@article{dd9b78637d944b998f0c5db5caf43158,

title = "Relations between observables and the infrared fixed point in QCD",

abstract = "We investigate the possibility that αs freezes as function of Nf within perturbation theory. We use two approaches - direct search for a zero in the effective-charge (ECH) β 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 three-loop ECH β functions can lead to freezing for Nf ≳ 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 Nf ≲ 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.",

keywords = "Banks-Zaks expansion, Beta function, Effective charge, Infrared fixed point, Infrared freezing of the strong coupling, QCD",

author = "Einan Gardi and Marek Karliner",

note = "Funding Information: E.G. would like to thank G.P. Korchemskyfo r very useful discussionsa nd to the organizerso f the YKIS '97 InternationaSle minarin Kyoto, in Decembe'r9 7, where a part of this work was done. The authorsa lso thank J. Ellis for commentos n the manuscriptS.p ecialt hanksa re due to G. Grunbergfo r very useful discussionas nd for constructivcer iticismo f the originalv ersiono f the paperT. his researchw ass upporteidn part by the Israel ScienceF oundationa dministerebdy the Israel Academyo f Sciences and Humanitiesa, nd by a Grant from the G.I.E, the German-IsraeFlio undationf or ScientificR esearcha nd Developmenatn d by the CharlesC lore doctorafl ellowship.",

year = "1998",

month = sep,

day = "28",

doi = "10.1016/S0550-3213(98)00392-7",

language = "אנגלית",

volume = "529",

pages = "383--423",

journal = "Nuclear Physics B",

issn = "0550-3213",

publisher = "Elsevier",

number = "1-2",

}