Three-loop verification of a new algorithm for the calculation of a β-function in supersymmetric theories regularized by higher derivatives for the case of N=1 SQED

Nuclear Physics B, vol. 956, pp. 115020

Abstract

We verify a recently proposed method for obtaining a β-function of N=1 supersymmetric gauge theories regularized by higher derivatives by an explicit calculation. According to this method, a β-function can be found by calculating specially modified vacuum supergraphs instead of a much larger number of the two-point superdiagrams. The result is produced in the form of a certain integral of double total derivatives with respect to the loop momenta. Here we compare the results obtained for the three-loop β-function of N=1 SQED in the general ξ-gauge with the help of this method and with the help of the standard calculation. Their coincidence confirms the correctness of the new method and the general argumentation used for its derivation. Also we verify that in the considered approximation the NSVZ relation is valid for the renormalization group functions defined in terms of the bare coupling constant and for the ones defined in terms of the renormalized coupling constant in the HD+MSL scheme, both its sides being gauge-independent.

Authors 12

1. S. S. Aleshin

   Institute for Information Transmission Problems

   Affiliation as printed

   Institute for Information Transmission Problems, 127051, Moscow, Russia

2. I.S. Durandina

   Lomonosov Moscow State University

   Affiliation as printed

   Moscow State University, Faculty of Physics, Department of Theoretical Physics, 119991, Moscow, Russia

3. D. S. Kolupaev

   Lomonosov Moscow State University

   Affiliation as printed

   Moscow State University, Faculty of Physics, Department of Theoretical Physics, 119991, Moscow, Russia

4. Dmitrii Korneev Aachen Faculty of Mathematics, Computer Science and Natural Science Institute for Theoretical Particle Physics and Cosmology

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Faculty of Mathematics, Computer Science and Natural Science, Institute for Theoretical Particle Physics and Cosmology, 52062, Aachen, Germany

5. Mikhail Kuzmichev

   Lomonosov Moscow State University

   Affiliation as printed

   Moscow State University, Faculty of Physics, Department of Theoretical Physics, 119991, Moscow, Russia

6. N. P. Meshcheriakov

   Lomonosov Moscow State University

   Affiliation as printed

   Moscow State University, Faculty of Physics, Department of Theoretical Physics, 119991, Moscow, Russia

7. S. V. Novgorodtsev

   Lomonosov Moscow State University

   Affiliation as printed

   Moscow State University, Faculty of Physics, Department of Theoretical Physics, 119991, Moscow, Russia

8. Ivailo Petrov

   Lomonosov Moscow State University

   Affiliation as printed

   Moscow State University, Faculty of Physics, Department of Theoretical Physics, 119991, Moscow, Russia

9. Victoria Shatalova

   Lomonosov Moscow State University

   Affiliation as printed

   Moscow State University, Faculty of Physics, Department of Theoretical Physics, 119991, Moscow, Russia

10. Ilya Shirokov

    Lomonosov Moscow State University

    Affiliation as printed

    Moscow State University, Faculty of Physics, Department of Theoretical Physics, 119991, Moscow, Russia

11. V. Yu. Shirokova

    Lomonosov Moscow State University

    Affiliation as printed

    Moscow State University, Faculty of Physics, Department of Theoretical Physics, 119991, Moscow, Russia

12. Konstantin Viktorovich Stepanyantz corresponding

    Lomonosov Moscow State University

    Affiliation as printed

    Moscow State University, Faculty of Physics, Department of Theoretical Physics, 119991, Moscow, Russia