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arXiv · hep-ph/9802218

Relations between Observables and the Infrared Fixed-Point in QCD

Einan Gardi·Marek Karliner
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Abstract

We investigate the possibility that alpha_s freezes as function of N_f within perturbation theory. We use two approaches -- direct search for a zero in the effective-charge (ECH) beta function, and the Banks-Zaks (BZ) expansion. We emphasize the fundamental difference between quantities with space-like vs. those with time-like momentum. We show that within the ECH approach several space-like quantities exhibit similar behavior. In general the 3-loop ECH beta functions can lead to freezing for N_f\gsim 5, but higher-order calculations are essential for a conclusive answer. The BZ expansion behaves differently for different observables. Assuming that the existence of a fixed point requires convergence of the BZ expansion for any observable, we can be pretty sure that there is no fixed point for N_f\lsim 12. The consequences of the Crewther relation concerning perturbative freezing are analyzed. We also emphasize that time-like quantities have a consistent infrared limit only when the corresponding space-like effective charge has one. We show that perturbative freezing can lead to an analyticity structure in the complex momentum-squared plane that is consistent with causality.

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Einan Gardi, Marek Karliner. 1998-06-25. Relations between Observables and the Infrared Fixed-Point in QCD. https://doi.org/10.1016/s0550-3213(98)00392-7

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