New form of the exact NSVZ β-function: the three-loop verification for terms containing Yukawa couplings

• Published in: The journal of high energy physics 2018-04, Vol.2018 (4), p.1-37, Article 130
• Main Authors: Kazantsev, A. E., Shakhmanov, V. Yu, Stepanyantz, K. V.
• Format: Article
• Language: English
• Subjects: Classical and Quantum Gravitation; Couplings; Derivatives; Elementary Particles; Gauge theory; Ghosts; High energy physics; Integrals; Physics; Physics and Astronomy; Program verification (computers); Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Regularization; Relativity Theory; Renormalization Regularization and Renormalons; String Theory; Subtraction; Supersymmetric Gauge Theory; Supersymmetry
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP04(2018)130

A bstract We investigate a recently proposed new form of the exact NSVZ β -function, which relates the β -function to the anomalous dimensions of the quantum gauge superfield, of the Faddeev-Popov ghosts, and of the chiral matter superfields. Namely, for the general renormalizable N = 1 supersymmetric gauge theory, regularized by higher covariant derivatives, the sum of all three-loop contributions to the β -function containing the Yukawa couplings is compared with the corresponding two-loop contributions to the anomalous dimensions of the quantum superfields. It is demonstrated that for the considered terms both new and original forms of the NSVZ relation are valid independently of the subtraction scheme if the renormalization group functions are defined in terms of the bare couplings. This result is obtained from the equality relating the loop integrals, which, in turn, follows from the factorization of the integrals for the β-function into integrals of double total derivatives. For the renormalization group functions defined in terms of the renormalized couplings we verify that the NSVZ scheme is obtained with the higher covariant derivative regularization supplemented by the subtraction scheme in which only powers of ln Λ /μ are included into the renormalization constants.