The structure of generic anomalous dimensions and no-π theorem for massless propagators
Abstract Extending an argument of [1] for the case of 5-loop massless propagators we prove a host of new exact model-independent relations between contributions proportional to odd and even zetas in generic MS¯ $$ \overline{\mathrm{MS}} $$ anomalous dimensions as well as in generic massless correlat...
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Online Access: | http://link.springer.com/article/10.1007/JHEP06(2018)141 |
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doaj-a7ce89aa24154d259cdeec1c7421f85f2020-11-25T02:01:47ZengSpringerOpenJournal of High Energy Physics1029-84792018-06-012018612510.1007/JHEP06(2018)141The structure of generic anomalous dimensions and no-π theorem for massless propagatorsP. A. Baikov0K. G. Chetyrkin1Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State UniversityII Institut für Theoretische Physik, Universität HamburgAbstract Extending an argument of [1] for the case of 5-loop massless propagators we prove a host of new exact model-independent relations between contributions proportional to odd and even zetas in generic MS¯ $$ \overline{\mathrm{MS}} $$ anomalous dimensions as well as in generic massless correlators. In particular, we find a new remarkable connection between coefficients in front of ζ 3 and ζ 4 in the 4-loop and 5-loop contributions to the QCD β-function respectively. It leads to a natural explanation of a simple mechanics behind mysterious cancellations of the π-dependent terms in one-scale Renormalization Group (RG) invariant Euclidean quantities recently discovered in [2]. We give a proof of this no-π theorem for a general case of (not necessarily scheme-independent) one-scale massless correlators. All π-dependent terms in the six-loop coefficient of an anomalous dimension (or a β-function) are shown to be explicitly expressible in terms of lower order coefficients for a general one-charge theory. For the case of a scalar O(n) ϕ 4 theory all our predictions for π-dependent terms in 6-loop anomalous dimensions are in full agreement with recent results of [3–5].http://link.springer.com/article/10.1007/JHEP06(2018)141Perturbative QCDRenormalization Group |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
P. A. Baikov K. G. Chetyrkin |
spellingShingle |
P. A. Baikov K. G. Chetyrkin The structure of generic anomalous dimensions and no-π theorem for massless propagators Journal of High Energy Physics Perturbative QCD Renormalization Group |
author_facet |
P. A. Baikov K. G. Chetyrkin |
author_sort |
P. A. Baikov |
title |
The structure of generic anomalous dimensions and no-π theorem for massless propagators |
title_short |
The structure of generic anomalous dimensions and no-π theorem for massless propagators |
title_full |
The structure of generic anomalous dimensions and no-π theorem for massless propagators |
title_fullStr |
The structure of generic anomalous dimensions and no-π theorem for massless propagators |
title_full_unstemmed |
The structure of generic anomalous dimensions and no-π theorem for massless propagators |
title_sort |
structure of generic anomalous dimensions and no-π theorem for massless propagators |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2018-06-01 |
description |
Abstract Extending an argument of [1] for the case of 5-loop massless propagators we prove a host of new exact model-independent relations between contributions proportional to odd and even zetas in generic MS¯ $$ \overline{\mathrm{MS}} $$ anomalous dimensions as well as in generic massless correlators. In particular, we find a new remarkable connection between coefficients in front of ζ 3 and ζ 4 in the 4-loop and 5-loop contributions to the QCD β-function respectively. It leads to a natural explanation of a simple mechanics behind mysterious cancellations of the π-dependent terms in one-scale Renormalization Group (RG) invariant Euclidean quantities recently discovered in [2]. We give a proof of this no-π theorem for a general case of (not necessarily scheme-independent) one-scale massless correlators. All π-dependent terms in the six-loop coefficient of an anomalous dimension (or a β-function) are shown to be explicitly expressible in terms of lower order coefficients for a general one-charge theory. For the case of a scalar O(n) ϕ 4 theory all our predictions for π-dependent terms in 6-loop anomalous dimensions are in full agreement with recent results of [3–5]. |
topic |
Perturbative QCD Renormalization Group |
url |
http://link.springer.com/article/10.1007/JHEP06(2018)141 |
work_keys_str_mv |
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