The four-loop -function from vacuum supergraphs and the NSVZ relation for SQED regularized by higher derivatives

I. E. Shirokov; V. Yu. Shirokova

doi:10.1140/epjc/s10052-024-12587-y

EPJ

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2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2024) 84: 249
https://doi.org/10.1140/epjc/s10052-024-12587-y

Regular Article - Theoretical Physics

The four-loop $β$ $\beta$ -function from vacuum supergraphs and the NSVZ relation for $N = 1$ ${{{\mathcal {N}}}}=1$ SQED regularized by higher derivatives

I. E. Shirokov^a and V. Yu. Shirokova

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

^a shi95@yandex.ru

Received: 27 October 2023
Accepted: 17 February 2024
Published online: 9 March 2024

Abstract

In $N = 1$ ${{{\mathcal {N}}}}=1$ SQED with $N_{f}$ $$N_f$$ flavors regularized by higher derivatives we obtain the four-loop beta function using a method based on calculating vacuum supergraphs. For this purpose we use a special C++ program which obtain contributions to the $β$ $\beta$ -function from supergraphs without external legs in the form of integrals of double total derivatives. After that the result was compared with the three-loop anomalous dimension calculated earlier. We explicitly check the NSVZ relation in this order.

© The Author(s) 2024

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