All-orders infrared freezing of Re+e− in perturbative QCD

Howe, D.M.; Maxwell, C.J.

doi:10.1016/s0370-2693(02)02192-5

All-orders infrared freezing of Re+e− in perturbative QCD

Howe, D.M.; Maxwell, C.J.

Authors

D.M. Howe

C.J. Maxwell

Abstract

We consider the behaviour of the perturbative QCD corrections to the Re+e− ratio, in the limit that the c.m. energy vanishes. Writing , with Qf denoting the electric charge of quark flavour f, we find that for Nf<9 flavours of massless quarks, the perturbative correction to the parton model result smoothly approaches from below the infrared limit , as s→0. Here b=(33−2Nf)/6 is the first QCD beta-function coefficient. This 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.

Citation

Howe, D., & Maxwell, C. (2002). All-orders infrared freezing of Re+e− in perturbative QCD. Physics Letters B, 541(1-2), 129-134. https://doi.org/10.1016/s0370-2693%2802%2902192-5

Journal Article Type	Article
Publication Date	Aug 8, 2002
Deposit Date	Dec 18, 2006
Journal	Physics Letters B
Print ISSN	0370-2693
Publisher	Elsevier
Peer Reviewed	Peer Reviewed
Volume	541
Issue	1-2
Pages	129-134
DOI	https://doi.org/10.1016/s0370-2693%2802%2902192-5
Keywords	Operator product expansion, Total cross-section, Tau-Lepton decay, Renormalization-group analysis, Interval 1350-2400 MEV, To-leading order, Of-mass energies, E&E annihilation, Form-factor, Renormalon resummations.