-diagram technique for , superfields

D. Bason; M. Billò

doi:10.1140/epjc/s10052-023-11893-1

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2023) 83: 892
https://doi.org/10.1140/epjc/s10052-023-11893-1

Regular Article - Theoretical Physics

$θ$ $\theta$ -diagram technique for $N = 1$ ${\mathcal {N}}=1$ , $d = 4$ superfields

D. Bason¹^,2 and M. Billò³^,4^b

¹ Dipertimento di Fisica, Università degli Studi di Trieste, Via Alfonso Valerio, 2, 34127, Trieste, Italy
² I.N.F.N.-Sezione di Trieste, Via Alfonso Valerio, 2, 34127, Trieste, Italy
³ Dipartimento di Fisica, Università degli Studi di Torino, Via P. Giuria 1, 10125, Turin, Italy
⁴ I.N.F.N.-Sezione di Torino, Via P. Giuria 1, 10125, Turin, Italy

^b marco.billo@unito.it

Received: 3 July 2023
Accepted: 31 July 2023
Published online: 4 October 2023

Abstract

We describe a diagrammatic procedure to carry out the Grassmann integration in super-Feynman diagrams of 4d theories expressed in terms of $N = 1$ ${\mathcal {N}}=1$ superfields. This method is alternative to the well known D-algebra approach. We develop it in detail for theories containing vector, chiral and anti-chiral superfields, with the type of interactions which occur in $N = 2$ ${\mathcal {N}}=2$ SYM theories with massless matter, but it would be possible to extend it to other cases. The main advantage is that this method is algorithmic; we implemented it as a Mathematica program that, given the description of a super Feynman diagram in momentum space, returns directly the polynomial in the momenta produced by the Grassmann integration.

Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epjc/s10052-023-11893-1.

© The Author(s) 2023

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.