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All-orders infra-red freezing of R(e+e-) in perturbative QCD

D. M. Howe·C. J. Maxwell
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Abstract

We consider the behaviour of the perturbative QCD corrections to the R(e+e-) ratio in the limit that the c.m. energy sqrt(s) vanishes. We find that for N(f)<9 flavours of massless quarks, the perturbative correction to the parton model result freezes to the infra-red limit 2/b as s-->0. Here b=(33-2N(f))/6 is the first QCD beta-function coefficient. The freezing holds to all-orders in perturbation theory. The s-dependence can be written analytically in closed form in terms of the Lambert W function.

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D. M. Howe, C. J. Maxwell. 2002-06-24. All-orders infra-red freezing of R(e+e-) in perturbative QCD. https://doi.org/10.1016/s0370-2693(02)02192-5

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