Abstract

For theories with multiple couplings we construct simple expressions for the four-dimensional (or, in general, integer-dimensional) renormalization constants assuming that all divergences are logarithmical. These expressions allow relating all coefficients at $\epsilon$-poles, logarithms, and (if exist) mixed terms to the coefficients of the renormalization group functions in any order of the perturbation theory for MS-like renormalization prescriptions. The result admits such a formulation in that $\epsilon$-poles and $\ln \Lambda /\mu$ enter on the same footing. For theories with two and three couplings we present explicit expressions for the pole/logarithm structure of renormalization constants in the lowest orders of the perturbation theory. They are verified by comparisons with the two-loop explicit calculation for $\mathcal{N}=1$ SQCD+SQED and also with the previously known three-loop calculations for the ${\phi }^4$-theory with two couplings.

Comments: 27 pages, 1 figure, the version accepted for publication in Nuclear Physics B