arXiv subjects

Victoria Shatalova

Publications and source records attributed to Victoria Shatalova.

5 recordsLinked to original sources

arXiv2025

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

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.

hep-th↗

arXiv2024

Higher $\varepsilon$-poles and logarithms in the MS-like schemes from the algebraic structure of the renormalization group

We investigate the structure of renormalization constants within the MS-like renormalization prescriptions for a version of dimensional regularization in which the dimensionful regularization parameter $\Lambda$ differs from the renormalization point $\mu$. Namely, we rewrite the all-loop equations relating coefficients at higher $\varepsilon$-poles and higher powers of $\ln\Lambda/\mu$ to the coefficients of the renormalization group functions in a simple unified form. It is argued that this form follows from the algebraic structure of the renormalization group.

hep-th↗

arXiv2023

Higher logarithms and $\varepsilon$-poles for the MS-like renormalization prescriptions

We consider a version of dimensional regularization (reduction) in which the dimensionful regularization parameter $\Lambda$ is in general different from the renormalization scale $\mu$. Then in the scheme analogous to the minimal subtraction the renormalization constants contain $\varepsilon$-poles, powers of $\ln\Lambda/\mu$, and mixed terms of the structure $\varepsilon^{-q}\ln^{p}\Lambda/\mu$. For the MS-like schemes we present explicit expressions for the coefficients at all these structures which relate them to the coefficients in the renormalization group functions, namely in the $\beta$-function and in the anomalous dimension. In particular, for the pure $\varepsilon$-poles we present explicit solutions of the 't~Hooft pole equations. Also we construct simple all-loop expressions for the renormalization constants (also written in terms of the renormalization group functions) which produce all $\varepsilon$-poles and logarithms and establish a number of relations between various coefficients at $\varepsilon$-poles and logarithms. The results are illustrated by some examples.

hep-th↗

arXiv2022

Coefficients at powers of logarithms in the HD+MSL renormalization scheme

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 (HD+MSL) renormalization prescription the renormalization constants include only powers of $\lnΛ/μ$, where $Λ$ and $μ$ 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 $β$-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 NSVZ equation.

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arXiv2021

Finiteness of the triple gauge-ghost vertices in ${\cal N}=1$ supersymmetric gauge theories: the two-loop verification

By an explicit calculation we demonstrate that the triple gauge-ghost vertices in a general renormalizable ${\cal N}=1$ supersymmetric gauge theory are UV finite in the two-loop approximation. For this purpose we calculate the two-loop divergent contribution to the $\bar c^+ V c$-vertex proportional to $(C_2)^2$ and use the finiteness of the two-loop contribution proportional to $C_2 T(R)$ which has been checked earlier. The theory under consideration is regularized by higher covariant derivatives and quantized in a manifestly ${\cal N}=1$ supersymmetric way with the help of ${\cal N}=1$ superspace. The two-loop finiteness of the vertices with one external line of the quantum gauge superfield and two external lines of the Faddeev--Popov ghosts has been verified for a general $ξ$-gauge. This result agrees with the nonrenormalization theorem proved earlier in all orders, which is an important step for the all-loop derivation of the exact NSVZ $β$-function.

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