Coefficients at powers of logarithms in the higher-derivatives and minimal-subtractions-of-logarithms renormalization scheme

Meshcheriakov, N.P.; Shatalova, V.V.; Stepanyantz, K.V.

Авторы: Meshcheriakov N.P., Shatalova V.V., Stepanyantz K.V.
Журнал: Physical Review D
Том: 106
Год издания: 2022
Издательство: American Physical Society
Местоположение издательства: United States
Номер статьи: 105011
DOI: 10.1103/PhysRevD.106.105011
Аннотация: For renormalizable theories with a single coupling constant regularized by higher derivatives we investigate the coefficients at powers of logarithms present in the renormalization constants assuming that divergences are removed by minimal subtractions of logarithms. According to this higher-derivatives and minimal-subtractions-of-logarithms (HD+MSL) renormalization prescription, the renormalization constants include only powers of $\ln\Lambda/\mu$, where $\Lambda$ and $\mu$ are the dimensionful regularization parameter and the renormalization point, respectively. We construct general explicit expressions for arbitrary coefficients at powers of this logarithm present in the coupling constant renormalization and in the field renormalization constant which relate them to the $\beta$-function and (in the latter case) to the corresponding anomalous dimension. To check the correctness, we compare the results with the explicit four-loop calculation made earlier for ${\cal N}=1$ SQED and (for the supersymmetric case) rederive a relation between the renormalization constants following from the Novikov, Shifman, Vainshtein, and Zakharov equation.
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Coefficients at powers of logarithms in the higher-derivatives and minimal-subtractions-of-logarithms renormalization schemeстатья

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