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Infrared freezing of Euclidean QCD observables

Brooks, P.M.; Maxwell, C.J.

Authors

P.M. Brooks

C.J. Maxwell



Abstract

We consider the leading one-chain term in a skeleton expansion for QCD observables and show that for energies Q2>Lambda2, where Q2=Lambda2 is the Landau pole of the coupling, the skeleton expansion result is equivalent to the standard Borel integral representation, with ambiguities related to infrared (IR) renormalons. For Q2<Lambda2 the skeleton expansion result is equivalent to a previously proposed modified Borel representation where the ambiguities are connected with ultraviolet (UV) renormalons. We investigate the Q2-dependence of the perturbative corrections to the Adler-D function, the GLS sum rule and the polarized and unpolarized Bjorken sum rules. In all these cases the one-chain result changes sign in the vicinity of Q2=Lambda2, and then exhibits freezing behavior, vanishing at Q2=0. Finiteness at Q2=Lambda2 implies specific relations between the residues of IR and UV renormalon singularities in the Borel plane. These relations, only one of which has previously been noted (though it remained unexplained), are shown to follow from the continuity of the characteristic function in the skeleton expansion. By considering the compensation of nonperturbative and perturbative ambiguities we are led to a result for the Q2-dependence of these observables at all Q2, in which there is a single undetermined nonperturbative parameter, and which involves the skeleton expansion characteristic function. The observables freeze to zero in the infrared. We briefly consider the freezing behavior of the Minkowskian Re+e- ratio.

Citation

Brooks, P., & Maxwell, C. (2006). Infrared freezing of Euclidean QCD observables. Physical Review D, Particles and fields, 74, https://doi.org/10.1103/physrevd.74.065012

Journal Article Type Article
Publication Date Sep 1, 2006
Deposit Date Apr 28, 2008
Publicly Available Date Apr 28, 2008
Journal Physical Review D, Particles and fields
Print ISSN 0556-2821
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 74
DOI https://doi.org/10.1103/physrevd.74.065012
Public URL https://durham-repository.worktribe.com/output/1565942
Publisher URL http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRVDAQ000074000006065012000001&idtype=cvips&gifs=yes

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