RELATIONS BETWEEN OBSERVABLES AND THE INFRARED FIXED-POINT IN QCD

We investigate the possibility that alpha(s) freezes as function of N- f within perturbation theory. We use two approaches - direct search fo r a zero in the effective-charge (ECH) beta function, and the Banks-Za ks (BZ) expansion. We emphasize the fundamental difference between qua ntities with space-like vs, those with time-like momentum. We show tha t within the ECH approach several space-like quantities exhibit simila r behavior. In general the three-loop ECH beta functions can lead to f reezing for N-f greater than or similar to 5, but higher-order calcula tions 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 observa ble, we can be pretty sure that there is no fixed point for N-f less t han or similar to 12. The consequences of the Crewther relation concer ning perturbative freezing are analyzed. We also emphasize that time-l ike quantities have a consistent infrared limit only when the correspo nding space-like effective charge has one. We show that perturbative f reezing can lead to an analyticity structure in the complex momentum-s quared plane that is consistent with causality. (C) 1998 Elsevier Scie nce B.V.