Exact renormalization of the photino mass in softly broken N $$ \mathcal{N} $$ = 1 SQED with N f flavors regularized by higher derivatives

2017

Nuclear Physics B

We demonstrate that in non-Abelian N = 1 supersymmetric gauge theories the NSVZ relation is valid for terms quartic in the Yukawa couplings independently of the subtraction scheme if the renormalization group functions are defined in terms of the bare couplings and the theory is regularized by higher covariant derivatives. The terms quartic in the Yukawa couplings appear in the three-loop β-function and in the two-loop anomalous dimension of the matter superfields. We have obtained that the three-loop contribution to the βfunction quartic in the Yukawa couplings is given by an integral of double total derivatives. Consequently, one of the loop integrals can be taken and the three-loop contribution to the β-function is reduced to the two-loop contribution to the anomalous dimension. The remaining loop integrals have been calculated for the simplest form of the higher derivative regularizing term. Then we construct the renormalization group functions defined in terms of the renormalized couplings. In the considered approximation they do not satisfy the NSVZ relation for a general renormalization prescription. However, we verify that the recently proposed boundary conditions defining the NSVZ scheme in the non-Abelian case really lead to the NSVZ relation between the terms of the considered structure.

Section: Introductionmentioning

confidence: 62%

Three-loop NSVZ relation for terms quartic in the Yukawa couplings with the higher covariant derivative regularization

Shakhmanov

2017

Nuclear Physics B

“…Note that this result is valid in an arbitrary subtraction scheme, because the RG functions defined in terms of the bare coupling constant are scheme-independent for a fixed regularization [26]. NSVZ-like relations for such RG functions have also been proved in all orders for the Adler D-function [27] in N = 1 SQCD [28,29] and for the anomalous dimension of the photino mass in the softly broken N = 1 SQED [30]. All these NSVZ and NSVZ-like relations appear due to factorization of loop integrals into integrals of (double) total derivatives in the limit of the vanishing external momentum [31,32].…”

Section: Introductionmentioning

confidence: 69%

NSVZ-like scheme for the photino mass in softly broken N = 1 SQED regularized by higher derivatives

Nartsev

2017

Jetp Lett.

Self Cite

In the case of using the higher derivative regularization we construct the subtraction scheme which gives the NSVZ-like relation for the anomalous dimension of the photino mass in softly broken N = 1 SQED with N f flavors in all loops. The corresponding renormalization prescription is determined by simple boundary conditions imposed on the renormalization constants. It allows fixing an arbitrariness of choosing finite counterterms in every order of the perturbation theory in such a way that the renormalization group functions defined in terms of the renormalized coupling constant satisfy the NSVZ-like relation.

“…For example, it allows deriving the NSVZ-like expressions for the Adler D-function [44] in N = 1 SQCD [45,46] or for the anomalous dimension of the photino mass in softly broken N = 1 SQED [47]. (NSVZ-like relations for the renormalization of the gaugino mass in theories with softly broken supersymmetry have first been constructed in [48][49][50].)…”

Section: Jhep04(2018)130mentioning

confidence: 99%

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

Kazantsev

Shakhmanov

2018

J. High Energ. Phys.

Self Cite

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.