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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.06799 |
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Table of Contents:
- We study the three-loop gauge $β$-functions in general $\mathcal{N}=1$ supersymmetric gauge theories regularized by higher covariant derivatives (HCD) supplemented with Pauli--Villars subtraction. The all-structure three-loop form of the $β$-functions in the HCD framework is known and involves regulator-dependent parameters. Here we evaluate these parameters explicitly for the exponential regulators $R(x)=e^{x^n}$ and $F(x)=e^{x^m}$. We obtain the constants $A(n)$ and $B(m)$ in closed form, together with their large-$n,m$ asymptotics, and substitute them into the general three-loop expressions. This yields fully explicit, regulator-parameterized $β$-functions and a systematic expansion in $1/n$ and $1/m$ that organizes finite, scheme-dependent terms. We then exhibit finite coupling redefinitions that map the renormalized $\overline{\mathrm{DR}}$ result to a scheme compatible with the Novikov--Shifman--Vainshtein--Zakharov relation. Our analysis clarifies how exponential higher-derivative regulators preserve this relation at the bare level and illustrates the regulator-driven structure of supersymmetric renormalization group flows.