babylonpolice.com

We discuss quantum scale invariance in (scale invariant) gauge theories with
both ultraviolet (UV) and infrared (IR) divergences. Firstly, their BRST
invariance is checked in two apparently unrelated approaches using a scale
invariant regularisation (SIR). These approaches are then shown to be
equivalent. Secondly, for the Abelian case we discuss both UV and IR quantum
corrections present in such theories. We present the Feynman rules in a form
suitable for offshell Green functions calculations, together with their
one-loop renormalisation. This information is then used for the muon production
cross section at one-loop in a quantum scale invariant theory. Such a theory
contains not only new UV poles but also IR poles. While the UV poles bring new
quantum corrections (in the form of counterterms), finite or divergent, that we
compute, it is shown that the IR poles do not bring new physics. The IR quantum
corrections, both finite and divergent, cancel out similarly to the way the IR
poles themselves cancel in the traditional approach to IR divergences (in the
cross section, after summing over virtual and real corrections). Hence, the
evanescent interactions induced by the scale-invariant analytical continuation
of the SIR scheme do not affect IR physics, as illustrated at one-loop for the
muon production ($e^+ e^- \to \mu^+\mu^-$) cross section.