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arXiv · 2509.03437

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

Gleb Kovyrshin·Nikolai Meshcheriakov·Victoria Shatalova·Konstantin Stepanyantz
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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 $\varepsilon$-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 $\varepsilon$-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 ${\cal N}=1$ SQCD+SQED and also with the previously known three-loop calculations for the $\varphi^4$-theory with two couplings.

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Gleb Kovyrshin, Nikolai Meshcheriakov, Victoria Shatalova, Konstantin Stepanyantz. 2025-09-03. Structure of renormalization constants for theories with multiple couplings in the MS-like subtraction schemes. https://arxiv.org/abs/2509.03437

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