Corrections of order $α_s^3$ to $R_{had}$ in pQCD with light gluinos

TL;DR

The paper provides an independent verification of the ${\cal O}(\alpha_s^3)$ massless correction to R(s) in pQCD and extends the analysis to include light gluinos in a colour-octet representation. It introduces a global IRR/R*-operation framework that yields a compact expression for the UV renormalization constant in terms of bare p-integrals, enabling automated calculations with MINCER. The authors demonstrate gauge independence of the result and present explicit gluino-dependent corrections to R(s), including a numerical evaluation for five active flavours. They also discuss phenomenological implications and highlight the need for higher-order running (the ${\cal O}(\beta_2)$ gluino contribution) to fully assess the gluino impact on coupling evolution.

Abstract

By a completely independent analytic calculation made in general covariant gauge we confirm the known result for the massless $α_s^3$ correction to $R_{had}$ and check explicitly its gauge independence. We extend the calculations to include contributions due to a hypothetical existence of a colour octet of (light) neutral fermions known also under the name of gluinos.