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arXiv · 2102.12314

Finiteness of the two-loop matter contribution to the triple gauge-ghost vertices in ${\cal N}=1$ supersymmetric gauge theories regularized by higher derivatives

Mikhail Kuzmichev·Nikolai Meshcheriakov·Sergey Novgorodtsev·Ilya Shirokov·Konstantin Stepanyantz
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Abstract

For a general renormalizable ${\cal N}=1$ supersymmetric gauge theory with a simple gauge group we verify the ultraviolet (UV) finiteness of the two-loop matter contribution to the triple gauge-ghost vertices. These vertices have one leg of the quantum gauge superfield and two legs corresponding to the Faddeev--Popov ghost and antighost. By an explicit calculation made with the help of the higher covariant derivative regularization we demonstrate that the sum of the corresponding two-loop supergraphs containing a matter loop is not UV divergent in the case of using a general $\xi$-gauge. In the considered approximation this result confirms the recently proved theorem that the triple gauge-ghost vertices are UV finite in all orders, which is an important ingredient of the all-loop perturbative derivation of the Novikov-Shifman-Vainshtein-Zakharov relation.

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Mikhail Kuzmichev, Nikolai Meshcheriakov, Sergey Novgorodtsev, Ilya Shirokov, Konstantin Stepanyantz. 2021-02-24. Finiteness of the two-loop matter contribution to the triple gauge-ghost vertices in ${\cal N}=1$ supersymmetric gauge theories regularized by higher derivatives. https://doi.org/10.1103/physrevd.104.025008

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