Explicit closed-form evaluation of A(n) and B(m) for exponential regulators R(x)=e^{x^n} and F(x)=e^{x^m} yields fully parameterized three-loop beta functions in general N=1 SUSY gauge theories and demonstrates finite redefinitions mapping to an NSVZ-compatible scheme.
Introduce a complex regulators, Ip(s)≡ ∫ ∞ 0 xs−1e−xp dx= 1 p Γ (s p ) ,Re(s)>0
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Three-Loop Gauge Beta Functions in Supersymmetric Theories with Exponential Higher Covariant Derivative Regularization
Explicit closed-form evaluation of A(n) and B(m) for exponential regulators R(x)=e^{x^n} and F(x)=e^{x^m} yields fully parameterized three-loop beta functions in general N=1 SUSY gauge theories and demonstrates finite redefinitions mapping to an NSVZ-compatible scheme.