K. V. Stepanyantz's research while affiliated with Moscow State Textile University and other places

... The choice of the higher covariant derivative regularization is motivated by the fact that the NSVZ equation in supersymmetric theories is valid in all loops in the HD þ MSL scheme [44,45], so that the β-function in a certain loop can easily be obtained starting from the expressions for the anomalous dimensions of chiral matter superfields in the previous loops, see, e.g., [68,74,75]. Moreover, there are various versions of this regularization, which differ in the form of the higher derivative terms and the Pauli-Villars masses. ...

... The choice of the higher covariant derivative regularization is motivated by the fact that the NSVZ equation in supersymmetric theories is valid in all loops in the HD þ MSL scheme [44,45], so that the β-function in a certain loop can easily be obtained starting from the expressions for the anomalous dimensions of chiral matter superfields in the previous loops, see, e.g., [68,74,75]. Moreover, there are various versions of this regularization, which differ in the form of the higher derivative terms and the Pauli-Villars masses. ...

... By definition, in the HD þ MSL scheme a theory is regularized by higher covariant derivatives and divergences are removed by minimal subtraction of logarithms when only powers of ln Λ=μ (where Λ is the dimensionful regularization parameter and μ is a renormalization scale) are present in the renormalization constants, while all finite constants are set to 0. (The proof was based on the all-order perturbative derivation of the NSVZ β-function made in [47] for N ¼ 1 supersymmetric electrodynamics and in [45,48,49] for the N ¼ 1 non-Abelian supersymmetric theories. Its various parts have been verified and confirmed by numerous explicit calculations (see, e.g., [50][51][52][53][54][55][56][57][58]), some of them being made in such orders of the perturbation theory where the scheme dependence becomes essential.) ...

... By definition, in the HD þ MSL scheme a theory is regularized by higher covariant derivatives and divergences are removed by minimal subtraction of logarithms when only powers of ln Λ=μ (where Λ is the dimensionful regularization parameter and μ is a renormalization scale) are present in the renormalization constants, while all finite constants are set to 0. (The proof was based on the all-order perturbative derivation of the NSVZ β-function made in [47] for N ¼ 1 supersymmetric electrodynamics and in [45,48,49] for the N ¼ 1 non-Abelian supersymmetric theories. Its various parts have been verified and confirmed by numerous explicit calculations (see, e.g., [50][51][52][53][54][55][56][57][58]), some of them being made in such orders of the perturbation theory where the scheme dependence becomes essential.) ...

... This implies that the NSVZ equation is valid only for special renormalization prescriptions, which are usually called the NSVZ schemes. According to [35][36][37][38], these schemes constitute an infinite set and are related by finite renormalizations which satisfy a special constraint. A simple prescription giving some NSVZ schemes was obtained in the case of using the higher covariant derivative regularizaton [39][40][41] in the supersymmetric version [42,43]. ...

... In our previous work [40] we initiated the study of the two-loop divergent contribution to the effective action of 6D, N = (1, 1) SYM theory in the harmonic superfield formalism and calculated the divergent contributions proportional to 1 ε 2 in the gauge superfield sector of the model. In the present paper we will analyze the general structure of the two-loop divergent contributions to the effective action in both gauge and hypermultiplet sectors. ...

... By definition, in the HD þ MSL scheme a theory is regularized by higher covariant derivatives and divergences are removed by minimal subtraction of logarithms when only powers of ln Λ=μ (where Λ is the dimensionful regularization parameter and μ is a renormalization scale) are present in the renormalization constants, while all finite constants are set to 0. (The proof was based on the all-order perturbative derivation of the NSVZ β-function made in [47] for N ¼ 1 supersymmetric electrodynamics and in [45,48,49] for the N ¼ 1 non-Abelian supersymmetric theories. Its various parts have been verified and confirmed by numerous explicit calculations (see, e.g., [50][51][52][53][54][55][56][57][58]), some of them being made in such orders of the perturbation theory where the scheme dependence becomes essential.) ...

... This in particular implies that the DR scheme is NSVZ for N ¼ 2 supersymmetric gauge theories, at least, in the lowest orders. 2 However, it is known that the finiteness in the DR scheme does not in general ensure the finiteness for an arbitrary renormalization prescription. For instance, one-loop finite N ¼ 1 supersymmetric theories in the DR scheme are finite in the two-loop approximation [65], but are not two-loop finite for a general N ¼ 1 supersymmetric renormalization prescription [66]. Moreover, there are DR calculations for N ¼ 2 supersymmetric Yang-Mills theory in the component formulation which reveal the three-loop divergences. ...

... We use the abbreviations, s α (c α ) = sin α(cos α), s β (c β ) = sin β(cos β), t β = tan β, etc. We identify the physical state h as the SM-like observed Higgs boson of mass 125 GeV as all the Higgs signal strength measurements [45][46][47][48][49][50][51][52][53][54][55][56][57] are consistent with SM. Throughout the paper we collectively call H, A and H ± as the beyond SM (BSM) Higgs bosons. ...

... Higher loops are obtained as a result of certain "anomaly" in the measure revealing itself in the calculation of the second and higher loops, in analogy with Yang-Mills theory. 5 A general proof is presented in [8][9][10][11] while the direct perturbative all-loop calculations are given in [40][41][42]. One can complexify the coupling constants in the Lagrangians introducing their holomorphic counterpartners, ...